Analysis of Queuing Delay and Medium Access Distribution Over Wireless Multihop PANs

This paper proposes a novel analytical approach to the analysis of the queuing delay and medium access distribution of carrier sense multiple access with collision avoidance (CSMA-CA) protocols over multihop personal area networks (MPANs). The proposed approach considers a general case without restrictions on the topology, traffic generation patterns, or multipath routing policy, and it accounts for heterogeneous traffic patterns, all possible packet loss scenarios, and the effect of the length of the backoff on the channel assessment. This paper uses statistical theorems to derive the moment generating function (mgf) of the time required to service a packet and then uses this function as a service distribution in a GI/G/1 queuing model to derive the interdeparture and total queuing delays. From these functions, the end-to-end delay, jitter, throughput, and failure transmission probability over a path are derived. In addition to determining these metrics, this paper exploits the statistical features of the mgf to determine the rare-event probability of the service function. The proposed approach is exemplified using the state-of-the-art IEEE 802.15.4 CSMA-CA protocol, and its accuracy is demonstrated through comparison with simulations.