Delay Analysis for Wireless Local Area Networks with Multipacket   Reception under Finite Load
  To date, most analysis of WLANs has been focused on their operation under saturation condition. This work is an attempt to understand the fundamental performance of WLANs under unsaturated condition. In particular, we are interested in the delay performance when collisions of packets are resolved by an exponential backoff mechanism. Using a multiple-vacation queueing model, we derive an explicit expression for packet delay distribution, from which necessary conditions for finite mean delay and delay jitter are established. It is found that under some circumstances, mean delay and delay jitter may approach infinity even when the traffic load is way below the saturation throughput. Saturation throughput is therefore not a sound measure of WLAN capacity when the underlying applications are delay sensitive. To bridge the gap, we define safe-bounded-mean-delay (SBMD) throughput and safe-bounded-delay-jitter (SBDJ) throughput that reflect the actual network capacity users can enjoy when they require bounded mean delay and delay jitter, respectively. The analytical model in this paper is general enough to cover both single-packet reception (SPR) and multi-packet reception (MPR) WLANs, as well as carrier-sensing and non-carrier-sensing networks. We show that the SBMD and SBDJ throughputs scale super-linearly with the MPR capability of a network. Together with our earlier work that proves super-linear throughput scaling under saturation condition, our results here complete the demonstration of MPR as a powerful capacity-enhancement technique for both delay-sensitive and delay-tolerant applications. 
Ying Jun Zhang, Soung Chang Liew, and Darui Chen