Statistical Delay Analysis of TDMA and ALOHA in Wireless Multihop Networks

We employ discrete-time queueing theory to analyze wireless multihop networks and derive an explicit end-to-end (e2e) delay distribution. The analysis takes into account the scheduling scheme, which is a two-level problem including both the (global) channel access scheduler (MAC) and the (local) packet scheduler at each node. Two MAC schemes, TDMA and ALOHA, are considered. Queueing models are established in such a way that the access delay can be incorporated into the service process. Characterizing the wireless channel by a capture model, the individual nodes are modeled as GI/Geom/1 queueing systems. However, in TDMA with constant bit rate (CBR) traffic, the corresponding D/Geom/1 system has a non-integer interarrival time and thus cannot be analyzed as usual. We use an eigenvalue approach to derive closed-form queue length and delay distributions of such D/Geom/1 systems. The error-prone wireless channel transforms the smooth and deterministic CBR traffic to bursty and correlated on-off, causing correlations in the delays at different nodes. We propose an approximative approach that includes the long-distance correlations in the correlation between the neighboring nodes. Based on a set of simulation results, an empirical model for the correlation coefficient is established. Then the network is modeled as a series of independent servers, but the delay variances are scaled by the correlation coefficient. Finally, TDMA and ALOHA are quantitatively compared in terms of the delay and the delay outage probability. The support of the Center for Applied Mathematics (CAM) Fellowship of the University of Notre Dame and the partial support of NSF (grants ECS03-29766 and CAREER CNS04-47869) are gratefully acknowledged.