CN105704735B - A kind of modeling and simulating method of the wireless sensor network energy consumption estimation model based on geometry probability - Google Patents
A kind of modeling and simulating method of the wireless sensor network energy consumption estimation model based on geometry probability Download PDFInfo
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Abstract
The present invention relates to a kind of, and the wireless sensor network energy consumption based on geometry probability estimates the modeling and simulating method of model, belongs to computer simulation technique field.The present invention sows in predetermined region and at random wireless sensor node under regulation communication mode, obtains the theoretical probability distribution function and its fitting function of inter-node communication distance；The node energy consumption model for introducing half Markov chain obtains the energy consumption rating formula of wireless sensor network related to time；According to the mathematic expectaion of distance between node, node energy computation model is added according to energy consumption ratio and energy consumption rating formula of the node under four kinds of states and obtains the energy consumption estimation function of wireless sensor network；The energy consumption estimation function image of wireless sensor network is obtained by emulation, and is crossed Monte-Carlo Simulation Method and obtained the fitting image of energy consumption estimation function.The present invention combines the probability-distribution function of inter-node communication distance with the calculating of energy consumption, obtains the total energy consumption of wireless sensor network.
Description
Technical field
The present invention relates to a kind of, and the wireless sensor network energy consumption based on geometry probability estimates the modeling and simulating side of model
Method belongs to computer simulation technique field.
Background technique
Wireless sensor network is made of large number of wireless sensor network node, most of wireless biography
Sensor node, which once arranges, easily to be moved, and be in a unserviced state, therefore sensor node is basic
The new energy can not be supplemented by way of substituting battery.The research of wireless sensor network energy consumption is just become increasingly
It is important.
In an arbitrary wireless sensor network, a kind of geometrical model is established according to its basic euclidean distance between node pair, is used
Refer to analyze the performances such as the loss of the energy consumption between wireless sensor network such as k adjacent node, path and the transmission of data
Mark.It is available so preferably to distribute strategy rationally, to improve the energy transfer rate of wireless sensor network, to reduce transmission
The loss in path.The Node distribution of wireless sensor network has important work for the service life length of wireless sensor network
With.By the optimization to Node distribution, we can achieve the optimum programming to wireless sensor network energy consumption, realize energy consumption
Allocation optimum.
In previous studies, be mostly by square and the universal region such as rectangle to wireless sensor energy consumption into
Row research.There is scholar and compares studies have shown that just analyzing under the geometrical model of regular hexagon wireless sensor network performance
Research is more nearly true situation under square and rectangular geometrical model.The present invention is made by regular hexagon geometrical model
For the method for survey region, the state of node is considered, propose a kind of energy consumption estimation model.Estimate model to wireless by energy consumption
The total energy consumption of sensor network estimated, for massive wireless sensor energy consumption prediction and estimation provide it is theoretical according to
According to.
Summary of the invention
The present invention provides a kind of, and the wireless sensor network energy consumption based on geometry probability estimates the modeling and simulating of model
Method, with the energy consumption estimation problem for solving massive wireless sensor.
The technical scheme is that a kind of wireless sensor network energy consumption estimation model based on geometry probability is built
Mould emulation mode, sows first in predetermined region and at random wireless sensor node under regulation communication mode, obtains between node
The theoretical probability distribution function and its fitting function of communication distance；The node energy consumption model for introducing half Markov chain, obtain and when
Between related wireless sensor network energy consumption rating formula；Then it according to the mathematic expectaion of distance between node, is added
Node energy computation model is wirelessly passed according to energy consumption ratio and energy consumption rating formula of the node under four kinds of states
The energy consumption estimation function of sensor network；The energy consumption estimation function image of wireless sensor network is obtained finally by emulation, is covered special
Monte Carlo Simulation of Ions Inside method obtains the fitting image of energy consumption estimation function.
Specific step is as follows for the method:
Step1, inter-node communication distance theoretical probability distribution function acquisition:
Wireless sensor node is sowed in predetermined region and at random under regulation communication mode, passes through the method for geometric integration
Acquisition theoretical probability distribution function is u1(d) or u2(d), Monte-Carlo Simulation Method point is passed through to theoretical probability distribution function
Its fitting function is not obtained；
Fitting function u when the predetermined region is single regular hexagon3(d) formula are as follows:
Fitting function u when the predetermined region is two adjacent regular hexagons4(d) formula are as follows:
u4(d)=- 3.60 × 10-3d10M2 -10+6.63×10-2d9M2 -9-5.20×10-1d8M2 -8+2.26×d7M2 -7-
5.94d6M2 6+9.65d5M2 -5-9.59d4M2 -4+5.68d3M2 -3-1.72d2M2 -2+2.59×10-1dM2 -1Wherein, u1(d)、u2(d)
Theoretical probability distribution function when predetermined region is single regular hexagon, two adjacent regular hexagons is respectively indicated, d indicates node
Between communication distance；M1Indicate side length when predetermined region is single regular hexagon, M2Indicate predetermined region be two it is adjacent just
Side length when hexagon；
Step2, the node energy consumption model for introducing half Markov chain, obtain the energy of wireless sensor network related to time
Consume rating formula u5(d)；
The u5(d) formula are as follows:
u5(d)=t × (P1,1×PS+P2,2×PT+P3,3×PR+P4,4×PF)
Wherein, P1,1、P2,2、P3,3And P4,4Respectively stable state of the node under four kinds of S state, T state, R state and F state states is general
Rate, the energy consumption power that node consumes under these four states is respectively PS、PT、PRAnd PF；T is the total time of state conversion, S state
Indicate sleep, T state indicates to send, and R state indicates to receive, and F state indicates idle；
Step3, according to the mathematic expectaion of distance between node, node energy computation model u is added8(d), existed according to node
Energy consumption ratio and energy consumption rating formula u under four kinds of states5(d), the energy consumption estimation function u of wireless sensor network is obtained9
(d) or u10(d)；
Step3.1, pass through fitting function u3(d) or u4(d) mathematic expectaion for respectively obtaining distance between node is u6
(d) or u7(d):
The u6(d) formula are as follows: u6(d)≈0.8262542775M1；
The u7(d) formula are as follows: u7(d)≈1.858336696M2；
Wherein, u6(d)、u7(d) section when predetermined region is single regular hexagon, two adjacent regular hexagons is respectively indicated
The mathematic expectaion of distance between point；
Step3.2, node energy computation model u is added8(d)；Wherein, u8(d) energy needed for indicating node work, u8
(d)=(alpha+beta dm)·L；Energy needed for α indicates one bit information of transmission and the energy including being consumed when starting, β expression transmission
The loss of unit energy, L indicate that the length of sent out data, m indicate the abatement factor of signal in the process；
Step3.3, in node energy computation model u8(d) on the basis of, both members then have P=simultaneously divided by time t
(α+βdm)·ν；Wherein, P indicates that energy consumption power, ν indicate message transmission rate；
Step3.4, energy consumption ratio and energy consumption rating formula u according to node under four kinds of states5(d), nothing is obtained
The energy consumption estimation function of line sensor network is u9(d) or u10(d):
The u9(d) formula are as follows:
The u10(d) formula are as follows:
Wherein, u9(d)、u10(d) it respectively indicates wireless when predetermined region is single regular hexagon, two adjacent regular hexagons
The energy consumption estimation function of sensor network；
Step4, wireless sensor node is sowed at random in predetermined region and under regulation communication mode, obtained by emulation
The energy consumption estimation function u of wireless sensor network9(d) or u10(d) image, Monte-Carlo Simulation Method obtain energy consumption estimation letter
Several fitting images.
The predetermined region is single regular hexagon or two adjacent regular hexagons；The regulation communication mode is nothing
It can be communicated between the node of line sensor network.
The working principle of the invention is:
Pass through the integral relation of geometry, it is assumed that spread at random in single regular hexagon and two adjacent regular hexagon regions
Two points are derived in single regular hexagon and two adjacent positive six border regions by the distance between the two points, are saved
The calculation formula of the probability density function and probability-distribution function of distance between point.By simulation study it can be concluded that, on positive six side
The range distribution of region lower node is closest with true situation.Then, it on the basis of considering node state conversion, is added
The computation model of the energy of node, because the energy between node is closely related with the state of distance and node between node.
Then according to the four of node kinds of energy consumption ratios of state and the mathematic expectaion of nodal distance, the node of combining with wireless sensor network
Energy balane model is derived by the energy consumption estimation function u of wireless sensor network9(d) and u10(d)；Estimate in obtained energy consumption
The image of meter function can intuitively obtain the relationship and specific network that the total energy consumption of wireless sensor network changes with node
Total energy consumption.
Wherein, theoretical probability density function u1(d) and probability-distribution function u2It (d) is Yanyan Zhuang and
It is proposed in Jianping Pan, Random Distances Associated with Hexagons.In document,
Indicate the probability-distribution function u in the case of single regular hexagon1(d),In the case of indicating two adjacent regular hexagons
Probability-distribution function u2(d)。
The beneficial effects of the present invention are:
1, node sows a certain number of nodes at different node conversion time t, state conversion and energy by node
The calculating of consumption combines, and obtains the total energy consumption of wireless sensor network.
2, at specific time t, different number of nodes are sowed, by the probability-distribution function and energy of inter-node communication distance
The calculating of consumption combines, and obtains the total energy consumption of wireless sensor network.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 is that the single regular hexagon of predetermined region of the invention spreads point diagram；
Fig. 3 is that two adjacent regular hexagons of predetermined region of the invention spread point diagram；
Fig. 4 is communication mode explanatory diagram of the invention；
Fig. 5 is single positive six sides interior nodes range distribution function and analogous diagram of the invention；
The probability-distribution function and analogous diagram of Fig. 6 communication distance between two adjacent positive six side interior nodes of the invention；
Fig. 7 is the state transition graph of wireless sensor network node of the invention；
Fig. 8 is the network total energy consumption estimation function and analogous diagram of t=200s in single regular hexagon of the invention；
Fig. 9 is the network total energy consumption estimation function and analogous diagram of t=200s in two adjacent regular hexagons of the invention.
Specific embodiment
Embodiment 1: as shown in figs 1-9, a kind of wireless sensor network energy consumption estimation model based on geometry probability
Modeling and simulating method sows first in predetermined region and at random wireless sensor node under regulation communication mode, obtains node
Between communication distance theoretical probability distribution function and its fitting function；The node energy consumption model for introducing half Markov chain, obtain with
The energy consumption rating formula of time related wireless sensor network；Then according to the mathematic expectaion of distance between node, add
Ingress energy balane model obtains wireless according to energy consumption ratio and energy consumption rating formula of the node under four kinds of states
The energy consumption estimation function of sensor network；The energy consumption estimation function image of wireless sensor network is obtained finally by emulation, is covered
Special Monte Carlo Simulation of Ions Inside method obtains the fitting image of energy consumption estimation function.
Specific step is as follows for the method:
Step1, inter-node communication distance theoretical probability distribution function acquisition:
Wireless sensor node is sowed in predetermined region and at random under regulation communication mode, passes through the method for geometric integration
Acquisition theoretical probability distribution function is u1(d) or u2(d), Monte-Carlo Simulation Method point is passed through to theoretical probability distribution function
Its fitting function is not obtained；
Fitting function u when the predetermined region is single regular hexagon3(d) formula are as follows:
Fitting function u when the predetermined region is two adjacent regular hexagons4(d) formula are as follows:
u4(d)=- 3.60 × 10-3d10M2 -10+6.63×10-2d9M2 -9-5.20×10-1d8M2 -8+2.26×d7M2 -7-
5.94d6M2 6+9.65d5M2 -5-9.59d4M2 -4+5.68d3M2 -3-1.72d2M2 -2+2.59×10-1dM2 -1
Wherein, u1(d)、u2(d) reason when predetermined region is single regular hexagon, two adjacent regular hexagons is respectively indicated
By probability-distribution function, d indicates the communication distance between node；M1Indicate side length when predetermined region is single regular hexagon, M2
Indicate side length when predetermined region is two adjacent regular hexagons；
Step2, the node energy consumption model for introducing half Markov chain, obtain the energy of wireless sensor network related to time
Consume rating formula u5(d)；
The u5(d) formula are as follows:
u5(d)=t × (P1,1×PS+P2,2×PT+P3,3×PR+P4,4×PF)
Wherein, P1,1、P2,2、P3,3And P4,4Respectively stable state of the node under four kinds of S state, T state, R state and F state states is general
Rate, the energy consumption power that node consumes under these four states is respectively PS、PT、PRAnd PF；T is the total time of state conversion, S state
Indicate sleep, T state indicates to send, and R state indicates to receive, and F state indicates idle；
Step3, according to the mathematic expectaion of distance between node, node energy computation model u is added8(d), existed according to node
Energy consumption ratio and energy consumption rating formula u under four kinds of states5(d), the energy consumption estimation function u of wireless sensor network is obtained9
(d) or u10(d)；
Step3.1, pass through fitting function u3(d) or u4(d) mathematic expectaion for respectively obtaining distance between node is u6
(d) or u7(d):
The u6(d) formula are as follows: u6(d)≈0.8262542775M1；
The u7(d) formula are as follows: u7(d)≈1.858336696M2；
Wherein, u6(d)、u7(d) section when predetermined region is single regular hexagon, two adjacent regular hexagons is respectively indicated
The mathematic expectaion of distance between point；
Step3.2, node energy computation model u is added8(d)；Wherein, u8(d) energy needed for indicating node work, u8
(d)=(alpha+beta dm)·L；Energy needed for α indicates one bit information of transmission and the energy including being consumed when starting, β expression transmission
The loss of unit energy, L indicate that the length of sent out data, m indicate the abatement factor of signal in the process；
Step3.3, in node energy computation model u8(d) on the basis of, both members then have P=simultaneously divided by time t
(α+βdm)·ν；Wherein, P indicates that energy consumption power, ν indicate message transmission rate；
Step3.4, energy consumption ratio and energy consumption rating formula u according to node under four kinds of states5(d), nothing is obtained
The energy consumption estimation function of line sensor network is u9(d) or u10(d):
The u9(d) formula are as follows:
The u10(d) formula are as follows:
Wherein, u9(d)、u10(d) it respectively indicates wireless when predetermined region is single regular hexagon, two adjacent regular hexagons
The energy consumption estimation function of sensor network；
Step4, wireless sensor node is sowed at random in predetermined region and under regulation communication mode, obtained by emulation
The energy consumption estimation function u of wireless sensor network9(d) or u10(d) image, Monte-Carlo Simulation Method obtain energy consumption estimation letter
Several fitting images.
The predetermined region is single regular hexagon；It is described to provide communication mode between the node of wireless sensor network all
It can communicate.
Embodiment 2: it is as shown in figs 1-9, substantially the same manner as Example 1, the difference is that: the predetermined region is two
A adjacent regular hexagon；
Embodiment 3: as shown in figs 1-9, a kind of wireless sensor network energy consumption estimation model based on geometry probability
Modeling and simulating method sows first in predetermined region and at random wireless sensor node under regulation communication mode, obtains node
Between communication distance theoretical probability distribution function and its fitting function；The node energy consumption model for introducing half Markov chain, obtain with
The energy consumption rating formula of time related wireless sensor network；Then according to the mathematic expectaion of distance between node, add
Ingress energy balane model obtains wireless according to energy consumption ratio and energy consumption rating formula of the node under four kinds of states
The energy consumption estimation function of sensor network；The energy consumption estimation function image of wireless sensor network is obtained finally by emulation, is covered
Special Monte Carlo Simulation of Ions Inside method obtains the fitting image of energy consumption estimation function.
Specific step is as follows for the method:
Step1, inter-node communication distance theoretical probability distribution function acquisition:
Wireless sensor node is sowed in predetermined region and at random under regulation communication mode, passes through the method for geometric integration
Acquisition theoretical probability distribution function is u1(d) or u2(d), Monte-Carlo Simulation Method point is passed through to theoretical probability distribution function
Its fitting function is not obtained；
Fitting function u when the predetermined region is single regular hexagon3(d) formula are as follows:
Fitting function u when the predetermined region is two adjacent regular hexagons4(d) formula are as follows:
u4(d)=- 3.60 × 10-3d10M2 -10+6.63×10-2d9M2 -9-5.20×10-1d8M2 -8+2.26×d7M2 -7-
5.94d6M2 6+9.65d5M2 -5-9.59d4M2 -4+5.68d3M2 -3-1.72d2M2 -2+2.59×10-1dM2 -1
Wherein, u1(d)、u2(d) reason when predetermined region is single regular hexagon, two adjacent regular hexagons is respectively indicated
By probability-distribution function, d indicates the communication distance between node；M1Indicate side length when predetermined region is single regular hexagon, M2
Indicate side length when predetermined region is two adjacent regular hexagons；
Step2, the node energy consumption model for introducing half Markov chain, obtain the energy of wireless sensor network related to time
Consume rating formula u5(d)；
The u5(d) formula are as follows:
u5(d)=t × (P1,1×PS+P2,2×PT+P3,3×PR+P4,4×PF)
Wherein, P1,1、P2,2、P3,3And P4,4Respectively stable state of the node under four kinds of S state, T state, R state and F state states is general
Rate, the energy consumption power that node consumes under these four states is respectively PS、PT、PRAnd PF；T is the total time of state conversion, S state
Indicate sleep, T state indicates to send, and R state indicates to receive, and F state indicates idle；
Step3, according to the mathematic expectaion of distance between node, node energy computation model u is added8(d), existed according to node
Energy consumption ratio and energy consumption rating formula u under four kinds of states5(d), the energy consumption estimation function u of wireless sensor network is obtained9
(d) or u10(d)；
Step3.1, pass through fitting function u3(d) or u4(d) mathematic expectaion for respectively obtaining distance between node is u6
(d) or u7(d):
The u6(d) formula are as follows: u6(d)≈0.8262542775M1；
The u7(d) formula are as follows: u7(d)≈1.858336696M2；
Wherein, u6(d)、u7(d) section when predetermined region is single regular hexagon, two adjacent regular hexagons is respectively indicated
The mathematic expectaion of distance between point；
Step3.2, node energy computation model u is added8(d)；Wherein, u8(d) energy needed for indicating node work, u8
(d)=(alpha+beta dm)·L；Energy needed for α indicates one bit information of transmission and the energy including being consumed when starting, β expression transmission
The loss of unit energy, L indicate that the length of sent out data, m indicate the abatement factor of signal in the process；
Step3.3, in node energy computation model u8(d) on the basis of, both members then have P=simultaneously divided by time t
(α+βdm)·ν；Wherein, P indicates that energy consumption power, ν indicate message transmission rate；
Step3.4, energy consumption ratio and energy consumption rating formula u according to node under four kinds of states5(d), nothing is obtained
The energy consumption estimation function of line sensor network is u9(d) or u10(d):
The u9(d) formula are as follows:
The u10(d) formula are as follows:
Wherein, u9(d)、u10(d) it respectively indicates wireless when predetermined region is single regular hexagon, two adjacent regular hexagons
The energy consumption estimation function of sensor network；
Step4, wireless sensor node is sowed at random in predetermined region and under regulation communication mode, obtained by emulation
The energy consumption estimation function u of wireless sensor network9(d) or u10(d) image, Monte-Carlo Simulation Method obtain energy consumption estimation letter
Several fitting images.
Embodiment 4: as shown in figs 1-9, a kind of wireless sensor network energy consumption estimation model based on geometry probability
Modeling and simulating method sows first in predetermined region and at random wireless sensor node under regulation communication mode, obtains node
Between communication distance theoretical probability distribution function and its fitting function；The node energy consumption model for introducing half Markov chain, obtain with
The energy consumption rating formula of time related wireless sensor network；Then according to the mathematic expectaion of distance between node, add
Ingress energy balane model obtains wireless according to energy consumption ratio and energy consumption rating formula of the node under four kinds of states
The energy consumption estimation function of sensor network；The energy consumption estimation function image of wireless sensor network is obtained finally by emulation, is covered
Special Monte Carlo Simulation of Ions Inside method obtains the fitting image of energy consumption estimation function.
Embodiment 5: as shown in figs 1-9, a kind of wireless sensor network energy consumption estimation model based on geometry probability
Modeling and simulating method, specific step is as follows for the method:
Step1, inter-node communication distance theoretical probability distribution function acquisition:
In side length M1Sow wireless sensor node at random in the single regular hexagon of=100m, as shown in Fig. 2,
Side length M2Wireless sensor node is sowed at random in two adjacent regular hexagons of=100m, as shown in Figure 3, it is specified that wireless pass
Communication mode between sensor network node can communicate between node, as shown in figure 4, all communicating between 3 nodes.Pass through
It is u that the method for geometric integration, which obtains theoretical probability distribution function,1(d) or u2(d), special by covering to theoretical probability distribution function
Monte Carlo Simulation of Ions Inside method respectively obtains its fitting function；
Fitting function u when the predetermined region is single regular hexagon3(d) formula are as follows:
Fitting function u when the predetermined region is two adjacent regular hexagons4(d) formula are as follows:
u4(d)=- 3.60 × 10-3d10M2 -10+6.63×10-2d9M2 -9-5.20×10-1d8M2 -8+2.26×d7M2 -7-
5.94d6M2 6+9.65d5M2 -5-9.59d4M2 -4+5.68d3M2 -3-1.72d2M2 -2+2.59×10-1dM2 -1
Wherein, u1(d)、u2(d) reason when predetermined region is single regular hexagon, two adjacent regular hexagons is respectively indicated
By probability-distribution function, d indicates the communication distance between node；M1Indicate side length when predetermined region is single regular hexagon, M2
Indicate side length when predetermined region is two adjacent regular hexagons；
Using the probability-distribution function u in document Random Distances Associated with Hexagons1
(d) and u2(d).Wireless sensor node 100000 are sowed in predetermined region and at random under regulation communication mode, passes through illiteracy
Special calot's method simulating, verifying probability-distribution function u1(d) and u2(d) its correctness.As shown in figure 5, being existed by Monte Carlo method
Emulation obtains probability-distribution function u in single regular hexagon in MATLAB1(d) theory function and fitting function u3(d)；Such as Fig. 6
It is shown, it is emulated and is obtained in MATLAB by Monte Carlo method, probability-distribution function u in two adjacent regular hexagons2(d) reason
Number-theoretic function and fitting function u4(d).Illustrate probability-distribution function u1(d) and u2(d), it removes other than the point changed greatly individually, with
The truth of Node distribution is fairly close, demonstrates theoretical correctness.
Step2, the energy consumption of node are related with the state conversion of node, four kinds of state relations of node, as shown in Figure 7.Draw
The node energy consumption model for entering half Markov chain obtains the energy consumption rating formula u of wireless sensor network related to time5
(d)；
The u5(d) formula are as follows:
u5(d)=t × (P1,1×PS+P2,2×PT+P3,3×PR+P4,4×PF)
Wherein, P1,1、P2,2、P3,3And P4,4The respectively probability of stability of the node under four kinds of S state, T state, R state and F state states
(P1,1=P2,2=P3,3=P4,4=1/4) the energy consumption power that, node consumes under these four states is respectively PS、PT、PRAnd PF；t
For the total time of state conversion, S state indicates sleep, and T state indicates to send, and R state indicates to receive, and F state indicates idle；
Step3, according to the mathematic expectaion of distance between node, node energy computation model u is added8(d), existed according to node
Energy consumption ratio and energy consumption rating formula u under four kinds of states5(d), the energy consumption estimation function u of wireless sensor network is obtained9
(d) or u10(d)；
Step3.1, pass through fitting function u3(d) or u4(d) mathematic expectaion for respectively obtaining distance between node is u6
(d) or u7(d):
The u6(d) formula are as follows:
The u7(d) formula are as follows:
Wherein, fDFor fTDFor theoretical probability distribution function u1(d) and u2(d) derivative function；u6(d)、u7(d) difference table
Show the mathematic expectaion of distance between node when predetermined region is single regular hexagon, two adjacent regular hexagons；
Step3.2, node energy computation model u is added8(d)；Wherein, u8(d) energy needed for indicating node work, u8
(d)=(alpha+beta dm)·L；Energy needed for α indicates one bit information of transmission and the energy including being consumed when starting, β expression transmission
The loss of unit energy, L indicate that the length of sent out data, m indicate the abatement factor of signal in the process；
Step3.3, in node energy computation model u8(d) on the basis of, both members then have P=simultaneously divided by time t
(α+βdm)·ν；Wherein, P indicates that energy consumption power, ν indicate that message transmission rate, general value are as follows: α=50nJ/bit, β=
0.0013pJ/bit/m4, m=4, ν=10kb/s；
Step3.4, energy consumption ratio (2000:400:400:1) and energy consumption power calculation according to node under four kinds of states
Formula u5(d), the energy consumption estimation function for obtaining wireless sensor network is u9(d) or u10(d):
The u9(d) formula are as follows:
The u10(d) formula are as follows:
Wherein, u9(d)、u10(d) it respectively indicates wireless when predetermined region is single regular hexagon, two adjacent regular hexagons
The energy consumption estimation function of sensor network；
Step4, wireless sensor node (same step is sowed in predetermined region and under regulation communication mode at random
Step1), the conversion time that node state is arranged is t=200s, estimates letter by the energy consumption that emulation obtains wireless sensor network
Number u9(d) and u10(d) image, Monte-Carlo Simulation Method obtain the fitting image of energy consumption estimation function.Fig. 8 is single positive six
Network total energy consumption estimation function and fitted figure in the shape of side, Fig. 9 are that network total energy consumption estimates letter in two adjacent regular hexagons
Several and fitted figure.
Above in conjunction with attached drawing, the embodiment of the present invention is explained in detail, but the present invention is not limited to above-mentioned
Embodiment within the knowledge of a person skilled in the art can also be before not departing from present inventive concept
It puts and makes a variety of changes.
Claims (2)
1. a kind of modeling and simulating method of the wireless sensor network energy consumption estimation model based on geometry probability, feature exist
In: wireless sensor node is sowed first in predetermined region and at random under regulation communication mode, obtains inter-node communication distance
Theoretical probability distribution function and its fitting function；The node energy consumption model for introducing half Markov chain obtains related to time
The energy consumption rating formula of wireless sensor network；Then according to the mathematic expectaion of distance between node, node energy is added
Computation model obtains wireless sensor network according to energy consumption ratio and energy consumption rating formula of the node under four kinds of states
Energy consumption estimation function；The energy consumption estimation function image of wireless sensor network, Monte Carlo simulation are obtained finally by emulation
Method obtains the fitting image of energy consumption estimation function；
Specific step is as follows for the method:
Step1, inter-node communication distance theoretical probability distribution function acquisition:
Wireless sensor node is sowed in predetermined region and at random under regulation communication mode, is obtained by the method for geometric integration
Theoretical probability distribution function is u1(d) or u2(d), theoretical probability distribution function is obtained respectively by Monte-Carlo Simulation Method
To its fitting function；
Fitting function u when the predetermined region is single regular hexagon3(d) formula are as follows:
Fitting function u when the predetermined region is two adjacent regular hexagons4(d) formula are as follows:
u4(d)=- 3.60 × 10-3d10M2 -10+6.63×10-2d9M2 -9-5.20×10-1d8M2 -8+2.26×d7M2 -7-5.94d6M2 6
+9.65d5M2 -5-9.59d4M2 -4+5.68d3M2 -3-1.72d2M2 -2+2.59×10-1dM2 -1
Wherein, u1(d)、u2(d) theory respectively indicated when predetermined region is single regular hexagon, two adjacent regular hexagons is general
Rate distribution function, d indicate the communication distance between node；M1Indicate side length when predetermined region is single regular hexagon, M2It indicates
Side length when predetermined region is two adjacent regular hexagons；
Step2, the node energy consumption model for introducing half Markov chain, obtain the energy wasted work of wireless sensor network related to time
Rate calculation formula u5(d)；
The u5(d) formula are as follows:
u5(d)=t × (P1,1×PS+P2,2×PT+P3,3×PR+P4,4×PF)
Wherein, P1,1、P2,2、P3,3And P4,4The respectively probability of stability of the node under four kinds of S state, T state, R state and F state states, section
The energy consumption power that point consumes under these four states is respectively PS、PT、PRAnd PF；T is the total time of state conversion, and the expression of S state is slept
It sleeps, T state indicates to send, and R state indicates to receive, and F state indicates idle；
Step3, according to the mathematic expectaion of distance between node, node energy computation model u is added8(d), according to node at four kinds
Energy consumption ratio and energy consumption rating formula u under state5(d), the energy consumption estimation function u of wireless sensor network is obtained9(d)
Or u10(d)；
Step3.1, pass through fitting function u3(d) or u4(d) mathematic expectaion for respectively obtaining distance between node is u6(d) or
Person u7(d):
The u6(d) formula are as follows: u6(d)≈0.8262542775M1；
The u7(d) formula are as follows: u7(d)≈1.858336696M2；
Wherein, u6(d)、u7(d) respectively indicate predetermined region be single regular hexagon, two adjacent regular hexagons when node it
Between distance mathematic expectaion；
Step3.2, node energy computation model u is added8(d)；Wherein, u8(d) energy needed for indicating node work, u8(d)=
(α+βdm)·L；Energy needed for α indicates one bit information of transmission and the energy including being consumed when starting, β expression transmission process
The loss of middle unit energy, L indicate that the length of sent out data, m indicate the abatement factor of signal；
Step3.3, in node energy computation model u8(d) on the basis of, both members then have P=(alpha+beta simultaneously divided by time t
dm)·ν；Wherein, P indicates that energy consumption power, ν indicate message transmission rate；
Step3.4, energy consumption ratio and energy consumption rating formula u according to node under four kinds of states5(d), wireless sensing is obtained
The energy consumption estimation function of device network is u9(d) or u10(d):
The u9(d) formula are as follows:
The u10(d) formula are as follows:
Wherein, u9(d)、u10(d) wireless sensing when predetermined region is single regular hexagon, two adjacent regular hexagons is respectively indicated
The energy consumption estimation function of device network；
Step4, wireless sensor node is sowed at random in predetermined region and under regulation communication mode, obtained by emulation wireless
The energy consumption estimation function u of sensor network9(d) or u10(d) image, Monte-Carlo Simulation Method obtain energy consumption estimation function
It is fitted image.
2. the modeling and simulating of the wireless sensor network energy consumption estimation model according to claim 1 based on geometry probability
Method, it is characterised in that: the predetermined region is single regular hexagon or two adjacent regular hexagons；The regulation communication
Mode can communicate between the node of wireless sensor network.
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