A closed-form expression for queuing delay in Rayleigh fading channels using stochastic network calculus

Abstract

Stochastic Network Calculus is a modern theory for studying the delay performance of a queuing system. So far, this theory proved very effective in studying QoS in the wireline transmission media. In fact, it provides an upper bound to the probability tail of the queuing delay and requires only the expression of an arrival curve, which models the traffic source, and of a service curve, which models the scheduling discipline. In this paper, we propose a model of the wireless channel based on Stochastic Network Calculus and provide an analytical expression for the first two moments of the service curve of a wireless channel capacity varies over time according to a Rayleigh fading process, such as in the WiMAX and LTE systems. We also provide an approximate closed-form expression for the probability tail of the queuing delay. Finally, we compare our results to simulations in order to assess the validity of our approach.