A Simple Analysis Method for ALOHA Network Throughput under Transmission Time Limit

Abstract

The present invention provides a simple analysis method for ALOHA network throughput under transmission time limit, including determining relevant parameters of Markov process, determining the probability τ of successful transmission of any data packet, and then determining the network throughput under transmission time limit. The present invention aims to provide a simple analysis method for ALOHA network throughput under transmission time limit, so as to provide assistance for ALOHA network throughput analysis under transmission time limit and transmission number limit.

Description

Technical Field

[0001] The invention relates to the technical field of wireless network communications, and in particular to a simple analysis method for ALOHA network throughput under transmission time limit. Background Art

[0002] In recent years, with the emergence of various real-time wireless communication services, people have continuously increased their requirements for the timeliness and reliability of wireless network data transmission, so they need to pay attention to the above communication performance indicators under the transmission time limit. At this time, such networks are quite different from traditional wireless networks without transmission time limit constraints. In order to communicate more efficiently, the Medium Access Control (MAC) layer of the wireless network protocol specifies how multiple users can fairly share and use wireless communication resources. It plays a vital role in various communication performance indicators of wireless networks and is one of the key mechanisms to ensure efficient communication in wireless networks. Among them, ALOHA random multiple access is suitable for unpredictable burst transmission scenarios under transmission time limits because of its flexibility, ease of use and low control overhead. However, the previous ALOHA network throughput analysis method under transmission time limits did not consider the transmission number limit and the different values ​​of successful data transmission at different urgency levels for practical applications. Therefore, it is necessary to propose a more accurate analysis method for network throughput based on these two points. Summary of the invention

[0003] The present invention aims to provide a simple analysis method of ALOHA network throughput under transmission time limit, so as to optimize the network throughput of ALOHA random multiple access with fixed transmission time limit constraint, and provide assistance for the effective implementation of ALOHA random multiple access under transmission time limit.

[0004] The technical solution to achieve the purpose of the present invention is: a simple analysis method for ALOHA network throughput under transmission time limit, the specific steps are:

[0005] Step 1: Determine the relevant parameters of the Markov process, which include: describing the individual state of the tag user at the beginning of time slot t {(d t ,r t )∈S:t=0,1,2,…}, describing the label user individual in state {(d t =d,r t = r)∈S} to the state {(d t+1 =d',r t+1 =r')∈S}, and the steady-state probability π describing the individual state of the labeled user in (d, r) d,r ;

[0006] Step 2: Based on the steady-state probability of the individual state, determine the probability τ of successful transmission of any data packet;

[0007] Step 3: Determine the network throughput rate under the transmission time limit.

[0008] Compared with the prior art, the present invention is based on ALOHA random multiple access, comprehensively considers the transmission time limit and transmission number constraints, and performs Markov modeling on multi-user scenarios from the perspective of individual users based only on the urgency information of the head-of-line data packet, so that the modeling complexity can be applicable to any multi-user scenario, and therefore can provide effective help for simple analysis of network throughput under transmission time limit. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 It is a flow chart of the present invention.

[0010] Figure 2 This is a comparison chart of the theoretical value and the simulated value of the ALOHA network throughput when γ=1 in Example 1.

[0011] Figure 3 This is a comparison chart of the theoretical value and the simulated value of the ALOHA network throughput when γ=0.9 in Example 1. DETAILED DESCRIPTION

[0012] The present invention is applied to a fully connected and globally clock-synchronized wireless network consisting of N ≥ 2 users and an access point. The N users share a channel whose time axis is divided into a number of time slots t, t∈{1,2,3...} with equal boundary-aligned lengths. All users can accurately locate the time slot boundary and attempt to send the head-of-queue data packet to the access point with probability p. The probability that a new data packet arrives at the beginning of each time slot t for each user is 0<λ≤1. Assume that the transmission time limit of each data packet is D ≥ 1 time slots, that is, the data packet will be removed from the queue if the stay time in the queue reaches D. Under this assumption, it can be seen that the maximum queue length of each user is D. In addition, it is assumed that each data packet is allowed to be transmitted at most 1≤R≤D times. At the beginning of time slot t, if the queue of user n is not empty, the head-of-line data packet is sent with probability p, and its transmission time and access point feedback response time together occupy a time slot; if user n sends a data packet in time slot t, user n can obtain access point feedback information at the end of time slot t to know whether the head-of-line data packet is successfully or unsuccessfully transmitted; finally, if the head-of-line data packet is successfully transmitted, or the stay time reaches the transmission time limit D, or the number of transmissions reaches the upper limit R, it will be discarded. When a user sends a data packet at the beginning of time slot t, this data packet can be successfully received by the access point if and only if no other user sends a data packet in this time slot; and at the end of this time slot, this user can confirm whether the data packet is successfully transmitted through access point feedback. If the transmission fails, this data packet will be allowed to continue to stay in the queue until its queue stay time reaches D or the number of transmissions of this data packet reaches R. A simple analysis method for ALOHA network throughput under transmission time limit, the specific steps are:

[0013] Step 1: Determine the relevant parameters of the Markov process, which include: describing the individual state of the tag user at the beginning of time slot t {(d t ,r t )∈S:t=0,1,2,…}, describing the label user individual in state {(d t =d,r t = r)∈S} to the state {(d t+1 =d',r t+1 =r')∈S}, and the steady-state probability π describing the individual state of the labeled user in (d, r) d,r ;

[0014] Step 2: Based on the steady-state probability of the individual state, determine the probability τ of successful transmission of any data packet;

[0015] Step 3: Determine the network throughput rate under the transmission time limit.

[0016] Preferably, the method for determining the relevant parameters of the Markov process described in step 1 is specifically:

[0017] Step 1-1: Determine the probability of data packets arriving at the start of the time slot as λ, the probability of data transmission when the tag user data queue is not empty p, and the individual state of the tag user {(d t ,r t )∈S}, where d t ∈{-1,0,…,D-1},r t ∈{0,…,R-1}. When 0≤d t ≤D-1, d t represents the residence time of the first data packet of the user team at the beginning of time slot t, and D is the transmission time limit of the data packet; when d t = -1, indicating that the user data queue is empty at the beginning of time slot t. t ≤R-1, r t represents the number of transmissions of the first packet of the tag user team at the beginning of time slot t, and R represents the transmission limit of the packet. t =0, it indicates that the user data queue is empty at the beginning of time slot t.

[0018] Step 1-2: Determine the classification of the individual status of the tagged user, and divide the set S of the individual status of the tagged user into the following four categories:

[0019] (1) Classification S1 = {(-1,0)}: indicates that the tag user has no data packet waiting to be sent at the beginning of the current time slot;

[0020] (2) Classification S2 = {(d,0)∈S:0≤d≤D-2}: indicates that the tag user has a data packet waiting to be sent at the beginning of the current time slot, its stay time is less than D-1 and the number of transmissions is 0;

[0021] ⑶ Classification S3 = {(d,r)∈S:1≤r≤d≤D-2,1≤r≤R-1}: It means that the tag user has a data packet waiting to be sent at the beginning of the current time slot, its stay time is less than D-1 and the number of transmissions is greater than 0, and this data packet has been sent in the previous time slot but the transmission failed;

[0022] (4) Classification S4 = {(D-1, r)∈S:0≤r≤R-1}: It means that the tag user has a data packet waiting to be sent at the beginning of the current time slot, but its stay time is equal to D-1, then this data packet will be discarded at the end of the current time slot.

[0023] Step 1-3: Determine the transition probability β(d,r,d',r') of the labeled user individual from state {(d,r)∈S} to state {(d',r')∈S}, which is specifically expressed as follows:

[0024] (1) When the tag user is in state classification S1, there is no data packet waiting to be sent in the tag user at the beginning of the current time slot, so the stay time of the first data packet in the queue at the beginning of the next time slot can only be -1 or 0, so that the state transition from classification S1 includes the following two situations:

[0025] ① At the beginning of the next time slot, a new data packet arrives at the user (indicating that the stay time of the first data packet in the next time slot is d'=0), we can get:

[0026] β(-1,0,0,0)=λ

[0027] ② No new data packet arrives at the user at the beginning of the next time slot, indicating that the stay time of the first data packet in the next time slot is d' = -1, so

[0028] β(-1,0,-1,0)=1-λ

[0029] (2) When the tag user is in state classification S2 or S3, there are data packets waiting to be sent in the tag user at the beginning of the current time slot, and the stay time is 0≤d≤D-2. Therefore, the first data packet at the end of the current time slot will not be discarded because the stay time exceeds D-1, so the state transition from classification S2 or S3 includes the following four situations:

[0030] ① The user did not send the first packet at the beginning of the current time slot. The stay time of the first packet in the next time slot is d'=d+1, and the number of transmissions is r'=r. Therefore, we can get

[0031] β(d,r,d+1,r)=1-p

[0032] ② If the number of times the user's first packet has been transmitted is 0≤r<R-1 and the first packet is sent in the current time slot but fails to be transmitted, then the first packet stays in the next time slot for d'=d+1 and has been transmitted for r'=r+1, so we can get

[0033] β(d,r,d+1,r+1)=p(1-τ)

[0034] ③ The user's first packet is successfully transmitted or has been transmitted R times and is discarded, and the first packet stays for d'=-1 at the start of the next time slot, indicating that no new packets arrive in d time slots after the first packet arrives at the user at the start of the current time slot. This can be further divided into the following two sub-cases for discussion:

[0035] When 0≤r<R-1, it indicates that the first packet of the team is successfully transmitted in the current time slot and then discarded.

[0036] β(d,r,-1,0)=pτ(1-λ) d+1

[0037] When r = R-1, it indicates that the first packet of the queue is transmitted in the current time slot and then discarded, we can get

[0038] β(d,r,-1,0)=p(1-λ) d+1

[0039] ④ The user's first packet is successfully transmitted or has been transmitted for R times and is discarded, and the first packet stays at the beginning of the next time slot for 0≤d'≤d, indicating that the next new packet arrives d-d'+1 time slots after the first packet at the beginning of the current time slot arrives at the user. This can be further divided into the following two sub-cases for discussion:

[0040] When 0≤r<R-1, it indicates that the first packet of the team is successfully transmitted in the current time slot and then discarded.

[0041] β(d,r,d',0)=pτ(1-λ) d-d' λ

[0042] When r = R-1, it indicates that the first packet of the queue is transmitted in the current time slot and then discarded, we can get

[0043] β(d,r,d',0)=p(1-λ) d-d’ λ

[0044] ⑶ When the tag user is in state category S4, there is a data packet waiting to be sent at the beginning of the current time slot and the stay time is d=D-1. Therefore, the first data packet at the end of the current time slot is discarded because the stay time exceeds D-1, so the state transition from category S4 includes the following two situations:

[0045] ① When d'=-1, it means that no new data packets arrive in D-1 time slots after the first data packet of the team arrives at the user at the beginning of the current time slot, so we can get

[0046] β(D-1,r,-1,0)=(1-λ) D

[0047] ② When 0≤d'≤D-1, it means that the next new data packet arrives D-d' time slots after the first data packet of the team arrives at the user at the beginning of the current time slot, and we can get

[0048] β(D-1,r,d',0)=(1-λ) D-1-d' λ

[0049] Step 1-4: Determine the steady-state probability π of the individual state of the labeled user being in (d, r) d,r , and the steady-state probability of the individual state of the labeled user being in (d, r) is identified as π d,r , where d = -1, 0, 1, ..., D-1 and r = 0, 1, ..., R-1. Steady-state probability distribution {π d,r}The following set of equilibrium equations and normalization conditions are satisfied:

[0050]

[0051]

[0052] Preferably, in step 2, the method for determining the probability τ of successful transmission of any data packet based on the steady-state probability of the individual state is specifically as follows:

[0053] Step 2-1: Determine the probability μ that the tag user sends a data packet in any time slot. Given that the tag user will send a data packet with probability p when the individual state is (d, r), we can get:

[0054]

[0055] Step 2-2: Determine the probability τ that the tagged user successfully transmits a data packet in any time slot. Assume that the success rate τ of any data packet transmission is independent of its stay time and the number of transmissions. At this time, τ is the probability that the remaining N-1 users except the tagged user do not send data packets. Considering that all users are isomorphic, τ can be expressed as follows:

[0056] τ=(1-μ) N-1

[0057] Preferably, the method for determining the network throughput rate under the transmission time limit in step 3 is specifically as follows:

[0058] Step 3-1: Determine the network throughput definition for delay-sensitive applications. If the dwell time at the start of time slot t is d t =d≥0, the first packet of the tag user team is successfully received by the access point at the end of time slot t, then the throughput value of this packet is γ d , where 0<γ≤1 is the throughput value discount factor. In view of this, the network throughput under delay-sensitive applications can be defined as the average value of the throughput value of the successfully transmitted data packets in each time slot.

[0059] Step 3-2: Determine the network throughput. The throughput T of the tag user in the delay-sensitive application is defined as the average value of the throughput of the tag user's successfully transmitted data packets in each time slot. Therefore, when the individual state of the tag user is in (d, r), if the tag user successfully sends, the throughput value is γ d . Further, T can be obtained from the perspective of the tag user based on the steady-state probability of its individual state by the following formula:

[0060]

[0061] Since all users are homogeneous, we can know that the network throughput is NT.

[0062] Example 1

[0063] The present invention adopts MATLAB software to implement the method. The simulation experiment sets the number of users in the network N=50, the probability of data packet arrival λ=0.05, the throughput value discount factor γ=1,0.9, the transmission time limit D=20, and the transmission number limit R=1,2,D.

[0064] like Figure 2 As shown in the figure, when the throughput value discount factor γ = 1, the throughput theoretical results and simulation results under different sending probabilities p are consistent. At the same time, it can be found from the figure that the throughput increases first and then decreases with the increase of the sending probability p. The reason is that the increase in the initial sending probability p gives the data packet more sending opportunities, reducing its stay time until it reaches the transmission time limit D and is discarded, and the throughput increases accordingly. The continued increase in the sending probability p aggravates the data packet transmission conflict, and the throughput decreases accordingly. In addition, under the condition of a fixed sending probability p, the throughput decreases with the increase of the transmission number limit R. The reason is that the increase in the transmission number R causes more data packets to wait too long and reach the transmission time limit D and be discarded, so the throughput decreases.

[0065] like Figure 3As shown in Figure 2, when the throughput value discount factor γ = 0.9, the throughput theoretical results and simulation results under different transmission probabilities p are consistent. Figure 2 , under the condition of fixed sending probability p, the throughput decreases with the increase of transmission number limit R. In addition, when the transmission number R = 1, the throughput obviously increases first, then decreases, and then increases again with the increase of sending probability p. The reason is that: the increase of sending probability p at the beginning makes the data packet get more transmission opportunities, and the throughput increases. Then the continued increase of sending probability p aggravates the transmission conflict of data packet, and the throughput decreases. Finally, p continues to increase and approaches 1. The data packet is discarded after being transmitted once, avoiding the conflict between the data packet with low throughput value and the data packet with high throughput value, and improving the throughput value of the successfully transmitted data packet, resulting in an increase in throughput value.

Claims

1. A simple analysis method for ALOHA network throughput under transmission time limit, characterized in that: The specific steps are: Step 1: Determine the relevant parameters of the Markov process, which include: describing the individual state of the tag user at the beginning of time slot t {(d t ,r t )∈S:t=0,1,2,…}, describing the label user individual in state {(d t =d,r t = r)∈S} to the state {(d t+1 =d',r t+1 =r')∈S}, and the steady-state probability π describing the individual state of the labeled user in (d, r) d,r ; Step 2: Based on the steady-state probability of the individual state, determine the probability τ of successful transmission of any data packet; Step 3: Determine the network throughput rate under the transmission time limit; According to the simple analysis method of the network throughput under the transmission time limit, the method for determining the relevant parameters of the Markov process described in step 1 is specifically as follows: Step 1-1: Determine the probability of data packets arriving at the start of the time slot as λ, the probability of data transmission when the tag user data queue is not empty p, and the individual state of the tag user {(d t ,r t )∈S}, where d t ∈{-1,0,…,D-1},r t ∈{0,…,R-1}; when 0≤d t ≤D-1, d t represents the residence time of the first data packet of the user team at the beginning of time slot t, and D is the transmission time limit of the data packet. The following steps will t Written as d; when d t = -1, indicating that the user data queue is empty at the beginning of time slot t; when 0≤r t ≤R-1, r t represents the number of transmissions of the first packet of the tag user team at the beginning of time slot t, and R represents the transmission limit of the packet. The following steps will t Written as r, when r t =0, indicating that the user data queue is empty at the beginning of time slot t; Step 1-2: Determine the classification of the individual status of the tagged user, and divide the set S of the individual status of the tagged user into the following four categories: (1) Classification S1 = {(-1,0)]: indicates that the tag user has no data packet waiting to be sent at the beginning of the current time slot; (2) Classification S2 = {(d,0)∈S:0≤d≤D-2}: indicates that the tag user has a data packet waiting to be sent at the beginning of the current time slot, its stay time is less than D-1 and the number of transmissions is 0; ⑶ Classification S3 = {(d,r)∈S:1≤r≤d≤D-2,1≤r≤R-1}: It means that the tag user has a data packet waiting to be sent at the beginning of the current time slot, its stay time is less than D-1 and the number of transmissions is greater than 0 (this data packet has been sent in the previous time slot but the transmission failed); (4) Classification S4 = {(D-1, r)∈S: 0≤r≤R-1}: indicates that the tag user has a data packet waiting to be sent at the beginning of the current time slot, but its stay time is equal to D-1, then this data packet will be discarded at the end of the current time slot; Step 1-3: Determine the transition probability β(d,r,d',r') of the labeled user individual from state {(d,r)∈S} to state {(d',r')∈S}, where d' represents the residence time of the first data packet of the user team at time slot t+1, and r' represents the number of transmissions of the first data packet of the user team at time slot t+1; the specific expression is as follows: (1) When the tag user is in state classification S1, there is no data packet waiting to be sent in the tag user at the beginning of the current time slot, so the stay time of the first data packet in the queue at the beginning of the next time slot can only be -1 or 0, so that the state transition from classification S1 includes the following two situations: ① At the beginning of the next time slot, a new data packet arrives at the user, indicating that the stay time of the first data packet in the next time slot is d'=0, so: β(-1,0,0,0)=λ ② No new data packet arrives at the user at the beginning of the next time slot, indicating that the stay time of the first data packet in the next time slot is d' = -1, so β(-1,0,-1,0)=1-λ (2) When the tag user is in state classification S2 or S3, there are data packets waiting to be sent in the tag user at the beginning of the current time slot, and the stay time is 0≤d≤D-2. Therefore, the first data packet at the end of the current time slot will not be discarded because the stay time exceeds D-1, so the state transition from classification S2 or S3 includes the following four situations: ① The user did not send the first packet at the beginning of the current time slot. The stay time of the first packet in the next time slot is d'=d+1, and the number of transmissions is r'=r. Therefore, we can get β(d,r,d+1,r)=1-p ② If the number of times the user's first packet has been transmitted is 0≤r<R-1 and the first packet is sent in the current time slot but fails to be transmitted, then the first packet stays in the next time slot for d'=d+1 and has been transmitted for r'=r+1, so we can get β(d,r,d+1,r+1)=p(1-τ) ③ The user's first packet is successfully transmitted or has been transmitted R times and is discarded, and the first packet stays for d'=-1 at the start of the next time slot, indicating that no new packets arrive in d time slots after the first packet arrives at the user at the start of the current time slot. This can be further divided into the following two sub-cases for discussion: When 0≤r<R-1, it indicates that the first packet of the team is successfully transmitted in the current time slot and then discarded. β(d,r,-1,0)=pτ(1-λ) d+1 When r = R-1, it indicates that the first packet of the queue is transmitted in the current time slot and then discarded, we can get β(d,r,-1,0)=p(1-λ) d+1 ④ The user's first packet is successfully transmitted or has been transmitted for R times and is discarded, and the first packet stays at the beginning of the next time slot for 0≤d'≤d, indicating that the next new packet arrives d-d'+1 time slots after the first packet at the beginning of the current time slot arrives at the user. This can be further divided into the following two sub-cases for discussion: When 0≤r<R-1, it indicates that the first packet of the team is successfully transmitted in the current time slot and then discarded. β(d,r,d',0)=pτ(1-λ) d-d' l When r = R-1, it indicates that the first packet of the queue is transmitted in the current time slot and then discarded, we can get β(d,r,d',0)=p(1-λ) d-d' l ⑶ When the tag user is in state category S4, there is a data packet waiting to be sent at the beginning of the current time slot and the stay time is d=D-1. Therefore, the first data packet at the end of the current time slot is discarded because the stay time exceeds D-1, so the state transition from category S4 includes the following two situations: ① When d'=-1, it means that no new data packets arrive in D-1 time slots after the first data packet of the team arrives at the user at the beginning of the current time slot, so we can get β(D-1,r,-1,0)=(1-λ) D ② When 0≤d'≤D-1, it means that the next new data packet arrives D-d' time slots after the first data packet of the team arrives at the user at the beginning of the current time slot, and we can get β(D-1,r,d',0)=(1-λ) D-1-d' l Step 1-4: Determine the steady-state probability π of the individual state of the labeled user being in (d, r) d,r , and the steady-state probability of the individual state of the labeled user being in (d, r) is identified as π d,r , where d = -1, 0, 1, ..., D-1 and r = 0, 1, ..., R-1; steady-state probability distribution {π d,r }The following set of equilibrium equations and normalization conditions are satisfied: where d'={-1,0,…,D-1}, r'={0,1,…,R-1} In step 2, based on the steady-state probability of the individual state, the method for determining the probability τ of successful transmission of any data packet is specifically as follows: Step 2-1: Determine the probability μ that the tag user sends a data packet in any time slot. Given that the tag user will send a data packet with probability p when the individual state is (d, r), we can get: Step 2-2: Determine the probability τ that the tagged user successfully transmits a data packet in any time slot. Assume that the success rate τ of any data packet transmission is independent of its stay time and the number of transmissions. At this time, τ is the probability that the remaining N-1 users except the tagged user do not send data packets. Considering that all users are isomorphic, τ can be expressed as follows: τ=(1-μ) N-1 The method for determining the ALOHA network throughput under the transmission time limit in step 3 is specifically as follows: Step 3-1: Determine the network throughput definition for delay-sensitive applications. If the dwell time at the start of time slot t is d t =d≥0, the first packet of the tag user team is successfully received by the access point at the end of time slot t, then the throughput value of this packet is γ d , where 0<γ≤1 is the throughput value discount factor; in view of this, the network throughput under delay-sensitive applications can be defined as the average value of the throughput value of the successfully transmitted data packets in each time slot; Step 3-2: Determine the network throughput. The throughput T of the tag user in the delay-sensitive application is defined as the average value of the throughput of the tag user's successfully transmitted data packets in each time slot. Therefore, when the individual state of the tag user is in (d, r), if the tag user successfully sends, the throughput value is γ d ; Further, T can be obtained from the perspective of the tag user based on the steady-state probability of its individual state by the following formula: Since all users are homogeneous, we can know that the network throughput is NT.

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