End-to-end delay analysis of the IEEE 802.11e with MMPP input-traffic

We investigate the performance of the IEEE 802.11e in respect of end-to-end delay, which is estimated by the sum of queuing delay and MAC delay. The MAC delay analysis is performed based on elementary probability theory (conditional probabilities) while avoiding the complex Markov Chain method. A comprehensive study of the MAC delay is presented by providing higher moments of the MAC delay distribution. To this end, we use the Z-transform of the backoff duration. The first moment corresponds to the mean MAC delay, while the second moment corresponds to the standard deviation of the MAC delay; the latter depicts the jitter. We also estimate the probability mass function (pmf) of the MAC delay through the lattice Poisson algorithm. As far as the queuing delay is concerned, we provide the mean queuing delay by considering a queuing system with one queue per Access Category (AC) per mobile station, with a single server (the wireless medium), common to all mobile stations, and a Markov modulated Poisson process as input, that expresses the bursty nature of Internet traffic. The presented analytical model provides results of the mean end-to-end delay for both saturated and non-saturated channel conditions.