Statistical Model of Accurately Estimating Service Delay Behavior in Saturated IEEE 802.11 Networks Based on 2-D Markov Chain

Abstract

To accurately estimate the service delay behavior of IEEE 802.11 networks, this paper comprehensively considers four main factors that affect the performance of IEEE 802.11 networks and establishes a service delay model with statistical characteristics. We analyzed the operation mechanism of 802.11 DCF, using the backoff stage and the backoff counter to portray the dynamic change characteristics of the system regarding the data frame transmission states. Afterward, we calculated the one-step transition probability of these states, establishing a 2-D Markov model, including the ICS procedure and the backoff procedure. Based on this model, we constructed steady-state equations to derive a relationship between the transmission probability and collision probability for each node transmission queue. By analyzing the ICS delay and the backoff delay, we obtained the probability generating function (PGF) of the average idle time. The analytical expressions of other service delays, such as the successful transmission time and collided transmission time, were derived to obtain the PGF of the total service delay. In the numerical simulation, we compared the first two statistical moments of the PGF with the Nav model, and it was found that our delay evaluation results were significantly better than the traditional evaluation results. The average service delay of the Nav model in all the scenarios was larger than that of the proposed model due to the lack of the ICS procedure in the Nav model. Since a DIFS duration is generally much shorter than a random backoff duration, our model saves the bandwidth and improves transmission efficiency.

Keywords

• 802.11 DCF
• initial carrier-sensing (ICS)
• 2-D Markov chain
• average idle time
• service delay
• PGF