Double basic service set system throughput evaluation method based on Markov chain model

Abstract

The invention discloses a double basic service set system throughput evaluation method based on a Markov chain model, and the method comprises the steps: representing a state in a double basic service set system as a state in a Markov chain, defining the transition probability between the states, and obtaining a state transition probability matrix of the Markov chain; obtaining the probability distribution of each state when the system is in a steady state by solving the feature vector of the state transition probability matrix; and calculating the total throughput of the system according to the average throughput and the steady-state probability of the system under different competition window combinations. According to the method, the steady-state probability of the system under different competition window combinations is calculated by establishing the Markov chain model, so that the average throughput and the total throughput of the system can be estimated, and theoretical support is provided for throughput evaluation and system performance optimization of the WLAN system.

Description

Technical Field

[0001] This invention relates to a communication method, specifically to a method for evaluating the throughput of a wireless system. Background Technology

[0002] With the rapid development of wireless communication technology, Wireless Local Area Networks (WLANs) have become an indispensable part of people's daily lives and work. In WLAN systems, channel access control is a key factor affecting network performance. Traditional WLAN channel access methods are mainly based on the CSMA / CA (Carrier Sense Multiple Access with Collision Avoidance) protocol, using a contention mechanism to achieve communication between multiple nodes. However, as the network scales up and the number of devices increases, channel contention becomes increasingly fierce, leading to decreased system throughput and increased latency.

[0003] Currently, various improvement schemes have been proposed, such as adjusting the contention window size and optimizing the backoff algorithm, to improve the throughput of WLAN systems. However, most of these methods rely on empirical parameter tuning and lack systematic theoretical analysis and optimization guidance. Summary of the Invention

[0004] Purpose of the invention: As throughput S is one of the performance indicators for WLAN systems, this invention proposes a throughput evaluation method for dual basic service set (BSS) systems based on the Markov chain model, in response to the aforementioned existing technologies.

[0005] Technical solution: A throughput evaluation method for dual basic service set systems based on Markov chain models, including:

[0006] The states in the dual basic service set system are represented as states in a Markov chain. The transition probabilities between each state are defined to obtain the state transition probability matrix of the Markov chain.

[0007] By solving the eigenvectors of the state transition probability matrix, the probability distribution of each state of the system in steady state can be obtained;

[0008] The total throughput of the system is calculated based on the average throughput and steady-state probability under different combinations of competition windows.

[0009] Furthermore, in the dual basic service set system, each state represents the backoff count of two APs within a contention window. The state is represented by a pair of retransmission counts (r1, r2), where r1 and r2 are the retransmission counts of the two APs, respectively. The transition probability represents the probability of transitioning from one state to another, and the state transition rule is as follows:

[0010]

[0011] Where BO1 and BO2 represent the backoff numbers randomly drawn by the two APs from [0,CW1-1] and [0,CW2-1] respectively, and CW1 and CW2 represent the sizes of the two competition windows respectively; comparing BO1 and BO2, the transition probability corresponding to the state transition rule is expressed as:

[0012]

[0013] Where max is the function for finding the maximum value.

[0014] Furthermore, the average throughput S is a throughput metric for measuring the contention window, expressed as:

[0015]

[0016] Where E[P] is the effective payload transmission duration, T s,total T c,total T E,total These represent the total time slots for successful signal transmission without collision under all random backoff scenarios, the total time slots for successful signal transmission with collision, and the total idle time during random backoff.

[0017] Furthermore, the total throughput of the system is the steady-state probability of each combination of competing windows. With average throughput The sum of products is expressed as:

[0018]

[0019] Among them, S sys This represents the total throughput of the system.

[0020] Furthermore, the average throughput S specifically refers to:

[0021]

[0022] Where Payload is the effective payload, MIN = min{CW1, VW2}, W is the physical layer rate, and T S and T C T represents the time slot length for successful transmission and the time slot length for transmission collision, respectively. eis the idle slot length, BO n represents the backoff number randomly selected by the backoff timer from [0, CW n - 1], where n takes 1, 2.

[0023] Beneficial effects: The present invention proposes a method for analyzing the throughput of a dual - BSS system based on a Markov chain model. Through accurate modeling and analysis, the average throughput is obtained to measure the throughput index of the contention window, providing theoretical support for the throughput evaluation and system performance optimization of the WLAN system. Specific implementation manner

[0024] The following further explains the present invention.

[0025] A method for evaluating the throughput of a dual - basic service set system based on a Markov chain model represents the states in the dual - BSS system as states in a Markov chain and defines the transition probabilities between the states.

[0026] In the dual - basic service set system, each state represents the backoff counts of two APs (Access Points) in the contention window. The state of the system is represented by a pair of re - transmission times (r1, r2), where r1 and r2 are the re - transmission times of the two APs respectively. The transition probability reflects the dynamic change of the system between different states, that is, the probability of transferring from one state to another state.

[0027] The system state is converted from the backoff counts of the dual - BSS into a binary tuple, that is, the system state is represented by a pair of re - transmission times r1, r2). Analyze the state transition probability of this binary tuple. On the premise that the two BSSs listen to each other and cannot be concurrent, the two APs respectively randomly select backoff numbers BO1 and BO2 from [0, CW1 - 1] and [0, CW2 - 1]. As the re - transmission times change, the value ranges of the contention windows CW1 and CW2 will also change accordingly. The value of the contention window CW n The relationship with the re - transmission times r generally satisfies:

[0028]

[0029] Define the state transition rules as follows:

[0030] When BO1 ≠ BO2:

[0031] If BO1 < BO2, it means that AP1 successfully transmits data and AP2 enters the backoff state. At this time, the state transition is (r1, r2) → (r1, 0);

[0032] If BO1 > BO2, it means that AP2 successfully transmits data and AP1 enters the backoff state. At this time, the state transition is (r1, r2) → (0, r2);

[0033] When BO1 = BO2, a collision occurs, and both APs need to retransmit. At this time, the state transition is (r1,r2) → (r1+1,r2+1).

[0034] The above state transition rules can be expressed as:

[0035]

[0036] Therefore, the general formula for the probability of transition between any two states can be obtained as follows:

[0037]

[0038] In the above general formula, it is obvious that when BO1 = BO2, the critical values ​​are the same for both cases.

[0039] Since (r1, r2) is an integer pair, the number of states is finite, and we can use Markov chains to analyze the state transitions. Therefore, based on the probabilities of different states, we can obtain the state transition probability matrix of the Markov chain. This matrix describes the behavior of the system, with each element representing the probability of transitioning from one state to another.

[0040] Next, using the properties of Markov chains, the eigenvectors of the state transition probability matrix are solved to obtain the probability distribution of each state in the steady state of the system. Specifically, an initial state distribution is set, and the steady-state probabilities of each state after long-term operation are obtained by iterative calculation or direct solution of the eigenvectors. After determining the steady-state probability distribution, the probability value of each state represents the relative frequency of each state occurring in the steady state of the system.

[0041] Throughput S, as one of the performance indicators for WLAN systems, is directly affected by the size of the payload in the data frame, the random backoff number BO, and the success or failure of signal transmission. A detailed analysis follows:

[0042] 1. Payload. A data frame consists of a PHY header, a MAC header, and a payload. The PHY header has a fixed duration, and the transmission duration (in μs) of the MAC header and payload can be derived from the ratio of their byte length (in bits) to the physical layer rate W (in Mbps).

[0043] 2. Random rollback number BO n During the random backoff process, the backoff timer will start from [0, CW]. n Random number BO is drawn from [-1] n Because of BO n The values ​​of BO are not all the same, and the random backoff number BO is used before entering the channel. n Total time T to roll back to 0E The value of will also change accordingly, that is:

[0044] T E =T e ×(BO n +1)

[0045] Among them, T e This is the length of the idle time slot. For example, when the backoff number BO... n When the value is 5, it needs to pass through 6 idle time slots before entering the channel, i.e., T E =54μs, while the backoff number BO n When the time is 7, it needs to pass through 8 idle time slots before entering the channel, i.e., T E =72μs.

[0046] 3. Signal transmission. For a successful transmission, the time slot length T... S The time slot length T of the transmission collision C They are respectively:

[0047] T s =T E +H+E[P]+SIFS+ACK+DIFS

[0048] T c =T E +H+E * [P]+ACKTimesout+DIFS

[0049] Where H is the data frame header, including the MAC layer header and the PHY layer header, E[P] and E * [P] represents the payload transmission duration, SIFS represents the short frame interval duration, ACK represents the acknowledgment frame duration, DIFS represents the distributed frame interval duration, and ACKTimesout represents the acknowledgment timeout. In this embodiment, if the payload length of both APs sending packets is 1500 bytes (1 byte = 8 bits), the MAC header is 30 bytes, the PHY header duration is 13.6 μs, and the MAC header and payload are sent at a physical layer rate of 455.8 Mbps, since the data frame length of all nodes is the same, E[P] and E * Since [P] are equal, the time slot length for a successful transmission and the time slot length for a transmission collision are respectively:

[0050]

[0051] Based on the above conditions, this invention introduces average throughput S to measure the throughput metric of a contention window. Average throughput describes the average throughput generated during signal transmission by contention windows with different initial values. Its value is the product of the total duration of all successfully transmitted signals under random backoff conditions for that type of contention window and the physical layer rate, divided by the total duration under all random backoff conditions. Since the SIR is low during concurrency, if two APs simultaneously backoff to 0 and transmit data, it will cause data transmission failures for both APs. Therefore, the total duration of all successfully transmitted signals only includes the time slots of successful transmissions without collisions, i.e.:

[0052]

[0053] Among them, T s,total T c,total T E,total These represent the total time slots for successful signal transmission without collisions, the total time slots for successful signal transmission with collisions, and the total idle time slots during random backoffs, respectively. Substituting these values, we can obtain the formula for average throughput:

[0054]

[0055] Where MIN = min{CW1, CW2}. This formula can be simplified to:

[0056]

[0057] The system throughput can be calculated from the steady-state probability and the average throughput. The system throughput is the steady-state probability of each combination of competing windows. With average throughput The sum of the products reflects a relatively stable throughput value that the system eventually reaches in a steady state. System throughput S sys The expression is:

[0058]

[0059] Through the above process, this invention can effectively establish and solve the throughput of a dual basic service set (BSS) system based on a Markov chain model, provide an accurate steady-state probability distribution, and provide theoretical support for WLAN system throughput evaluation and system performance optimization.

[0060] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A throughput evaluation method for a dual-basic service set system based on a Markov chain model, characterized in that, include: The states in the dual basic service set system are represented as states in a Markov chain. The transition probabilities between each state are defined to obtain the state transition probability matrix of the Markov chain. By solving the eigenvectors of the state transition probability matrix, the probability distribution of each state of the system in steady state can be obtained; The total throughput of the system is calculated based on the average throughput and steady-state probability under different combinations of competition windows.

2. The throughput evaluation method for a dual-basic service set system based on a Markov chain model according to claim 1, characterized in that, In the dual basic service set system, each state represents the backoff count of two APs within a contention window. The state is represented by a pair of retransmission counts (r1, r2), where r1 and r2 are the retransmission counts of the two APs, respectively. The transition probability represents the probability of transitioning from one state to another, and the state transition rule is as follows: Where BO1 and BO2 represent the backoff numbers randomly drawn by the two APs from [0,CW1-1] and [0,CW2-1] respectively, and CW1 and CW2 represent the sizes of the two competition windows respectively; comparing BO1 and BO2, the transition probability corresponding to the state transition rule is expressed as: Where max is the function for finding the maximum value.

3. The throughput evaluation method for a dual basic service set system based on a Markov chain model according to claim 1 or 2, characterized in that, The average throughput S is a metric for measuring the throughput of the contention window, expressed as: Where E[P] is the effective payload transmission duration, T s,total T c,total T E,total These represent the total time slots for successful signal transmission without collision under all random backoff scenarios, the total time slots for successful signal transmission with collision, and the total idle time during random backoff.

4. The throughput evaluation method for a dual basic service set system based on a Markov chain model according to claim 3, characterized in that, The total throughput of the system is the steady-state probability of each combination of competing windows. With average throughput The sum of products is expressed as: Among them, S sys This represents the total throughput of the system.

5. The throughput evaluation method for a dual basic service set system based on a Markov chain model according to claim 3, characterized in that, The average throughput S is specifically: Where Payload is the effective payload, MIN = min{CW1,CW2}, W is the physical layer rate, and T S and T C T represents the time slot length for successful transmission and the time slot length for transmission collision, respectively. e BO is the length of the idle time slot. n This indicates that the backoff timer starts from [0, CW]. n The backoff number is randomly selected from [-1], where n takes values ​​of 1 or 2.

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