CN105373930B - RFID label tag evaluation method and device applied to traceability system - Google Patents
RFID label tag evaluation method and device applied to traceability system Download PDFInfo
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Abstract
The invention discloses the RFID label tag evaluation methods and device that are applied to traceability system, method includes: to carry out XOR operation with the second random number generated by LFSR using the first random number that system time is obtained as seed, and carry out cyclic shift in a register and generate third random number;The observed value of the free timeslot in previous frame, exclusive time slot and the time slot that conflicts is obtained respectively;Reach the Poisson frequency function obeyed Poisson distribution and obtain parameter as λ according to label;The number expectation value expression of the idle tag in same frame, exclusive label and the label that conflicts is respectively obtained according to Poisson frequency function;According to the observed value of free timeslot, exclusive time slot and the time slot that conflicts in previous frame, and the number expectation value expression of the idle tag, exclusive label and the label that conflicts in same frame, calculate separately the number estimated value for obtaining idle tag, exclusive label and the label that conflicts.The present invention quickly, accurately estimate using number of the maximum likelihood method to RFID label tag.
Description
Technical field
The present invention relates to wireless communication technology fields, and in particular to applied to traceability system RFID label tag evaluation method and
Device.
Background technique
In food safety traceability system, to ensure food in cultivation, production, processing, transport, wholesale, port examination, zero
It sells etc. in full industrial chain and is monitored, tracked, generally use and stick on RFID electronic label in the outer packing of food, pass through RFID
Electronic label reader can trace back to the source information of food.
Due to being the consistency of data transmission and complete by wirelessly being transmitted between RFID label tag and reader
Property just embody RFID system performance for wireless communications, and influence data transmission consistency and integrality the main reason for have 2: one
It is external signal interference.External signal is interfered, can be solved in transmission data plus parity check bit;Second is that channel
Conflict is assigned with the same channel simultaneously that is, between label and reader, to produce channel confliction.For channel confliction,
Propose a variety of anti-collision algorithms in the industry to solve this problem.And wherein most important anti-collision algorithm is dynamic frame slot
ALOHA algorithm (DFSA).The key of dynamic Frame Slotted Aloha algorithm is by obtaining the frame length of previous frame, collision time slot and sky
Idle gap is next quickly, accurately estimates current number of tags, calculates reasonable frame length further according to number of tags dynamic.
Currently, the number of tags evaluation method that industry proposes mainly has three kinds of algorithms such as Vogt, Quan, UPE.First is that Vogt
Algorithm.Vogt algorithm mainly uses traversal search algorithm to meet collision time slot, empty slot, exclusive 3 kinds of time slots of time slot to all
Number is traversed, and a kind of optimal algorithm is searched out, and algorithm estimation is accurate, but computation complexity is too high.Meanwhile Vogt algorithm
A linear combination has been done also according to the relationship between exclusive time slot, empty slot, then has estimated number of tags according to this combination.
This algorithm computation complexity is lower, can more conveniently be estimated, but since estimation error is also directly proportional to number of tags
Relationship, therefore, when number of tags is larger, estimation error is higher.Second is that UPE algorithm.UPE algorithm be also according to monopolize time slot,
Linear relationship between empty slot is estimated that the algorithm computation complexity is low, easy to operate, but with the increasing of number of tags
Add, estimation error rate linear can also increase.Third is that Quan algorithm.Quan algorithm is according to exclusive between time slot, empty slot
Statistical relationship is estimated that algorithm estimation is accurate, but computation complexity is higher, with the increase of number of labels, error rate
Proportional increase.
The importance in dynamic Frame Slotted Aloha algorithm is estimated for clear number of tags, we first pass through to dynamic frame
CDMA slotted ALOHA efficiency of algorithm is analyzed, and is defined first:
S: the goodput of label communication, i.e. label successfully complete the average time of communication within the period.
G: period interior label averagely reaches number.
Pe: label completes the probability of communication.
Since the number that label reaches is according to Poisson distribution, then the probability for reaching n label at t seconds is:
Wherein λ is the number of tags of average arrival per second, then input load are as follows: G=λ T0, meanwhile, do not have in a time slot
The probability for thering are other label informations to reach are as follows: Pe=e-G, therefore, the goodput of label communication are as follows: S=GPe=Ge-G。
From the above equation, we can see that i.e. n=l, the throughput of label communication is maximum as G=1;As G < 1, i.e. n < l, mark
Label free timeslot just will increase, and the time is caused to waste;And as G > 1, i.e. n > l, tag-collision time slot just will increase, to make
Increase at the number for repeating to send, the time is caused to waste.Therefore, how the key that l is exactly efficiency of algorithm be reasonably set, and l
Setting first must accurately estimate number of labels n.
Summary of the invention
For overcome the deficiencies in the prior art, the purpose of the present invention is to provide the RFID label tags for being applied to traceability system to estimate
Method and apparatus are calculated, current label number is estimated using maximum likelihood method, meanwhile, hash function is realized using LFSR, so that
Label can the different time slot of uniform design, reduce the error of estimation.
To solve the above problems, the technical solution adopted in the present invention is as follows:
Scheme one:
RFID label tag evaluation method applied to traceability system, comprising the following steps:
S1: exclusive or is carried out with the second random number generated by LFSR using the first random number that system time is obtained as seed
Operation, and carry out cyclic shift in a register and generate third random number, to allow the tag to linearly select time slot;
S2: the observed value of the free timeslot in previous frame, exclusive time slot and the time slot that conflicts is obtained respectively;
S3: reaching obedience Poisson distribution according to label and obtain binomial frequency function, and obtaining parameter by binomial frequency function is λ
Poisson frequency function;
S4: the number of the idle tag in same frame, exclusive label and the label that conflicts is respectively obtained according to Poisson frequency function
Mesh it is expected value expression;
S5: according to the sky in the observed value of free timeslot, exclusive time slot and the time slot that conflicts in previous frame and same frame
The number of not busy label, exclusive label and the label that conflicts it is expected value expression, calculates separately and obtains idle tag, exclusive label and punching
The number estimated value of prominent label.
Preferably, in step sl, using system time as seed, the first random number is generated by voidsrand function.
Preferably, in step s 2, if estimating for the first time, then using the test frame of setting as previous frame, to obtain it
The observed value of middle free timeslot, exclusive time slot and the time slot that conflicts.
Preferably, in step s3, binomial frequency function are as follows: wherein, p
I time slot is the probability of free timeslot, and m is experiment number;Based on the assumption that mp=λ, λ are load factor, wherein λ=n/l, n are
The number of label, l is the number of time slot, as n → ∞, then the Poisson frequency function that parameter is λ can be obtained are as follows:
Preferably, in step s 4, the number of idle tag it is expected value expression are as follows: E [N0]≈le-λ, monopolize label
Number it is expected value expression are as follows: E [N1]≈lλe-λ, the number expectation value expression for the label that conflicts are as follows: E [N2]≈l-le-λ-lλe-λ;In step s 5, the observed value of free timeslot, exclusive time slot and the time slot that conflicts in previous frame is denoted as m respectively0、m1、m2,
The quantity of free timeslot, exclusive time slot and the time slot that conflicts in previous frame is denoted as M respectively0、M1、M2, by idle tag, monopolize
The number estimated value of label and conflict label is denoted as n0、n1、n2, then there is following relational expression: To acquire n0、n1、n2。
Scheme two:
RFID label tag applied to traceability system estimates device, comprises the following modules:
Random number generation module: the first random number for being obtained using system time as seed with generated by LFSR the
Two random numbers carry out XOR operation, and carry out cyclic shift in a register and generate third random number, linear to allow the tag to
Select time slot;
Time slot observed value obtains module: for obtaining the free timeslot in previous frame, exclusive time slot and conflict time slot respectively
Observed value;
Poisson frequency function generation module: obtaining binomial frequency function for reaching obedience Poisson distribution according to label, by
Binomial frequency function obtains the Poisson frequency function that parameter is λ;
Number of tags it is expected value expression generation module: for respectively obtaining the sky in same frame according to Poisson frequency function
The number of not busy label, exclusive label and the label that conflicts it is expected value expression;
Number of tags estimated value computing module: for according to free timeslot, exclusive time slot and the conflict time slot in previous frame
Observed value and the number of idle tag in same frame, exclusive label and the label that conflicts it is expected value expression, calculate separately
Obtain the number estimated value of idle tag, exclusive label and the label that conflicts.
Preferably, in random number generation module, using system time as seed, first is generated by voidsrand function
Random number.
Preferably, it is obtained in module in time slot observed value, if estimating for the first time, then using the test frame of setting as upper one
Frame, to obtain the observed value of wherein free timeslot, exclusive time slot and the time slot that conflicts.
Preferably, in Poisson frequency function generation module, binomial frequency function are as follows:
Wherein, p is the probability that i-th of time slot is free timeslot, and m is experiment number;Based on the assumption that mp=λ, λ are load factor, wherein
λ=n/l, n are the number of label, and l is the number of time slot, as n → ∞, then the Poisson frequency function that parameter is λ can be obtained are as follows:
Preferably, in number of tags expectation value expression generation module, the number of idle tag it is expected value expression are as follows:
E[N0]≈le-λ, monopolize the number expectation value expression of label are as follows: E [N1]≈lλe-λ, the number desired value expression for the label that conflicts
Formula are as follows: E [N2]≈l-le-λ-lλe-λ;In number of tags estimated value computing module, by previous frame free timeslot, it is exclusive when
Gap and the observed value of conflict time slot are denoted as m respectively0、m1、m2, by free timeslot, exclusive time slot and the time slot that conflicts in previous frame
Quantity is denoted as M respectively0、M1、M2, the number estimated value of idle tag, exclusive label and the label that conflicts is denoted as n0、n1、n2, then have
Following relational expression:
To acquire n0、n1、n2。
Compared with prior art, the beneficial effects of the present invention are: by quick, the accurate estimation to RFID label tag number,
The efficiency of DFSA is improved, to effectively solve the consistency and integrity issue of RFID data transmission.Especially by acquisition
Free timeslot number, conflict timeslot number, normal timeslot number and the current frame length of previous frame are estimated using maximum likelihood estimate
Current number of tags is calculated, meanwhile, hash function is realized using LFSR, the time slot for enabling label uniform design different,
The error of estimation is reduced, error rate is reduced.
Detailed description of the invention
Fig. 1 is the flow chart of the RFID label tag evaluation method applied to traceability system of the invention.
Fig. 2 is the Aerr experimental result picture of the RFID label tag evaluation method applied to traceability system of the invention.
Fig. 3 is three kinds of ERROR ALGORITHM application condition figures of the invention.
Specific embodiment
In the following, being described further in conjunction with attached drawing and specific embodiment to the present invention:
It is the RFID label tag evaluation method applied to traceability system of the invention with reference to Fig. 1, comprising the following steps:
S1: exclusive or is carried out with the second random number generated by LFSR using the first random number that system time is obtained as seed
Operation, and carry out cyclic shift in a register and generate third random number, to allow the tag to linearly select time slot;
S2: the observed value of the free timeslot in previous frame, exclusive time slot and the time slot that conflicts is obtained respectively;
S3: reaching obedience Poisson distribution according to label and obtain binomial frequency function, and obtaining parameter by binomial frequency function is λ
Poisson frequency function;
S4: the number of the idle tag in same frame, exclusive label and the label that conflicts is respectively obtained according to Poisson frequency function
Mesh it is expected value expression;
S5: according to the sky in the observed value of free timeslot, exclusive time slot and the time slot that conflicts in previous frame and same frame
The number of not busy label, exclusive label and the label that conflicts it is expected value expression, calculates separately and obtains idle tag, exclusive label and punching
The number estimated value of prominent label.
Executing step S1 is to reduce the collision between label to enable RFID label tag linearly to select time slot.According to Kazakhstan
The linear characteristic of function is wished to calculate selection time slot, i.e. H (key) ∈ [0, l-1].Hash function should meet three conditions: first is that
It is not repeated, i.e., for given k1, a possibility that value of k2, H (K1), H (K2) are equal essentially 0;Second is that one-way, i.e.,
A possibility that value for pushing away k1 counter by the value of H (K1) essentially 0;Third is that realizing simple, it can simply real by hardware and software device
It is existing.Therefore, hash function is realized using linear feedback shift register.
Linear feedback shift register (LFSR, Liner Feedback Shift Register) is posted by a series of displacements
Storage and a small amount of exclusive or element composition, for generating binary sequence, can be used for generating pseudo random number.Linear feedback shift register
Device is initialized by random number seed, each clock, then the value of register just moves right one, and the value generated carries out different
Or result is put into the Far Left of register cell, while exporting a position after operation.At this moment, if seed is not leaked,
Then LFSR just can produce the pseudo random number of encryption.Moreover, the pseudo random number that LFSR is generated has good statistical property, conveniently answer
It uses in statistic algorithm.The structure of LFSR can be indicated with generator polynomial: G (x)=gmxm+gm-1xm-1+...+g1x+g0.But
It is that there is also two disadvantages for the pseudo random number that LFSR is generated: first is that repeatability.Since the LFSR random number generated is with 2L- 1 is
Period, i.e., 2LRandom number will repeat after -1 step, therefore, if continuously obtaining 2LThe data of position, so that it may crack.Second is that LFSR is random
Number is that have linear characteristic from being derived by mathematics multinomial, data is caused to cannot be directly used to encrypt.Therefore, in this programme
In, be not directly but itself and real random number are subjected to XOR operation using LFSR random number, and in a register into
Row cyclic shift, the shortcomings that can effectively avoiding LFSR random number, and really random number passes through i.e. using system time as seed
The random number that voidsrand function generates.
In step s 2, it needs to obtain the observed value of the free timeslot in previous frame, exclusive time slot and the time slot that conflicts, and obtains
The observed value for taking time slot is the prior art.It should be noted that if to estimate for the first time, that is, when there is no previous frame, then by setting
Test frame is as previous frame, to obtain the observed value of wherein free timeslot, exclusive time slot and the time slot that conflicts.
In step s3, according to probability theory, the arrival of label is to obey Poisson distribution, and Poisson distribution can be by binomial point
The limit of cloth obtains, binomial frequency function are as follows: wherein, p is that i-th of time slot is idle
The probability of time slot, m are experiment number.Assuming that mp=λ, wherein λ is load factor, wherein λ=n/l, n are the number of label, l
For the number of time slot, then obtain: by
?As n → ∞, then have:Therefore the Poisson frequency function that parameter is λ can be obtained:
It in step s 4, will be free timeslot, exclusive time slot, conflict time slot respectively with X in the i-th time sloti、Yi、ZiIt indicates,
When the i-th time slot is free timeslot, then Xi=1, when the i-th time slot is exclusive time slot, then Yi=1, when the i-th time slot be conflict time slot, then
Zi=1.Then assume the i-th time slot be free timeslot when, have and due to having
Therefore P [Xi=1] ≈ e-λ, so as to obtain the number desired value of idle tag are as follows:
Similarly, it is assumed that when the i-th time slot is exclusive time slot, haveThen monopolize the number phase of label
Prestige value are as follows: E [N1]≈lλe-λ.And for the number desired value for the label that conflicts, due to there is Xi+Yi+Zi=1, therefore, conflict label
Number desired value are as follows: E [N2]≈l-le-λ-lλe-λ。
In step s 5, the observed value of free timeslot, exclusive time slot and the time slot that conflicts in previous frame is denoted as m respectively0、
m1、m2, the quantity of free timeslot, exclusive time slot and the time slot that conflicts in previous frame is denoted as M respectively0、M1、M2, by idle tag,
The number estimated value of exclusive label and the label that conflicts is denoted as n0、n1、n2.Due to λ=n/l, E [N0]=le-λ, so have,Similarly, it obtainsAnd
ByIt is available: n0=-l*ln (m0/ l) to get the number estimated value for arriving idle tag;But because with being super equation, according to the value of parameter
(m1* the size of e and l) it is divided into without solution, 1 solution and 2 solutions, three kinds of situations, i.e. the number estimated value of idle tag and conflict label
Needing to meet certain parameter value condition just has solution.
Below for the above-mentioned RFID label tag evaluation method applied to traceability system, emulation survey is carried out using Matlab software
Examination, simulation scale are 10*10 square metres, and simulation time is 60 seconds, and mean value uses 500 microseconds, request of data index of coincidence point
Cloth, simulated environment are free space transmission path loss, do not consider to decay.The reading/writing distance of RFID reader is 1.7 meters, work
Working frequency is 915MHz, and rate travel is no more than 0.5 meter per second, and reader is initially distributed at random.RFID label tag is uniformly distributed.
By the way of calculating average value, each result repeats 100 times all simulation results.Its calculation formula is:Obtained Aerr (%) experimental result is as shown in Figure 2.
As shown in Figure 2, when number of time slot l very little, estimation error rate is very big, more than 30%, i.e., as n > > l, in frame
All time slots will meet with conflict with high probability, and the error of estimation is very big, but as number of time slot l increases, i.e. load factor λ is gradually
It reduces, estimation error rate is successively reduced, and after more than 256, error rate is less than 5%.Meanwhile with the increase of number of tags n, carry
Enter factor lambda to gradually increase, estimation error rate also increases as, but as long as being estimated in estimated range, when timeslot number is more than
After 256, estimation error rate is both less than 5%.
As shown in figure 3, being the application condition figure of Vogt algorithm, UPE algorithm and ML algorithm, wherein ML algorithm is i.e. using this
The algorithm of the RFID label tag evaluation method applied to traceability system of invention.Available, the error rate and λ of Vogt algorithm from Fig. 3
Directly proportional, i.e., with the increase of λ, estimation error rate is with rising, but overall estimation is more accurate, substantially below 15%.This is
Due to Vogt algorithm be using meet collision time slot, empty slot, exclusive 3 kinds of time slots of time slot number traversed, search out most
Excellent algorithm, therefore estimation is more accurate.The error rate of UPE algorithm is also directly proportional to λ, but its estimation error rate is bigger, substantially
40% or more.ML Algorithm Error rate is inversely proportional with λ, and when λ > 2 or so, ML Algorithm Error rate maintains essentially in 5%, meanwhile,
As λ > 1.2, ML Algorithm Error rate ratio Vogt algorithm, the error rate of UPE algorithm are low.
Therefore, RFID label tag evaluation method of the invention, by quick, the accurate estimation to RFID label tag number, to mention
The efficiency of high DFSA, to effectively solve the consistency and integrity issue of RFID data transmission.Especially by upper the one of acquisition
Free timeslot number, conflict timeslot number, normal timeslot number and the current frame length of frame are estimated using maximum likelihood estimate
Number of tags at present, meanwhile, hash function is realized using LFSR, the time slot for enabling label uniform design different is reduced
The error of estimation reduces error rate.
Corresponding to the above-mentioned RFID label tag evaluation method applied to traceability system, the invention also discloses be applied to trace to the source
The RFID label tag of system estimates device, comprises the following modules:
Random number generation module: the first random number for being obtained using system time as seed with generated by LFSR the
Two random numbers carry out XOR operation, and carry out cyclic shift in a register and generate third random number, linear to allow the tag to
Select time slot;
Time slot observed value obtains module: for obtaining the free timeslot in previous frame, exclusive time slot and conflict time slot respectively
Observed value;
Poisson frequency function generation module: obtaining binomial frequency function for reaching obedience Poisson distribution according to label, by
Binomial frequency function obtains the Poisson frequency function that parameter is λ;
Number of tags it is expected value expression generation module: for respectively obtaining the sky in same frame according to Poisson frequency function
The number of not busy label, exclusive label and the label that conflicts it is expected value expression;
Number of tags estimated value computing module: for according to free timeslot, exclusive time slot and the conflict time slot in previous frame
Observed value and the number of idle tag in same frame, exclusive label and the label that conflicts it is expected value expression, calculate separately
Obtain the number estimated value of idle tag, exclusive label and the label that conflicts.
Preferably, in random number generation module, using system time as seed, first is generated by voidsrand function
Random number.
Preferably, it is obtained in module in time slot observed value, if estimating for the first time, then using the test frame of setting as upper one
Frame, to obtain the observed value of wherein free timeslot, exclusive time slot and the time slot that conflicts.
Preferably, in Poisson frequency function generation module, binomial frequency function are as follows:
Wherein, p is the probability that i-th of time slot is free timeslot, and m is experiment number;Based on the assumption that mp=λ, λ are load factor, wherein
λ=n/l, n are the number of label, and l is the number of time slot, as n → ∞, then the Poisson frequency function that parameter is λ can be obtained are as follows:
Preferably, in number of tags expectation value expression generation module, the number of idle tag it is expected value expression are as follows:
E[N0]≈le-λ, monopolize the number expectation value expression of label are as follows: E [N1]≈lλe-λ, the number desired value expression for the label that conflicts
Formula are as follows: E [N2]≈l-le-λ-lλe-λ;In number of tags estimated value computing module, by previous frame free timeslot, it is exclusive when
Gap and the observed value of conflict time slot are denoted as m respectively0、m1、m2, by free timeslot, exclusive time slot and the time slot that conflicts in previous frame
Quantity is denoted as M respectively0、M1、M2, the number estimated value of idle tag, exclusive label and the label that conflicts is denoted as n0、n1、n2, then have
Following relational expression:
To acquire n0、n1、n2。
It will be apparent to those skilled in the art that can make various other according to the above description of the technical scheme and ideas
Corresponding change and deformation, and all these changes and deformation all should belong to the protection scope of the claims in the present invention
Within.
Claims (8)
1. being applied to the RFID label tag evaluation method of traceability system, which comprises the following steps:
S1: exclusive or fortune is carried out with the second random number generated by LFSR using the first random number that system time is obtained as seed
It calculates, and carries out cyclic shift in a register and generate third random number, to allow the tag to linearly select time slot;
S2: the observed value of the free timeslot in previous frame, exclusive time slot and the time slot that conflicts is obtained respectively;
S3: reaching obedience Poisson distribution according to label and obtain binomial frequency function, obtains the pool that parameter is λ by binomial frequency function
Loose frequency function;
S4: the number phase of the idle tag in previous frame, exclusive label and the label that conflicts is respectively obtained according to Poisson frequency function
Hope value expression;
S5: according to the idle mark in the observed value of free timeslot, exclusive time slot and the time slot that conflicts in previous frame and previous frame
The number of label, exclusive label and the label that conflicts it is expected value expression, calculates separately and obtains idle tag, exclusive label and conflict mark
The number estimated value of label.
2. the RFID label tag evaluation method according to claim 1 applied to traceability system, which is characterized in that in step S1
In, using system time as seed, the first random number is generated by voidsrand function.
3. the RFID label tag evaluation method according to claim 1 applied to traceability system, which is characterized in that in step S2
In, if estimating for the first time, then using the test frame of setting as previous frame, to obtain wherein free timeslot, exclusive time slot and punching
The observed value of prominent time slot.
4. the RFID label tag evaluation method according to claim 1 applied to traceability system, which is characterized in that in step S3
In, binomial frequency function are as follows:Wherein, it is the general of free timeslot that p, which is i-th of time slot,
Rate, m are experiment number;Based on the assumption that mp=λ, λ are load factor, wherein λ=n/l, n are the number of label, and l is time slot
The Poisson frequency function that parameter is λ then can be obtained as n → ∞ in number are as follows:
5. the RFID label tag for being applied to traceability system estimates device, which is characterized in that comprise the following modules:
Random number generation module: the first random number for being obtained using system time as seed with generated by LFSR second with
Machine number carries out XOR operation, and carries out cyclic shift in a register and generate third random number, to allow the tag to linearly select
Time slot;
Time slot observed value obtains module: for obtaining the sight of the free timeslot in previous frame, exclusive time slot and the time slot that conflicts respectively
Examine value;
Poisson frequency function generation module: binomial frequency function is obtained for reaching obedience Poisson distribution according to label, by binomial
Frequency function obtains the Poisson frequency function that parameter is λ;
Number of tags it is expected value expression generation module: for respectively obtaining the idle mark in previous frame according to Poisson frequency function
The number of label, exclusive label and the label that conflicts it is expected value expression;
Number of tags estimated value computing module: for the sight according to free timeslot, exclusive time slot and the time slot that conflicts in previous frame
The number expectation value expression for examining the idle tag in value and previous frame, exclusive label and the label that conflicts, calculates separately and obtains
The number estimated value of idle tag, exclusive label and the label that conflicts.
6. the RFID label tag according to claim 5 applied to traceability system estimates device, which is characterized in that in random number
In generation module, using system time as seed, the first random number is generated by voidsrand function.
7. the RFID label tag according to claim 5 applied to traceability system estimates device, which is characterized in that seen in time slot
Examine value obtain module in, if estimating for the first time, then using the test frame of setting as previous frame, thus obtain wherein free timeslot,
The observed value of exclusive time slot and the time slot that conflicts.
8. the RFID label tag according to claim 5 applied to traceability system estimates device, which is characterized in that in Poisson frequency
In rate function generation module, binomial frequency function are as follows:Wherein, it is empty that p, which is i-th of time slot,
The probability of idle gap, m are experiment number;Based on the assumption that mp=λ, λ are load factor, wherein λ=n/l, n are the number of label,
L is the number of time slot, as n → ∞, then the Poisson frequency function that parameter is λ can be obtained are as follows:
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