CN103269508A - Access control method for fusion of cellular network and wireless local area network - Google Patents

Abstract

The invention discloses an access control method for fusion of a cellular network and a wireless local area network. The method is characterized in that a calculation method of an access domain is given by distinguishing the difference among physical layer data rates of users and adopting a segmental access strategy under the consideration of a business model, a service model and a mobile model, so that users with low data rates in the wireless local area network access the cellular network possibly, users with high data rates access the wireless local area network possibly, the dragging effects of the user with low data rates are relieved, the service quality of the user is ensured, and the system throughput is increased.

Description

The connection control method that a kind of Cellular Networks and WLAN (wireless local area network) merge

Technical field

The invention belongs to the heterogeneous wireless network convergence communication technical field, particularly the connection control method of Cellular Networks and WLAN (wireless local area network) fusion.

Background technology

In wireless lan (wlan) communication, rate adaptation is the important method that improves system transmissions efficient, strengthens QoS (QoS), writes " international IEEE " (IEEE) 802.11 consensus standards.As, among the IEEE802.11a, support 6Mpbs to 54Mbps totally eight kinds of physical layers (PHY) data rate, IEEE802.11b supports 1Mbps to 11Mbps totally four kinds of physical layer data rate, and the IEEE802.11n support is above 15 kinds of physical layer data rate." international IEEE moving algorithm transactions " (IEEE Transactions on Mobile Computing, vol.1, no.4, pp.278-292,2002) provide conclusion in: dynamically carry out rate adaptation according to the current channel condition of user such as Signal to Interference plus Noise Ratio (SINR), can significantly improve throughput performance of WLAN.

" compunication international symposium " (IEEE INFOCOM Proc., June2002, pp.599-607) provided the WLAN (wireless local area network) data rate calculation formula that inserts based on distributed collaboration (DCF) in, can draw to draw a conclusion according to this formula: along with low physical layer data rate user in the WLAN (wireless local area network) increases, high physical layer data rate user's service speed and the throughput of WLAN (wireless local area network) can sharply reduce.

" international IEEE radio communication proceedings " (IEEE Transactions on Wireless Communications, vol.6, no.5, pp.1932 – 1952,2007) a kind of access strategy at Cellular Networks and WLAN (wireless local area network) fusion of proposition guides the user to carry out network insertion by differentiated service type and employing restriction access in.This method is not because distinguishing the physical layer data rate of user in WLAN (wireless local area network), the user of different physical layer data rate is linked into WLAN (wireless local area network) with identical probability, thereby causes the throughput of whole system and high physical layer data rate user's service speed sharply to descend.

Summary of the invention

The invention provides the connection control method that a kind of Cellular Networks and WLAN (wireless local area network) merge, by distinguishing the difference of user's physical layer data rate, adopt the segmentation access strategy, to improve throughput of system and QoS of customer.

The connection control method that Cellular Networks of the present invention and WLAN (wireless local area network) merge comprises calculating and the access network selection of input field; It is characterized in that: cellular network base stations and wireless local network connecting point are according to method given below, and calculated off-line goes out the input field of the various users under the different business density conditions, make corresponding question blank; Guide user's access then according to following access network selecting method; Divide two parts to describe:

One, access network selecting method

Note only has zone that Cellular Networks covers to be cellular network coverage co(cell-only only), be overlapping covered dc(double-coverage area by the zone of cellular network and WLAN (wireless local area network) covering simultaneously), the zone that neighbours' Cellular Networks covers is neighbours' Cellular Networks zone nc, and overlapping covered dc is divided into higher data rates modes overlay area (being designated hereinafter simply as the first area) S1 and low data rate mode overlay area (being designated hereinafter simply as second area) S2 again; Higher data rates modes or low data rate mode are made up of several higher or lower physical layer data rate patterns in the WLAN (wireless local area network) respectively, and the zone of covering is determined by corresponding Signal to Interference plus Noise Ratio (SINR); In the note Cellular Networks coverage, maximum new user inserts number and is in the Cellular Networks

The maximum access number that switches the user is In the WLAN (wireless local area network) coverage, the maximum user who inserts the first area S1 of WLAN (wireless local area network) inserts number and is

The maximum user of second area S2 inserts number

It namely is input field; Insert algorithm and be divided into following four steps:

Insert the algorithm first step: by the user of cellular network coverage co and overlapping covered dc only being arrived the statistics of density, determine only cellular network coverage co and overlapping covered dc user's arrival rate λ ^CoAnd λ ^w, by searching the input field table

Determine current input field

Value;

Insert second step of algorithm: new arrival user and switching user for from overlapping covered dc, at first select WLAN (wireless local area network) as access network; If number of users n in the current wireless local area network (LAN) ^wSatisfy

Then the new user of first area S1 and switching user insert WLAN (wireless local area network); If number of users n in the current wireless local area network (LAN) ^wSatisfy

Then the new user of second area S2 and switching user can insert WLAN (wireless local area network); If do not satisfy above-mentioned condition, then carried out for the 3rd step;

Insert the 3rd step of algorithm: for the user from overlapping covered dc, if do not satisfy condition in second step, then select to insert cellular network; If the active user in the cellular network counts n ^cSatisfy

Then newly arrive the user and be linked into cellular network, otherwise get clogged; If satisfy

Then switch the user and be linked into cellular network, otherwise gone offline;

Insert the 4th step of algorithm: for from the user of cellular network coverage co only, if the active user in the cellular network counts n ^cSatisfy

Then newly arrive the user and be linked into cellular network, otherwise get clogged; If the active user in the cellular network counts n ^cSatisfy

Then switch the user and be linked into cellular network, otherwise gone offline;

Two, the calculating of input field; The calculating of input field was divided into for six steps to be carried out, and before network system was implemented, off-line was calculated input field and traffic density (λ ^Co, λ ^w) correspondence table;

The input field first step: for every group of traffic density (λ ^Co, λ ^w), the traversal input field

The nonnegative integer value;

Second step of input field: for each input field traversal value

Calculate time-delay and blocking rate in the WLAN (wireless local area network); Process is as follows:

If the state of WLAN (wireless local area network) is

Represent to insert among first area S1 and the second area S2 number of users of WLAN (wireless local area network) respectively, then the infinitely small matrix of state transitions is:

$Q=\left[\begin{array}{ccccccc}{E}_0& B_0& 0& ...& 0& 0& 0\\ D_1& E1& \mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">B</figure-callout>}1& ...& 0& 0& 0\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ 0& 0& 0& ...& D_{N-1}& E_{N-1}& B_{N-1}\\ 0& 0& 0& ...& 0& D_N& E_N\end{array}\right]$

Three intermediate variable matrixes, the first intermediate variable matrix B wherein, the second intermediate variable matrix D and the 3rd intermediate variable matrix E are expressed as follows respectively:

Anti-indicator function wherein

$\stackrel{\&OverBar;}{\mathrm{\&delta;}}\left(i\right)=\left\{\begin{array}{cc}1,& i\&NotEqual;0\\ 0,& \mathrm{else}\end{array}\right.$

First intermediate variable

Second intermediate variable

With

Be respectively the arrival rate of customers among first area S1 and the second area S2,

S1 and s2 are respectively the area of first area S1 and second area S2;

With

The user who is respectively access cellular network among first area S1 and the second area S2 switches to the speed of WLAN (wireless local area network),

With

Be that the user will calculate in the 4th step from the transfer rate that first area S1 moves to second area S2 and moves to first area S1 from second area S2 in the WLAN (wireless local area network);

With

Be respectively first area S1 and the service speed of second area S2 user in WLAN (wireless local area network);

The note state

The probability of stability be π=(π ₀, π ₁, π ₂..., π _N), π _n=(π ^w(n, 0), π ^w(n, 1) ..., π ^w(n, M)), then the expression formula of the probability of stability is

${\mathrm{\&pi;}}^T={({\hat{Q}}^T\&CenterDot;\hat{Q})}^{-1}\hat{Q}{\&CenterDot;}^{T}b,$

Wherein

$\hat{Q}=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="Q\; T"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">Q</figure-callout>}}^T\\ 1_{1\&times;((N+1)\&CenterDot;(M+1))}\end{array}\right],$ $b=\left[\begin{array}{c}{0}_{((N+1)\&CenterDot;(M+1))\&times;1}\\ 1\end{array}\right];$

Then first area S1 and the blocking rate of second area S2 user in WLAN (wireless local area network) are respectively:

$B_1^w=\underset{i=0}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{2,\max }^w}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w({\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">N</figure-callout>}}_{1,\max }^w-i,i),$ $B_2^w=\underset{i=0}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{2,\max }^w}{\mathrm{\&Sigma;}}}\underset{j={\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{2,\max }^w-i}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">N</figure-callout>}}_{1,\max }^w-i}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w(j,i);$

Then the time-delay average of WLAN (wireless local area network) is:

$E\left[T^w\right]=\frac{\underset{j=0}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">N</figure-callout>}}_{1,\max }^w}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{2,\max }^w-j}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w(j,i)\&CenterDot;(i+j)}{({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})\&CenterDot;(1-B_2^w)+({\mathrm{\&lambda;}}_1^w+{\mathrm{\&lambda;}}_h^{c-1})\&CenterDot;(1-B_1^w)};$

The 3rd step of input field: for each traversal value

Calculate blocking rate, drop rate and time-delay in the cellular network, process is as follows:

The state of note cellular network is Expression originates from only cellular network coverage co respectively, first area S1, and second area S2, and be linked into the number of users of Cellular Networks always; Then the transfer rate between each state is expressed as follows

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c+1,n_1^c,n_2^c):$

(1) ${\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c={\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}_h^{c-c}+{\mathrm{\&lambda;}}_h^{w-c}$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

(2) ${\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c={\mathrm{\&lambda;}}_h^{c-c}+{\mathrm{\&lambda;}}_h^{w-c}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c+1{,n}_2^c):$

(3) ${\widetilde{\mathrm{\&lambda;}}}_{S1}^c={\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c,n_2^c+1):$

(4) ${\widetilde{\mathrm{\&lambda;}}}_{S2}^c={\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c-1,n_1^c{,n}_2^c):$

(5) ${\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}\left({-\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)\right)}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c-1{,n}_2^c):$

(6) ${\widetilde{\mathrm{\&mu;}}}_{S1}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{S1}\left({-\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)\right)}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c,n_2^c-1):$

(7) ${\widetilde{\mathrm{\&mu;}}}_{S2}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}\left({-\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)\right)}$

Wherein, Be respectively neighbours' Cellular Networks residential quarter and switch to the only speed of cellular network coverage co to switching rate and the WLAN (wireless local area network) of this residential quarter,

Be square generating function residence time, but interim symbolic variable x conventional letter co, S1, S2 will calculate in the 4th step;

Cellular Networks user's service speed is ${\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{C^c}{(n_{\mathrm{co}}^c+n_1^c+n_2^c)\&CenterDot;f_d},$ C ^cBe Cellular Networks total bandwidth, f _dIt is professional average data size;

The number of users that note inserts Cellular Networks is

Number of users n in the Cellular Networks then ^cDistribution probability be

${\mathrm{\&pi;}}^c\left(n^c\right)=\left\{\begin{array}{cc}\underset{i=1}{\overset{n^c}{\mathrm{\&Pi;}}}(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S1}^c}{{\widetilde{\mathrm{\&mu;}}}_{S1}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S2}^c}{{\widetilde{\mathrm{\&mu;}}}_{S2}^c\left(i\right)})\&CenterDot;\frac{{\mathrm{\&pi;}}^c\left(0\right)}{n^c!}& 0\&le;n^c\&le;N_{n,\max }^c\\ \underset{i=1}{\overset{N_{n,\max }^c}{\mathrm{\&Pi;}}}(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S1}^c}{{\widetilde{\mathrm{\&mu;}}}_{S1}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S2}^c}{{\widetilde{\mathrm{\&mu;}}}_{S2}^c\left(i\right)})\&CenterDot;\underset{j=N_{n,\max }^c+1}{\overset{n^c}{\mathrm{\&Pi;}}}{\left(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}\right)}^{n^c-N_{n,\max }^c}\&CenterDot;\frac{{\mathrm{\&pi;}}^c\left(0\right)}{n^c!}& N_{n,\max }^c+1\&le;n^c\&le;N_{h,\max }^c\end{array}\right.$

${\mathrm{\&pi;}}^c\left(0\right)=\frac{1}{1+\underset{i=1}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&pi;}}^c\left(i\right)}{{\mathrm{\&pi;}}^c\left(0\right)}}$

Then the blocking rate in the Cellular Networks and drop rate are respectively:

$B^c=\underset{i=N_{n,\max }^c}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^c\left(i\right),$ $D^c={\mathrm{\&pi;}}^c\left(N_{h,\max }^c\right)$

Average delay in the Cellular Networks is:

$E\left[T^c\right]=\frac{\underset{i=1}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}i\&CenterDot;{\mathrm{\&pi;}}^c\left(i\right)}{({\mathrm{\&lambda;}}^c+{\widetilde{\mathrm{\&lambda;}}}_{S1}^c+{\widetilde{\mathrm{\&lambda;}}}_{S2}^c)\&CenterDot;(1-B^c)+{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c\&CenterDot;(1-D^c)}$

Input field the 4th step: residence time moment function and switching rate calculating;

Conversion and the probability thereof of user's location status in Cellular Networks are described below: only insert the user of Cellular Networks among the cellular network coverage co, when only leaving cellular network coverage co, with transition probability p ^C-wEnter second area S2, with transition probability p ^C-c=1-p ^C-wEnter adjacent Cellular Networks; Enter in the S1 process of first area, with probability

(being the blocking rate of second area S2 in the WLAN (wireless local area network)) still inserts cellular network, with

Probability insert WLAN (wireless local area network); When the user of access Cellular Networks leaves second area S2 among the second area S2, with transition probability p ^2-1Enter first area S1, with transition probability p ^2-cEnter only cellular network coverage co, enter in the process of first area S1, with probability

Still insert Cellular Networks, with probability

Switch to WLAN (wireless local area network); When the user who inserts Cellular Networks for first area S1 leaves first area S1, with probability

Keep inserting Cellular Networks, with probability

Switch to WLAN (wireless local area network); Only providing, the square generating function of cellular network coverage co, first area S1, second area S2 user residence time is respectively

${\mathrm{\&psi;}}_c\left(s\right)=E\left[e^{s\&CenterDot;T_r^{\mathrm{co}}}\right]=\underset{0}{\overset{+\&infin;}{\&Integral;}}{e}^{s\&CenterDot;t}\&CenterDot;{\mathrm{\&eta;}}^{\mathrm{co}}\&CenterDot;e^{-{\mathrm{\&eta;}}^{\mathrm{co}}\&CenterDot;t}\mathrm{dt}=\frac{{\mathrm{\&eta;}}^{\mathrm{co}}}{{\mathrm{\&eta;}}^{\mathrm{co}}-s}$

${\mathrm{\&psi;}}_1\left(s\right)=E\left[e^{s\&CenterDot;T_r^{S1}}\right]=\frac{a}{a+1}\&CenterDot;\frac{a\&CenterDot;{\mathrm{\&eta;}}^{w1}}{a\&CenterDot;{\mathrm{\&eta;}}^{w1}-s}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{w1}}{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{w1}-s}$

${\mathrm{\&psi;}}_2\left(s\right)=E\left[e^{s\&CenterDot;T_r^{S2}}\right]=\frac{a}{a+1}\&CenterDot;\frac{a\&CenterDot;{\mathrm{\&eta;}}^{S2}}{a\&CenterDot;{\mathrm{\&eta;}}^{S2}-s}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}}{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{S2}-s}$

The square generating function of remembering residence time is

Origin area symbolic variable x1 represents user's origin area, the value set is { co, S1, S2, nc}, purpose zone symbolic variable x2 represents user's purpose zone, the value set is { co, S1, S2, nc}, conditional code variable con can value end condition symbol term, be in always and end at overlapping covered conditional code dc_term or jump condition symbol tran, expression ends at purpose zone (by the zone of purpose zone symbolic variable x2 representative) owing to switch to WLAN (wireless local area network) or adjacent Cellular Networks respectively, motion and end at the purpose zone or transfer to the purpose zone first time in overlapping covered dc always; Therefore the square generating function of residence time is The expression user originates from origin area (by origin area symbolic variable x1 representative), arrive purpose zone (by the symbolic variable x2 representative of purpose zone) according to the condition of the conditional code variable con representative square generating function of institute residence time before; Residence time the square generating function

The expression user originates from second area S2, and the square of residence time produces function before moving to for the first time cellular network coverage co only, for

${\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)=\underset{j=0}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-c}\&CenterDot;{[p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)]}^j=\frac{{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-c}}{1-p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)}$

Be similar to the derivation of top formula, can derive several residence time of square generating function

With

As follows:

${\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)=\frac{{\text{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;(1-B_2^w)}{1-B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)=\frac{{\text{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;(1-B_1^w)}{1-{p^{2-1}\&CenterDot;B}_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;[p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)]}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

The note square produces function

For originating from the origin area by origin area symbolic variable x1 representative, produce function and end at the square of this Cellular Networks coverage institute residence time; Can derive several squares and produce function

With Expression formula be:

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}\left(s\right)$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{S1}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}\left(s\right)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S1-S1}\left(s\right)$

Definition cellular network switching probability is

Expression inserts Cellular Networks and originates from the origin area that is represented by origin area symbolic variable x1 and switches to the purpose zone that is represented by purpose zone symbolic variable x2 and the probability that inserts other networks (WLAN (wireless local area network) and adjacent cellular network); Only then originating from, the user of cellular network coverage co by the probability that current cellular network is cut into neighbours' cellular network is:

$H_c^{\mathrm{co}-\mathrm{nc}}=\frac{p^{c-c}}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left({\stackrel{\&OverBar;}{-\mathrm{\&mu;}}}^c\right)$

The user who originates from second area S2, the probability that is cut into first area S1 and is linked into WLAN (wireless local area network) is:

$H_c^{S2-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left({-\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c\right)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_1^w}$

Similarly, can derive other several network switching probabilities

With

Expression formula be:

$H_c^{\mathrm{co}-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_1^w}$

$H_c^{S1-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{[\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)]}{1-B_1^w}$

$H_c^{S2-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;\left(\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\right)\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}$

$H_c^{S1-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}=\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S1-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;(\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w})$

$H_c^{\mathrm{co}-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}=\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}$

Definition inserts the user of WLAN (wireless local area network), switches to second area S2 by first area S1, and the probability that still is linked into WLAN (wireless local area network) is:

$H_w^{S1-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}=\frac{a}{a+1}\&CenterDot;\frac{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}}{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}}{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}$

Definition inserts the user of WLAN (wireless local area network), switches to first area S1 by second area S2, and the probability that still is linked into WLAN (wireless local area network) is:

User in the WLAN (wireless local area network), the probability that switches to honeycomb is:

$H_w^{w-c}=p^{2-c}\&CenterDot;[\frac{a}{a+1}\&CenterDot;\frac{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}}{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}}{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}]$

Wherein the draw service speed of Cellular Networks is

The WLAN (wireless local area network) average service rate is

Then switching arrival rate is:

${\mathrm{\&lambda;}}_h^{c-c}=H_c^{\mathrm{co}-\mathrm{nc}}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)$

$+{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)]$

${\mathrm{\&lambda;}}_h^{c-2}=H_c^{\mathrm{co}-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)]$

$+H_c^{S2-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}\&CenterDot;{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)+H_c^{S1-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}\&CenterDot;{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)$

${\mathrm{\&lambda;}}_h^{c-1}=H_c^{\mathrm{co}-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)]$

$+H_c^{S2-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}\&CenterDot;{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)+H_c^{S1-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}\&CenterDot;{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)$

${\mathrm{\&lambda;}}_h^{w-c}=H_w^{w-c}\&CenterDot;((1-B_2^w)\&CenterDot;({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})+{\mathrm{\&lambda;}}_{h12}^w)$

${\mathrm{\&lambda;}}_{h21}^w=H_w^{S2-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}\&CenterDot;((1-B_2^w)\&CenterDot;({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})+{\mathrm{\&lambda;}}_{h12}^w)$

${\mathrm{\&lambda;}}_{h12}^w=H_w^{S1-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}\&CenterDot;((1-B_1^w)\&CenterDot;({\mathrm{\&lambda;}}_1^w+{\mathrm{\&lambda;}}_h^{c-1})+{\mathrm{\&lambda;}}_{h21}^w)$

The 5th step of input field: moved for second step repeatedly to the 4th step, make each switching probability value restrain, and the WLAN (wireless local area network) after the preservation convergence and the time-delay of cellular network;

The 6th step of input field: traveled through all input fields

After the value set, seek optimum input field by following two conditions;

First condition: find to make cellular network blocking rate B ^cRequire (B less than blocking rate ^Req), and cellular network drop rate D ^cRequire (D less than drop rate ^Req) input field set; If set illustrates current business density (λ for empty ^Co, λ ^w) input field of condition is not in the traversal value set, needs are adjusted the scope of traversal value;

Second condition: in the input field set of satisfying first condition, select to make following weighting to delay time minimum input field as current business density (λ ^Co, λ ^w) optimum input field; The weighting time-delay is: $\stackrel{\&OverBar;}{\mathrm{\&lambda;}}=\frac{{\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}_1^w{B}_1^w+{\mathrm{\&lambda;}}_2^w{B}_2^w}{({\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}^w)}E\left[T^c\right]+\frac{{\mathrm{\&lambda;}}_1^w(1-B_1^w)+{\mathrm{\&lambda;}}_2^w(1-B_2^w)}{({\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}^w)}E\left[T^w\right].$

Compare with the access strategy that WLAN (wireless local area network) merges with existing cellular network, the inventive method is owing to the difference of having considered by the different user's physical layer data rate in WLAN (wireless local area network) that cause of channel condition, by the optimal selection to input field, ensureing user's blocking rate, under the condition of service quality such as drop rate and time-delay, low physical layer data rate user is linked into cellular network as much as possible in the WLAN (wireless local area network), and high physical layer data rate user inserts WLAN (wireless local area network) as much as possible, effectively alleviate low physical layer data rate user to the effect of tying down of other user's service speed and capacity of wireless local area network, thereby improved the throughput of quality of services for users and system.

Description of drawings

Fig. 1 is cellular network of the present invention and WLAN (wireless local area network) segmentation access strategy schematic diagram.

Fig. 2 covers and WLAN (wireless local area network) overlay area location status conversion schematic diagram in Cellular Networks for user of the present invention.

Fig. 3 is the concrete network architecture schematic diagram of implementing of the present invention.

Fig. 4 is overlapping covered (dc) throughput along with the contrast schematic diagram of cellular network coverage (co) area business variable density only.

Fig. 5 is that overlapping covered (dc) throughput is along with the contrast schematic diagram of the sane change in size of business.

Below in conjunction with drawings and Examples the present invention is described in further detail.

Embodiment

Embodiment 1:

Fig. 3 has provided the concrete network architecture schematic diagram of implementing of the present invention.Cellular network and WLAN (wireless local area network) are taked the loose coupling structure, cellular network base stations (ST) and WLAN (wireless local area network) launch point (AP) advanced optical fiber (OF1, OF2, OF3, OF4) be connected to (GT1 on the gateway of backbone network (BB), GT2), can communicate to work in coordination with by backbone network (BB) between them.Travelling carriage (MT1, MT2 MT3) is multimode terminal, can insert Cellular Networks and WLAN (wireless local area network), but arbitrary moment can only be inserted a network, and is only constantly moving in cellular network coverage (co), first area (S1), second area (S2) and the adjacent cellular network overlay area.Consider that WLAN (wireless local area network) adopts the IEEE802.11a standard.Consider downlink traffic transmission in this example.Be subjected to the restriction of wireless local network connecting point power and the influence of channel fading, in the WLAN (wireless local area network) coverage, signal strength signal intensity increases along with the distance from the WLAN (wireless local area network) launch point and successively decreases.Cause the covering of different physical layer data rate patterns to distribute circlewise, more near launch point, physical layer data rate is more high.The physical layer data rate pattern of IEEE802.11a and the corresponding relation of signal-noise ratio threshold are as shown in following table 1:

Table 1 simulation parameter table

Present embodiment is considered outdoor WLAN (wireless local area network) scene, adopts the COST231-Hata propagation model to come the analog channel decay, provides decay formula and is

PL(dB)＝46.3+33.9log ₁₀f-13.82log ₁₀Ht-α(Hr)+(44.9-6.55log ₁₀Ht)log ₁₀d+C _m

α (Hr)=3.2 (log wherein ₁₀11.75Hr) ²-4.97, f represents the operating frequency of WLAN (wireless local area network), and unit is megahertz (MHz), Ht be the WLAN (wireless local area network) launch point with respect to the height on ground, unit be rice (m), Hr is the height of user terminal (UE), d is the horizontal range of WLAN (wireless local area network) launch point and user terminal, C _m=3 corresponding dense city models.

In the present embodiment, establish Ht=30m, Hr=1m, transmitter antenna gain (dBi) are 4dB, and receiving antenna gain is 2dB, and the through-put power of launch point is 0.5W.By calculating, the signal-noise ratio threshold of associative list 1, the covering radius that provides each pattern is: d ₁=142m, d ₂=125m, d ₃=102m, d ₄=90m, d ₅=74m, d ₆=53m, d ₇=46m, d ₈=38m.Pattern 1 and pattern 2 are set at low PHY speed, and other 6 patterns are set at high PHY speed, and its cover part is set at low rate respectively and covers S1 and two-forty covering S2, and normalized area is respectively s1=0.516 separately, s2=0.484.The area that covers with each speed be ratio to simulate low PHY data rate be R2=7.6Mbps, high PHY data rate is R1=26.31Mbps.

Consider that the user is nonuniform motion at overlapping covered dc Move Mode, residence time

Obey hyperexponential distribution.Correspondingly, it is consistent with overlapping covering dc zone with second area S2 motor pattern at first area S1 to set the user, residence time

Also obey hyperexponential distribution.Providing its probability density function is

$f_{T_r^{\mathrm{wi}}}\left(t\right)=\frac{a}{a+1}a{\mathrm{\&eta;}}^{\mathrm{wi}}{e}^{-{\mathrm{a\&eta;}}^{\mathrm{wi}}t}+\frac{1}{a+1}\frac{{\mathrm{\&eta;}}^{\mathrm{wi}}}{a}{e}^{-\frac{{\mathrm{\&eta;}}^{\mathrm{wi}}t}{a}},$ a≥0,t≥0，i＝0,1,2

Wherein,

With

Be respectively With

Average.

If the user evenly distributes at overlapping covered dc, therefore have when S2 zone user switches, the probability that switches to the co zone is $p^{2-c}=\frac{\sqrt{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1+s2}}{\sqrt{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1+\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">s</figure-callout>}2}+\sqrt{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1}},$ The probability that switches to the S1 zone is $p^{2-1}\text{=}\frac{\sqrt{s1}}{\sqrt{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1+\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">s</figure-callout>}2}+\sqrt{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1}}.$

Be located at the movement in each zone, reached statistical equilibrium, then have: (1) s1 η ^W1=s2 η ^W2P ^2-1, the user moves and reaches statistical equilibrium between expression first area S1 and the second area S2; (2) (s1+s2) η ^W0=s2 η ^W2P ^2-c, the expression user moves to cellular network coverage co only from second area S2 speed is identical with the speed that is moved to cellular network coverage co only by user area in the overlapping covered dc.

Therefore can derive ${\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}=\sqrt{\frac{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1+s2}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1}}{\mathrm{\&eta;}}^{w0},$ ${\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}=\frac{\sqrt{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1+s2}(\sqrt{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">s</figure-callout>}1+\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">s</figure-callout>}2}+\sqrt{s1})}{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">s</figure-callout>}2}{\mathrm{\&eta;}}^{w0}$

Consider that the user is evenly motion in cellular network coverage co motion only, so residence time

Obeys index distribution, average residence time is

Consider single bag deliveries, service scripts size (L _d) obeys index distribution, average is f _d

Consider that WLAN (wireless local area network) adopts the access mechanism based on distributed contention collaborative (DCF), adopt and ask to send/allow to send the handshake mechanism of agreement (RTS/CTS).The physical layer transmission speed that can draw WLAN (wireless local area network) is (bag/time slot):

$\mathrm{\&xi;}({\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">n</figure-callout>}}_1,n_2)={({\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">n</figure-callout>}}_1\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="T\; sd"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{sd}}^{}+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">n</figure-callout>}}_2\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="T\; sd"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">T</figure-callout>}}_{\mathrm{sd}}^{}+\stackrel{\&OverBar;}{W_d}+\frac{1}{2}({\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">n</figure-callout>}}_1+n_2)\&CenterDot;\stackrel{\&OverBar;}{T_{\mathrm{cd}}})}^{-1}$

Wherein, n ₁And n ₂Number of users for first area S1 and second area S2 zone in the access WLAN (wireless local area network).

With

Be respectively the average time that first area S1 and second area S2 user are transmitted a frame,

T wherein _ControlFor transmitting the control time expense of a frame,

L is the payload in the frame.

For keeping out of the way the mean value of window,

Be the average time of conflict transmission.

Before network implementation, go out miscellaneous service according to following step calculated off-line and arrive density state (λ ^Co, λ ^w) corresponding input field table

The input field first step: for every group of traffic density (λ ^Co, λ ^w), the traversal input field

The nonnegative integer value;

Second step of input field: for each input field traversal value

Calculate time-delay and blocking rate in the WLAN (wireless local area network); Process is as follows:

If the state of WLAN (wireless local area network) is

Represent to insert among first area S1 and the second area S2 number of users of WLAN (wireless local area network) respectively, then the infinitely small matrix of state transitions is:

$Q=\left[\begin{array}{ccccccc}{E}_0& B_0& 0& ...& 0& 0& 0\\ D_1& E1& \mathrm{<figure-callout\; id="1"\; label="B"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">B</figure-callout>}1& ...& 0& 0& 0\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ 0& 0& 0& ...& D_{N-1}& E_{N-1}& B_{N-1}\\ 0& 0& 0& ...& 0& D_N& E_N\end{array}\right]$

Three intermediate variable matrixes, the first intermediate variable matrix B wherein, the second intermediate variable matrix D and the 3rd intermediate variable matrix E are expressed as follows respectively:

Anti-indicator function wherein

$\stackrel{\&OverBar;}{\mathrm{\&delta;}}\left(i\right)=\left\{\begin{array}{cc}1,& i\&NotEqual;0\\ 0,& \mathrm{else}\end{array}\right.$

First intermediate variable

Second intermediate variable

With

Be respectively the arrival rate of customers among first area S1 and the second area S2,

S1 and s2 are respectively the area of first area S1 and second area S2; With

The user who is respectively access cellular network among first area S1 and the second area S2 switches to the speed of WLAN (wireless local area network),

With

Be that the user will calculate in the 4th step from the transfer rate that first area S1 moves to second area S2 and moves to first area S1 from second area S2 in the WLAN (wireless local area network);

With

Be respectively first area S1 and the service speed of second area S2 user in WLAN (wireless local area network);

The note state

The probability of stability be π=(π ₀, π ₁, π ₂..., π _N), π _n=(π ^w(n, 0), π ^w(n, 1) ..., π ^w(n, M)), then the expression formula of the probability of stability is

${\mathrm{\&pi;}}^T={({\hat{Q}}^T\&CenterDot;\hat{Q})}^{-1}\&CenterDot;{\hat{Q}}^{T}b,$

Wherein

$\hat{Q}=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="Q\; T"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">Q</figure-callout>}}^T\\ 1_{1\&times;((N+1)\&CenterDot;(M+1))}\end{array}\right],$ $b=\left[\begin{array}{c}{0}_{((N+1)\&CenterDot;(M+1))\&times;1}\\ 1\end{array}\right];$

Then first area S1 and the blocking rate of second area S2 user in WLAN (wireless local area network) are respectively:

$B_1^w=\underset{i=0}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{2,\max }^w}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w({\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">N</figure-callout>}}_{1,\max }^w-i,i),$ $B_2^w=\underset{i=0}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{2,\max }^w}{\mathrm{\&Sigma;}}}\underset{j={\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{2,\max }^w-\mathrm{<figure-callout\; id="1"\; label="i\; N"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">i</figure-callout>}}{\overset{N_{}^{}}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w(j,i);$

Then the time-delay average of WLAN (wireless local area network) is:

$E\left[T^w\right]=\frac{\underset{j=0}{\overset{{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">N</figure-callout>}}_{1,\max }^w}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{{\mathrm{<figure-callout\; id="2"\; label="N"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">N</figure-callout>}}_{2,\max }^w-j}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w(j,i)\&CenterDot;(i+j)}{({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})\&CenterDot;(1-B_2^w)+({\mathrm{\&lambda;}}_1^w+{\mathrm{\&lambda;}}_h^{c-1})\&CenterDot;(1-B_1^w)};$

The 3rd step of input field: for each traversal value

Calculate blocking rate, drop rate and time-delay in the cellular network, process is as follows:

The state of note cellular network is

Expression originates from only cellular network coverage co respectively, first area S1, and second area S2, and be linked into the number of users of Cellular Networks always; Then the transfer rate between each state is expressed as follows:

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c+1,n_1^c,n_2^c):$

(1) ${\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c={\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}_h^{c-c}+{\mathrm{\&lambda;}}_h^{w-c}$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

(2) ${\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c={\mathrm{\&lambda;}}_h^{c-c}+{\mathrm{\&lambda;}}_h^{w-c}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c+1{,n}_2^c):$

(3) ${\widetilde{\mathrm{\&lambda;}}}_{S1}^c={\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c,n_2^c+1):$

(4) ${\widetilde{\mathrm{\&lambda;}}}_{S2}^c={\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c-1,n_1^c{,n}_2^c):$

(5) ${\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}\left({-\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)\right)}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c-1{,n}_2^c):$

(6) ${\widetilde{\mathrm{\&mu;}}}_{S1}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{S1}\left({-\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)\right)}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c,n_2^c-1):$

(7) ${\widetilde{\mathrm{\&mu;}}}_{S2}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}\left({-\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)\right)}$

Wherein,

Be respectively neighbours' Cellular Networks residential quarter and switch to the only speed of cellular network coverage co to switching rate and the WLAN (wireless local area network) of this residential quarter,

Be square generating function residence time, but interim symbolic variable x conventional letter co, S1, S2 will calculate in the 4th step;

Cellular Networks user's service speed is ${\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{C^c}{(n_{\mathrm{co}}^c+n_1^c+n_2^c)\&CenterDot;f_d},$ C ^cBe Cellular Networks total bandwidth, f _dIt is professional average data size;

The number of users that note inserts Cellular Networks is

Number of users n in the system then ^cDistribution probability be

${\mathrm{\&pi;}}^c\left(n^c\right)=\left\{\begin{array}{cc}\underset{i=1}{\overset{n^c}{\mathrm{\&Pi;}}}(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S1}^c}{{\widetilde{\mathrm{\&mu;}}}_{S1}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S2}^c}{{\widetilde{\mathrm{\&mu;}}}_{S2}^c\left(i\right)})\&CenterDot;\frac{{\mathrm{\&pi;}}^c\left(0\right)}{n^c!}& 0\&le;n^c\&le;N_{n,\max }^c\\ \underset{i=1}{\overset{N_{n,\max }^c}{\mathrm{\&Pi;}}}(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S1}^c}{{\widetilde{\mathrm{\&mu;}}}_{S1}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S2}^c}{{\widetilde{\mathrm{\&mu;}}}_{S2}^c\left(i\right)})\&CenterDot;\underset{j=N_{n,\max }^c+1}{\overset{n^c}{\mathrm{\&Pi;}}}{\left(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}\right)}^{n^c-N_{n,\max }^c}\&CenterDot;\frac{{\mathrm{\&pi;}}^c\left(0\right)}{n^c!}& N_{n,\max }^c+1\&le;n^c\&le;N_{h,\max }^c\end{array}\right.$

${\mathrm{\&pi;}}^c\left(0\right)=\frac{1}{1+\underset{i=1}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&pi;}}^c\left(i\right)}{{\mathrm{\&pi;}}^c\left(0\right)}}$

Then the blocking rate in the Cellular Networks and drop rate are respectively:

$B^c=\underset{i=N_{n,\max }^c}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^c\left(i\right),$ $D^c={\mathrm{\&pi;}}^c\left(N_{h,\max }^c\right)$

Average delay in the Cellular Networks is:

$E\left[T^c\right]=\frac{\underset{i=1}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}i\&CenterDot;{\mathrm{\&pi;}}^c\left(i\right)}{({\mathrm{\&lambda;}}^c+{\widetilde{\mathrm{\&lambda;}}}_{S1}^c+{\widetilde{\mathrm{\&lambda;}}}_{S2}^c)\&CenterDot;(1-B^c)+{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c\&CenterDot;(1-D^c)}$

Input field the 4th step: residence time moment function and switching rate calculating;

Provided conversion and the probability thereof of user's location status in Cellular Networks among Fig. 2, only inserted the user of Cellular Networks among the cellular network coverage co, when only leaving cellular network coverage co, with transition probability p ^C-wEnter second area S2, with transition probability p ^C-c=1-p ^C-wEnter adjacent Cellular Networks; Enter in the S1 process of first area, with probability

(being the blocking rate of second area S2 in the WLAN (wireless local area network)) still inserts cellular network, with

Probability insert WLAN (wireless local area network); When the user of access Cellular Networks leaves second area S2 among the second area S2, with transition probability p ^2-1Enter first area S1, with transition probability p ^2-cEnter only cellular network coverage co, enter in the process of first area S1, with probability Still insert Cellular Networks, with probability Switch to WLAN (wireless local area network); When the user who inserts Cellular Networks for first area S1 leaves first area S1, with probability

Keep inserting Cellular Networks, with probability

Switch to WLAN (wireless local area network); Only providing, the square generating function of cellular network coverage co, first area S1, second area S2 user residence time is respectively:

${\mathrm{\&psi;}}_c\left(s\right)=E\left[e^{s\&CenterDot;T_r^{\mathrm{co}}}\right]=\underset{0}{\overset{+\&infin;}{\&Integral;}}{e}^{s\&CenterDot;t}\&CenterDot;{\mathrm{\&eta;}}^{\mathrm{co}}\&CenterDot;e^{-{\mathrm{\&eta;}}^{\mathrm{co}}\&CenterDot;t}\mathrm{dt}=\frac{{\mathrm{\&eta;}}^{\mathrm{co}}}{{\mathrm{\&eta;}}^{\mathrm{co}}-s}$

${\mathrm{\&psi;}}_1\left(s\right)=E\left[e^{s\&CenterDot;T_r^{S1}}\right]=\frac{a}{a+1}\&CenterDot;\frac{a\&CenterDot;{\mathrm{\&eta;}}^{w1}}{a\&CenterDot;{\mathrm{\&eta;}}^{w1}-s}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}}{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{w1}-s}$

${\mathrm{\&psi;}}_2\left(s\right)=E\left[e^{s\&CenterDot;T_r^{S2}}\right]=\frac{a}{a+1}\&CenterDot;\frac{a\&CenterDot;{\mathrm{\&eta;}}^{S2}}{a\&CenterDot;{\mathrm{\&eta;}}^{S2}-s}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}}{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{S2}-s}$

The square generating function of remembering residence time is Origin area symbolic variable x1 represents user's origin area, the value set is { co, S1, S2, nc}, purpose zone symbolic variable x2 represents user's purpose zone, the value set is { co, S1, S2, nc}, conditional code variable con can value end condition symbol term, be in always and end at overlapping covered conditional code dc_term or jump condition symbol tran, expression ends at purpose zone (by the zone of purpose zone symbolic variable x2 representative) owing to switch to WLAN (wireless local area network) or adjacent Cellular Networks respectively, and the purpose zone is transferred in motion and end at the purpose zone in overlapping covered dc always the first time; Therefore the square generating function of residence time is

The expression user originates from origin area (by origin area symbolic variable x1 representative), arrive purpose zone (by the symbolic variable x2 representative of purpose zone) according to the condition of the conditional code variable con representative square generating function of institute residence time before; Residence time the square generating function

The expression user originates from second area S2, and the square of residence time produces function before moving to for the first time cellular network coverage co only, for

${\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)=\underset{j=0}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-c}\&CenterDot;{[p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)]}^j=\frac{{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-c}}{1-p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)};$

Be similar to the derivation of top formula, can derive several residence time of square generating function

With

As follows:

${\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)=\frac{{\text{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;(1-B_2^w)}{1-B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)=\frac{{\text{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;(1-B_1^w)}{1-{p^{2-1}\&CenterDot;B}_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;[p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)]}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

The note square produces function For originating from the origin area by origin area symbolic variable x1 representative, produce function and end at the square of this Cellular Networks coverage institute residence time; Can derive several squares and produce function

With

Expression formula be:

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}\left(s\right)$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{S1}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}\left(s\right)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S1-S1}\left(s\right)$

Definition cellular network switching probability is

Expression inserts Cellular Networks and originates from the origin area that is represented by origin area symbolic variable x1 and switches to the purpose zone that is represented by purpose zone symbolic variable x2 and the probability that inserts other networks (WLAN (wireless local area network) and adjacent cellular network); Only then originating from, the user of cellular network coverage co by the probability that current cellular network is cut into neighbours' cellular network is

$H_c^{\mathrm{co}-\mathrm{nc}}=\frac{p^{c-c}}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left({\stackrel{\&OverBar;}{-\mathrm{\&mu;}}}^c\right)$

The user who originates from second area S2, the probability that is cut into first area S1 and is linked into WLAN (wireless local area network) is:

$H_c^{S2-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left({-\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c\right)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_1^w}$

Similarly, can derive other several network switching probabilities

With

Expression formula be:

$H_c^{\mathrm{co}-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_1^w}$

$H_c^{S1-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{[\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)]}{1-B_1^w}$

$H_c^{S2-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;\left(\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\right)\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}$

$H_c^{S1-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}=\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S1-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;(\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w})$

$H_c^{\mathrm{co}-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}=\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}$

Definition inserts the user of WLAN (wireless local area network), switches to second area S2 by first area S1, and the probability that still is linked into WLAN (wireless local area network) is:

$H_w^{S1-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}=\frac{a}{a+1}\&CenterDot;\frac{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}}{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}}{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">w</figure-callout>}1}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}$

Definition inserts the user of WLAN (wireless local area network), switches to first area S1 by second area S2, and the probability that still is linked into WLAN (wireless local area network) is:

$H_w^{S2-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}=p^{2-1}\&CenterDot;[\frac{a}{a+1}\&CenterDot;\frac{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}}{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}}{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}]$

User in the WLAN (wireless local area network), the probability that switches to honeycomb is

${H_w^{w-c}=p}^{2-c}\&CenterDot;[\frac{a}{a+1}\&CenterDot;\frac{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}}{{\mathrm{a\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}}{\frac{1}{a}{\mathrm{\&eta;}}^{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">w</figure-callout>}2}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}]$

Wherein the draw service speed of Cellular Networks is The WLAN (wireless local area network) average service rate is

Then switching arrival rate is:

${\mathrm{\&lambda;}}_h^{c-c}=H_c^{\mathrm{co}-\mathrm{nc}}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)$

$+{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)]$

${\mathrm{\&lambda;}}_h^{c-2}=H_c^{\mathrm{co}-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)]$

$+H_c^{S2-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}\&CenterDot;{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)+H_c^{S1-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}\&CenterDot;{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)$

${\mathrm{\&lambda;}}_h^{c-1}=H_c^{\mathrm{co}-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)]$

$+H_c^{S2-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}\&CenterDot;{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)+H_c^{S1-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}\&CenterDot;{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)$

${\mathrm{\&lambda;}}_h^{w-c}=H_w^{w-c}\&CenterDot;((1-B_2^w)\&CenterDot;({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})+{\mathrm{\&lambda;}}_{h12}^w)$

${\mathrm{\&lambda;}}_{h21}^w=H_w^{S2-\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00003061771200012.png"\; state="\{\{state\}\}">S</figure-callout>}1}\&CenterDot;((1-B_2^w)\&CenterDot;({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})+{\mathrm{\&lambda;}}_{h12}^w)$

${\mathrm{\&lambda;}}_{h12}^w=H_w^{S1-\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA00003061771200012.png,HDA00003061771200022.png"\; state="\{\{state\}\}">S</figure-callout>}2}\&CenterDot;((1-B_1^w)\&CenterDot;({\mathrm{\&lambda;}}_1^w+{\mathrm{\&lambda;}}_h^{c-1})+{\mathrm{\&lambda;}}_{h21}^w)$

The 5th step of input field: moved for second step repeatedly to the 4th step, make each switching probability value restrain, and the WLAN (wireless local area network) after the preservation convergence and the time-delay of cellular network;

The 6th step of input field: traveled through all input fields

After the value set, seek optimum input field by following two conditions;

First condition: find to make cellular network blocking rate B ^cRequire (B less than blocking rate ^Req), and cellular network drop rate D ^cRequire (D less than drop rate ^Req) input field set; If set illustrates current business density (λ for empty ^Co, λ ^w) input field of condition is not in the traversal value set, needs are adjusted the scope of traversal value;

Second condition: in the input field set of satisfying first condition, select to make following weighting to delay time minimum input field as current business density (λ ^Co, λ ^w) optimum input field; The weighting time-delay is:

$\stackrel{\&OverBar;}{\mathrm{\&lambda;}}=\frac{{\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}_1^w{B}_1^w+{\mathrm{\&lambda;}}_2^w{B}_2^w}{({\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}^w)}E\left[T^c\right]+\frac{{\mathrm{\&lambda;}}_1^w(1-B_1^w)+{\mathrm{\&lambda;}}_2^w(1-B_2^w)}{({\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}^w)}E\left[T^w\right].$

Guide user's access then by following access strategy.

One, access network selecting method

Fig. 1 has provided network selecting method, can be divided into following four steps:

Network is selected the first step: by the user of cellular network coverage co and overlapping covered dc only being arrived the statistics of density, determine only cellular network coverage co and overlapping covered dc user's arrival rate λ ^CoAnd λ ^w, by searching the input field table Determine current input field

Value;

Network selected for second step: new arrival user and switching user for from overlapping covered dc, at first select WLAN (wireless local area network) as access network; If number of users n in the current wireless local area network (LAN) ^wSatisfy

Then the new user of first area S1 and switching user insert WLAN (wireless local area network); If number of users n in the current wireless local area network (LAN) ^wSatisfy

Then the new user of second area S2 and switching user can insert WLAN (wireless local area network); If do not satisfy above-mentioned condition, then carried out for the 3rd step;

Network selected for the 3rd step: for the user from overlapping covered dc, if do not satisfy condition in second step, then select to insert cellular network; If the active user in the cellular network counts n ^cSatisfy

Then newly arrive the user and be linked into Cellular Networks, otherwise get clogged; If satisfy Then switch the user and be linked into cellular network, otherwise gone offline;

Network selected for the 4th step: for from the user of cellular network coverage co only, if the active user in the cellular network counts n ^cSatisfy

Then newly arrive the user and be linked into Cellular Networks, otherwise get clogged; If the active user in the cellular network counts n ^cSatisfy

Then switch the user and be linked into cellular network, otherwise gone offline;

In this emulation, verified the excellence of the inventive method performance from theoretical simulation and actual emulation.Wherein, be that common WLAN (wireless local area network) preferentially inserts algorithm with reference to algorithm, namely do not distinguish the high, low speed data rate users.In Fig. 4 and Fig. 5, curve a1, a2 represent the actual emulation value of the inventive method, and curve b1, b2 represent the theoretical simulation value of the inventive method.Curve c1, c2 represent the actual emulation value with reference to algorithm, and curve d1, d2 represent the theoretical simulation value with reference to algorithm.

Fig. 4 has provided as service scripts average-size f _dDuring=500kbits, delay requirement E[T ^c]≤T ^Req, E[T ^w]≤T ^Req, blocking rate requires B ^c≤ B ^Req, drop rate requires D ^c≤ D ^Req, and under the condition of the fixing only professional arrival rate of cellular network coverage co, the method that the present invention proposes with reference to algorithm in the comparison that improves on the overlapping covered dc throughput.As seen from Figure 5, (a1 b1) always is better than that (c1, d1), and when only the professional arrival rate of cellular network coverage co was low, the inventive method can significantly improve throughput with reference to algorithm to the method that the present invention proposes.And along with the only increase of cellular network coverage co arrival rate, the throughput of two methods is monotone decreasing all, and the throughput that inventive method improves can reduce, until being 0.Reason is, when only cellular network coverage co traffic density is low, and the access thresholding of the low data rate users among the overlapping covered dc Smaller, therefore be linked into cellular network in large quantities, WLAN (wireless local area network) is mainly the high data rate user service like this, and throughput is higher.And when only cellular network coverage co traffic density increased, in order to guarantee requirements such as time-delay, blocking rate, low-rate users inserted thresholding Bigger, therefore be linked into WLAN (wireless local area network) more, cause the throughput of WLAN (wireless local area network) to reduce rapidly.When only the professional arrival rate of overlapping covered co is relatively lower, as λ ^Co=5calls/s, the method for invention can improve about 15% throughput than common WLAN (wireless local area network) priority algorithm, and this is extremely considerable.

Fig. 5 has only provided, and the arrival rate of cellular network coverage co is λ ^CoDuring=9 (calls/s), under the restrictive condition that satisfies time-delay, blocking rate and drop rate, throughput is along with the schematic diagram of service scripts change in size.As seen from the figure, (c2 is recessed d2) to the throughput curve of overlapping covered dc for a2, b2, and therefore, the throughput of overlapping covered dc (throughput=arrival rate * document size) can reduce along with the increase of document size.Reason is the increase along with document size, and only the traffic density of cellular network coverage co can increase, thereby the low rate traffic amount that causes being linked in the WLAN (wireless local area network) increases.

The access strategy of the Differentiated Services speed that the WLAN (wireless local area network) in Cellular Networks and WLAN (wireless local area network) merge that the present invention proposes is preferential not only can significantly improve the throughput of whole system, and easy to implement.In reality was implemented, the user of high service speed, low service speed distinguished by channel condition (as signal to noise ratio), and does not need the location.

Claims (1)

1. the connection control method that merges of a Cellular Networks and WLAN (wireless local area network) comprises that the calculating of input field and access network select; It is characterized in that: cellular network base stations and wireless local network connecting point are according to method given below, and calculated off-line goes out the input field of the various users under the different business density conditions, make corresponding question blank; Guide user's access then according to following access network selecting method; Divide two parts to describe:

One, access network selecting method

Note only has zone that Cellular Networks covers to be cellular network coverage only, conventional letter is co, be overlapping covered by the zone of cellular network and WLAN (wireless local area network) covering simultaneously, conventional letter is dc, the zone that neighbours' Cellular Networks covers is neighbours' Cellular Networks zone, and conventional letter is nc, overlapping covered higher data rates modes overlay area and the low data rate mode overlay area of being divided into again, below abbreviate first area and second area respectively as, conventional letter is respectively S1 and S2; High or low data rate mode is made up of several higher or lower physical layer data rate patterns in the WLAN (wireless local area network), and the zone of covering is determined by corresponding Signal to Interference plus Noise Ratio; In the note Cellular Networks coverage, maximum new user inserts number and is in the Cellular Networks

The maximum access number that switches the user is In the WLAN (wireless local area network) coverage, the maximum user who inserts the first area of WLAN (wireless local area network) inserts number and is

The maximum user of second area inserts number

It namely is input field; Insert algorithm and be divided into following four steps:

Insert the algorithm first step: by only cellular network coverage and overlapping covered user being arrived the statistics of density, determine only cellular network coverage and overlapping covered user's arrival rate λ ^CoAnd λ ^w, by searching the input field table $[N_{n,\max }^c({\mathrm{\&lambda;}}^{\mathrm{co}},{\mathrm{\&lambda;}}^w),N_{h,\max }^c({\mathrm{\&lambda;}}^{\mathrm{co}},{\mathrm{\&lambda;}}^w),N_{1,\max }^w({\mathrm{\&lambda;}}^{\mathrm{co}},{\mathrm{\&lambda;}}^w),N_{2,\max }^w({\mathrm{\&lambda;}}^{\mathrm{co}},{\mathrm{\&lambda;}}^w)],$ Determine current input field $(N_{n,\max }^c,N_{h,\max }^c,N_{1,\max }^w,N_{2,\max }^w)$ Value;

Insert second step of algorithm: for from overlapping covered new arrival user and switching user, at first select WLAN (wireless local area network) as access network; If number of users n in the current wireless local area network (LAN) ^wSatisfy

Then the new user of first area and switching user insert WLAN (wireless local area network); If number of users n in the current wireless local area network (LAN) ^wSatisfy

Then the new user of second area and switching user can insert WLAN (wireless local area network); If do not satisfy above-mentioned condition, then carried out for the 3rd step;

Insert the 3rd step of algorithm: for from overlapping covered user, if do not satisfy condition in second step, then select to insert cellular network; If the active user in the cellular network counts n ^cSatisfy

Then newly arrive the user and be linked into cellular network, otherwise get clogged; If satisfy

Then switch the user and be linked into cellular network, otherwise gone offline;

Insert the 4th step of algorithm: for from the user of cellular network coverage only, if the active user in the cellular network counts n ^cSatisfy Then newly arrive the user and be linked into cellular network, otherwise get clogged; If the active user in the cellular network counts n ^cSatisfy

Then switch the user and be linked into cellular network, otherwise gone offline;

Two, the calculating of input field; The calculating of input field was divided into for six steps to be carried out, and before network system was implemented, off-line was calculated input field and traffic density (λ ^Co, λ ^w) correspondence table;

The input field first step: for every group of traffic density (λ ^Co, λ ^w), the traversal input field

$[N_{n,\max }^c({\mathrm{\&lambda;}}^{\mathrm{co}},{\mathrm{\&lambda;}}^w),N_{h,\max }^c({\mathrm{\&lambda;}}^{\mathrm{co}},{\mathrm{\&lambda;}}^w),N_{1,\max }^w({\mathrm{\&lambda;}}^{\mathrm{co}},{\mathrm{\&lambda;}}^w),N_{2,\max }^w({\mathrm{\&lambda;}}^{\mathrm{co}},{\mathrm{\&lambda;}}^w)]$ The nonnegative integer value;

Second step of input field: for each input field traversal value

Calculate time-delay and blocking rate in the WLAN (wireless local area network); Process is as follows:

If the state of WLAN (wireless local area network) is

Represent to insert in first area and the second area number of users of WLAN (wireless local area network) respectively, then the infinitely small matrix of state transitions is:

$Q=\left[\begin{array}{ccccccc}{E}_0& B_0& 0& ...& 0& 0& 0\\ D_1& E1& B1& ...& 0& 0& 0\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ .& .& .& .& .& .& .\\ 0& 0& 0& ...& D_{N-1}& E_{N-1}& B_{N-1}\\ 0& 0& 0& ...& 0& D_N& E_N\end{array}\right]$

Three intermediate variable matrixes, the first intermediate variable matrix B wherein, the second intermediate variable matrix D and the 3rd intermediate variable matrix E are expressed as follows respectively:

Anti-indicator function wherein

$\stackrel{\&OverBar;}{\mathrm{\&delta;}}\left(i\right)=\left\{\begin{array}{cc}1,& i\&NotEqual;0\\ 0,& \mathrm{else}\end{array}\right.$

First intermediate variable

Second intermediate variable

With

Be respectively the arrival rate of customers in first area and the second area,

S1 and s2 are respectively the area of first area and second area;

With

The user who is respectively access cellular network in first area and the second area switches to the speed of WLAN (wireless local area network),

With

Be that the user moves to second area and moves to the transfer rate of first area from second area in the WLAN (wireless local area network) from the first area, will in the 4th step, calculate;

With

Be respectively first area and the service speed of second area user in WLAN (wireless local area network);

The note state

The probability of stability be π=(π ₀, π ₁, π ₂..., π _N), π _n=(π ^w(n, 0), π ^w(n, 1) ..., π ^w(n, M)), then the expression formula of the probability of stability is

Wherein

$\hat{Q}=\left[\begin{array}{c}{Q}^T\\ 1_{1\&times;((N+1)\&CenterDot;(M+1))}\end{array}\right],$ $b=\left[\begin{array}{c}{0}_{((N+1)\&CenterDot;(M+1))\&times;1}\\ 1\end{array}\right];$

Then first area and the blocking rate of second area user in WLAN (wireless local area network) are respectively:

${B_1}^w=\underset{i=0}{\overset{N_{2,\max }^{\text{w}}}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w(N_{1,\max }^w-i,i)\text{,}$ $B_2^w=\underset{i=0}{\overset{N_{2,\max }^w}{\mathrm{\&Sigma;}}}\underset{j=N_{2,\max }^w-i}{\overset{N_{1,\max }^w-i}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w(j,i);$

Then the time-delay average of WLAN (wireless local area network) is:

$E\left[T^w\right]=\frac{\underset{j=0}{\overset{N_{1,\max }^w}{\mathrm{\&Sigma;}}}\underset{i=0}{\overset{N_{2,\max }^w-j}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^w(j,i)\&CenterDot;(i+j)}{({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})\&CenterDot;(1-B_2^w)+({{\mathrm{\&lambda;}}_1}^w+{\mathrm{\&lambda;}}_h^{c-1})\&CenterDot;(1-B_1^w)};$

The 3rd step of input field: for each traversal value

Calculate blocking rate, drop rate and time-delay in the cellular network, process is as follows:

The state of note cellular network is

Expression originates from only cellular network coverage respectively, the first area, and second area, and be linked into the number of users of Cellular Networks always; Then the transfer rate between each state is expressed as follows:

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c+1,n_1^c,n_2^c):$

(1) ${\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c={\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}_h^{c-c}+{\mathrm{\&lambda;}}_h^{w-c}$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

(2) ${\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c={\mathrm{\&lambda;}}_h^{c-c}+{\mathrm{\&lambda;}}_h^{w-c}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c+1,n_2^c):$

(3) ${\widetilde{\mathrm{\&lambda;}}}_{S1}^c={\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c,n_2^c+1):$

(4) ${\widetilde{\mathrm{\&lambda;}}}_{S2}^c={{\mathrm{\&lambda;}}_2}^w\&CenterDot;B_2^w$ When $n_{\mathrm{co}}^c+n_1^c+n_2^c<N_{n,\max }^c$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c-1,n_1^c,n_2^c):$

(5) ${\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}(-{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c))}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c-1,n_2^c):$

(6) ${\widetilde{\mathrm{\&mu;}}}_{S1}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{S1}(-{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c))}$

$(n_{\mathrm{co}}^c,n_1^c,n_2^c)\&RightArrow;(n_{\mathrm{co}}^c,n_1^c,n_2^c-1):$

(7) ${\widetilde{\mathrm{\&mu;}}}_{S2}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)}{1-{\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}(-{\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c))}$

Wherein,

Be respectively neighbours' Cellular Networks residential quarter and switch to the only speed of cellular network coverage to switching rate and the WLAN (wireless local area network) of this residential quarter,

Be square generating function residence time, but interim symbolic variable x conventional letter co, S1, S2 will calculate in the 4th step;

Cellular Networks user's service speed is ${\mathrm{\&mu;}}^c(n_{\mathrm{co}}^c+n_1^c+n_2^c)=\frac{C^c}{(n_{\mathrm{co}}^c+n_1^c+n_2^c)\&CenterDot;f_d},$ C ^cBe Cellular Networks total bandwidth, f _dIt is professional average data size;

The number of users that note inserts Cellular Networks is

Number of users n in the Cellular Networks then ^cDistribution probability be

${\mathrm{\&pi;}}^c\left(n^c\right)=\left\{\begin{array}{cc}\underset{i=1}{\overset{n^c}{\mathrm{\&Pi;}}}(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S1}^c}{{\widetilde{\mathrm{\&mu;}}}_{S1}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S2}^c}{{\widetilde{\mathrm{\&mu;}}}_{S2}^c\left(i\right)})\&CenterDot;\frac{{\mathrm{\&pi;}}^c\left(0\right)}{n^c!}& 0\&le;n^c\&le;N_{n,\max }^c\\ \underset{i=1}{\overset{N_{n,\max }^c}{\mathrm{\&Pi;}}}(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}1}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S1}^c}{{\widetilde{\mathrm{\&mu;}}}_{S1}^c\left(i\right)}+\frac{{\widetilde{\mathrm{\&lambda;}}}_{S2}^c}{{\widetilde{\mathrm{\&mu;}}}_{S2}^c\left(i\right)})\&CenterDot;\underset{j=N_{n,\max }^c+1}{\overset{n^c}{\mathrm{\&Pi;}}}{\left(\frac{{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c}{{\widetilde{\mathrm{\&mu;}}}_{\mathrm{co}}^c\left(i\right)}\right)}^{n^c-N_{n,\max }^c}\&CenterDot;\frac{{\mathrm{\&pi;}}^c\left(0\right)}{n^c!}& N_{n,\max }^c+1\&le;n^c\&le;N_{h,\max }^c\end{array}\right.$

${\mathrm{\&pi;}}^c\left(0\right)=\frac{1}{1+\underset{i=1}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&pi;}}^c\left(i\right)}{{\mathrm{\&pi;}}^c\left(0\right)}}$

Then the blocking rate in the Cellular Networks and drop rate are respectively:

$\begin{array}{cc}{B}^c=\underset{i=N_{n,\max }^c}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}^c\left(i\right),& D^c={\mathrm{\&pi;}}^c\left(N_{h,\max }^c\right)\end{array}$

Average delay in the Cellular Networks is:

$E\left[T^c\right]=\frac{\underset{i=1}{\overset{N_{h,\max }^c}{\mathrm{\&Sigma;}}}i\&CenterDot;{\mathrm{\&pi;}}^c\left(i\right)}{({\mathrm{\&lambda;}}^c+{\widetilde{\mathrm{\&lambda;}}}_{S1}^c+{\widetilde{\text{\&lambda;}}}_{S2}^c)\&CenterDot;(1-B^c)+{\widetilde{\mathrm{\&lambda;}}}_{\mathrm{co}2}^c\&CenterDot;(1-D^c)}$

Input field the 4th step: residence time moment function and switching rate calculating;

Conversion and the probability thereof of user's location status in Cellular Networks are described below: only insert the user of Cellular Networks in the cellular network coverage, when only leaving cellular network coverage, with transition probability p ^C-wEnter second area, with transition probability p ^C-c=1-p ^C-wEnter adjacent Cellular Networks; Enter in the process of first area, with probability

(being the blocking rate of second area in the WLAN (wireless local area network)) still inserts cellular network, with

Probability insert WLAN (wireless local area network); When the user of access Cellular Networks leaves second area in the second area, with transition probability p ^2-1Enter the first area, with transition probability p ^2-cEnter only cellular network coverage, enter in the process of first area, with probability

Still insert Cellular Networks, with probability Switch to WLAN (wireless local area network); When the user who inserts Cellular Networks for the first area leaves the first area, with probability

Keep inserting Cellular Networks, with probability

Switch to WLAN (wireless local area network); Only providing, the square generating function of cellular network coverage, first area, second area user residence time is respectively:

${\mathrm{\&psi;}}_c\left(s\right)=E\left[e^{s\&CenterDot;T_r^{\mathrm{co}}}\right]=\underset{0}{\overset{+\&infin;}{\&Integral;}}{e}^{s\&CenterDot;t}\&CenterDot;{\mathrm{\&eta;}}^{\mathrm{co}}\&CenterDot;e^{-{\mathrm{\&eta;}}^{\mathrm{co}}\&CenterDot;t}\mathrm{dt}=\frac{{\mathrm{\&eta;}}^{\mathrm{co}}}{{\mathrm{\&eta;}}^{\mathrm{co}}-s}$

${\mathrm{\&psi;}}_1\left(s\right)=E\left[e^{s\&CenterDot;T_r^{S1}}\right]=\frac{a}{a+1}\&CenterDot;\frac{a\&CenterDot;{\mathrm{\&eta;}}^{w1}}{a\&CenterDot;{\mathrm{\&eta;}}^{w1}-s}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{w1}}{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{w1}-s}$

${\mathrm{\&psi;}}_2\left(s\right)=E\left[e^{s\&CenterDot;T_r^{S2}}\right]=\frac{a}{a+1}\&CenterDot;\frac{a\&CenterDot;{\mathrm{\&eta;}}^{S2}}{a\&CenterDot;{\mathrm{\&eta;}}^{S2}-s}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{S2}}{\frac{1}{a}\&CenterDot;{\mathrm{\&eta;}}^{S2}-s}$

The square generating function of remembering residence time is Origin area symbolic variable x1 represents user's origin area, the value set is { co, S1, S2, nc}, purpose zone symbolic variable x2 represents user's purpose zone, the value set is { co, S1, S2, nc}, but conditional code variable con value end condition symbol term, be in always and end at overlapping covered conditional code dc_term or jump condition symbol tran, expression is owing to switch to WLAN (wireless local area network) or adjacent Cellular Networks ends at the purpose zone respectively, motion and end at the purpose zone or transfer to the purpose zone first time in overlapping covered dc always; Therefore the square generating function of residence time is

The expression user originates from origin area, arrives the square generating function of residence time of institute before the purpose zone according to the condition of conditional code variable con representative; Residence time the square generating function

The expression user originates from second area, and the square of residence time produces function before moving to for the first time cellular network coverage only, for

${\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)=\underset{j=0}{\overset{+\&infin;}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-c}\&CenterDot;{[p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)]}^j=\frac{{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-c}}{1-p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)}$

Be similar to the derivation of top formula, derive several residence time of square generating function

With

As follows:

${\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)=\frac{{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;(1-B_2^w)}{1-B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)=\frac{{\mathrm{\&psi;}}_2\left(s\right)\&CenterDot;p^{2-1}\&CenterDot;(1-B_1^w)}{1-p^{2-1}\&CenterDot;B_1^w\&CenterDot;{\mathrm{\&psi;}}_1\left(s\right)\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&psi;}}_2\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;[p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)]}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}\left(s\right)=\frac{{\mathrm{\&psi;}}_c\left(s\right)\&CenterDot;p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)}{1-p^{c-w}\&CenterDot;B_2^w\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\&CenterDot;{\mathrm{\&psi;}}_c\left(s\right)}$

The note square produces function For originating from the origin area by origin area symbolic variable x1 representative, produce function and end at the square of this Cellular Networks coverage institute residence time; Derive several squares and produce function

With

Expression formula be:

${\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}\left(s\right)$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}\left(s\right)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}\left(s\right)$

${\mathrm{\&Phi;}}_{\mathrm{term}}^{S1}\left(s\right)={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}\left(s\right)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{S2}\left(s\right)+{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S1-S1}\left(s\right)$

Definition cellular network switching probability is Expression inserts Cellular Networks and originates from the origin area that is represented by origin area symbolic variable x1 and switches to the purpose zone that is represented by purpose zone symbolic variable x2 and the probability that inserts other network wireless local area network (LAN)s and adjacent cellular network; Only then originating from, the user of cellular network coverage by the probability that current cellular network is cut into neighbours' cellular network is

$H_c^{\mathrm{co}-\mathrm{nc}}=\frac{p^{c-c}}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}\left({\stackrel{\&OverBar;}{-\mathrm{\&mu;}}}^c\right)$

The user who originates from second area, the probability that is cut into the first area and is linked into WLAN (wireless local area network) is:

$H_c^{S2-S1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_1^w}$

Derive other several network switching probabilities similarly

With Expression formula be:

$H_c^{\mathrm{co}-S1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_1^w}$

$H_c^{S1-S1}=\frac{{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;[{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)]}{1-B_1^w}$

$H_c^{S2-S2}={\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;\left(\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\right)\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S2-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}$

$H_c^{S1-S2}=\frac{{\mathrm{\&Phi;}}_{\mathrm{dc}\_\mathrm{term}}^{S1-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}+{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;(\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w})$

$H_c^{\mathrm{co}-S2}=\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{p^{c-c}+p^{c-w}\&CenterDot;(1-B_2^w)}\&CenterDot;p^{c-w}+\frac{{\mathrm{\&Phi;}}_{\mathrm{term}}^{\mathrm{co}-S1}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)}{1-B_2^w}$

Definition inserts the user of WLAN (wireless local area network), switches to second area by the first area, and the probability that still is linked into WLAN (wireless local area network) is:

$H_w^{S1-S2}=\frac{a}{a+1}\&CenterDot;\frac{{\mathrm{a\&eta;}}^{w1}}{{\mathrm{a\&eta;}}^{w1}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}{\mathrm{\&eta;}}^{w1}}{\frac{1}{a}{\mathrm{\&eta;}}^{w1}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}$

Definition inserts the user of WLAN (wireless local area network), switches to the first area by second area, and the probability that still is linked into WLAN (wireless local area network) is:

$H_w^{S2-S1}=p^{2-1}\&CenterDot;[\frac{a}{a+1}\&CenterDot;\frac{{\mathrm{a\&eta;}}^{w2}}{{\mathrm{a\&eta;}}^{w2}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}+\frac{1}{a+1}\&CenterDot;\frac{\frac{1}{a}{\mathrm{\&eta;}}^{w2}}{\frac{1}{a}{\mathrm{\&eta;}}^{w2}+{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^w}]$

User in the WLAN (wireless local area network), the probability that switches to honeycomb is

Wherein the draw service speed of Cellular Networks is

The WLAN (wireless local area network) average service rate is

Then switching arrival rate is

${\mathrm{\&lambda;}}_h^{c-c}=H_c^{\mathrm{co}-\mathrm{nc}}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)$

$+{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S1-S2}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)+{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)\&CenterDot;{\mathrm{\&Phi;}}_{\mathrm{tran}}^{S2-\mathrm{co}}(-{\stackrel{\&OverBar;}{\mathrm{\&mu;}}}^c)]$

${\mathrm{\&lambda;}}_h^{c-2}=H_c^{\mathrm{co}-S2}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)]$

$+H_c^{S2-S2}\&CenterDot;{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)+H_c^{S1-S2}\&CenterDot;{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)$

${\mathrm{\&lambda;}}_h^{c-1}=H_c^{\mathrm{co}-S1}\&CenterDot;[{\mathrm{\&lambda;}}^c\&CenterDot;(1-B^c)+({\mathrm{\&lambda;}}_h^{w-c}+{\mathrm{\&lambda;}}_h^{c-c})\&CenterDot;(1-D^c)]$

$+H_c^{S2-S1}\&CenterDot;{\mathrm{\&lambda;}}_2^w\&CenterDot;B_2^w\&CenterDot;(1-B^c)+H_c^{S1-S1}\&CenterDot;{\mathrm{\&lambda;}}_1^w\&CenterDot;B_1^w\&CenterDot;(1-B^c)$

${\mathrm{\&lambda;}}_h^{w-c}=H_w^{w-c}\&CenterDot;((1-B_2^w)\&CenterDot;({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})+{\mathrm{\&lambda;}}_{h12}^w)$

${\mathrm{\&lambda;}}_{h21}^w=H_w^{S2-S1}\&CenterDot;((1-B_2^w)\&CenterDot;({\mathrm{\&lambda;}}_2^w+{\mathrm{\&lambda;}}_h^{c-2})+{\mathrm{\&lambda;}}_{h12}^w)$

${\mathrm{\&lambda;}}_{h12}^w=H_w^{S1-S2}\&CenterDot;((1-B_1^w)\&CenterDot;({\mathrm{\&lambda;}}_1^w+{\mathrm{\&lambda;}}_h^{c-1})+{\mathrm{\&lambda;}}_{h21}^w)$

The 5th step of input field: moved for second step repeatedly to the 4th step, make each switching probability value restrain, and the WLAN (wireless local area network) after the preservation convergence and the time-delay of cellular network;

The 6th step of input field: traveled through all input fields

After the value set, seek optimum input field by following two conditions;

First condition: find to make cellular network blocking rate B ^cRequire (B less than blocking rate ^Req), and cellular network drop rate D ^cRequire (D less than drop rate ^Req) input field set; If set illustrates current business density (λ for empty ^Co, λ ^w) input field of condition is not in the traversal value set, needs are adjusted the scope of traversal value;

Second condition: in the input field set of satisfying first condition, select to make following weighting to delay time minimum input field as current business density (λ ^Co, λ ^w) optimum input field; The weighting time-delay is:

$\stackrel{\&OverBar;}{\mathrm{\&lambda;}}=\frac{{\mathrm{\&lambda;}}^{\mathrm{co}}+{{\mathrm{\&lambda;}}_1}^w{B}_1^w+{{\mathrm{\&lambda;}}_2}^w{B}_2^w}{({\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}^w)}E\left[T^c\right]+\frac{{{\mathrm{\&lambda;}}_1}^w(1-B_1^w)+{{\mathrm{\&lambda;}}_2}^w(1-B_2^w)}{({\mathrm{\&lambda;}}^{\mathrm{co}}+{\mathrm{\&lambda;}}^w)}E\left[T^w\right].$

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