Analysis and Heuristics for the Characterization of Selective Repeat ARQ Delay Statistics over Wireless Channels

In this paper, we consider a point-to-point wireless transmission where link layer ARQ is used to counteract channel impairments. In particular, we refer, as an example, to a 3G cellular system, where a dedicated channel is used between a mobile terminal and its serving base station. Our aim is to find accurate and fast heuristics for the characterization of link layer and higher level (e.g., application level) packet delay. Existing methods to obtain such statistics are often based on recursive computations or large-sized matrix manipulations. For these reasons, they are too complex to be successfully applied in a mobile terminal due to memory, delay, and energy constraints. In this paper, we first present an analytical framework to compute link-layer packet delivery delay statistics as a function of the packet error rate; then we extend the model in order to find the statistics related to higher level packets (i.e., to aggregates of link layer packets). Both in-order and out-of-order delivery of link-layer packets to higher levels are considered. The goodness of the channel model considered in the analysis is proved by means of accurate channel simulation results. The obtained statistics are then characterized by highlighting their properties as a function of the round-trip time and the error rate at the link layer. Finally, fast and accurate heuristics are derived directly from the analysis. These heuristics are very simple (piecewise linear functions), so they can be effectively used in a mobile terminal to obtain accurate delay statistics estimates with little computational effort.