Towards an end-to-end delay analysis of wireless multihop networks

Abstract

We employ discrete-time queueing theory to analyze the end-to-end (e2e) delay of wireless multihop networks for two MAC schemes, m-phase TDMA and slotted ALOHA. Unlike general two-dimensional networks where there exists sufficient traffic multiplexing that would permit the arrival processes to be approximated as independent, in linear networks with multihop communication, the arrival processes are correlated due to the lack of traffic multiplexing. This paper studies an extreme scenario, a linear network fed with a single flow. A decomposition approach is used to decouple the whole network into isolated nodes. Each node is modeled as a GI/Geo/1 queueing system. We derive the complete per-node delay distribution, Preprint submitted to Elsevier 5 June 2007accounting for both the queueing delay and access delay. Additionally, we characterize the departure processes by a correlated and bursty on-off traffic model. The per-node analysis provides the e2e delay mean while for the e2e delay variance, the strong correlations between the arrival processes need to be considered. Our study shows that the sign of the correlation coefficients depends on both the MAC scheme and the traffic burstiness, both of which determine the relative burst size of the source flow compared to a Bernoulli process, which constitutes an "eigentraffic"process. There is a wide gap in the e2e delay variances for the source flows with different burst sizes even if they have identical average rates. The relative burst size also determines from which direction and at which rate the departure processes converge to the eigentraffic process after traversing multiple relay nodes.

On the recursive nature of end-to-end delay bound for heterogeneous wireless networks

“…Xie and Haenggi [3] investigate the end-to-end delay of a wireless multi-hop line network under both m-phase spatial TDMA and slotted ALOHA. They use a Gl/Geo/1 queuing model.…”

“…, n}, one has to consider the Mellin transform of the joint probabilistic service S L (τ, t) = S 1 ⊗ ... ⊗ S n in the SNR domain. 3 Once that Mellin transform can be determined, the delay bound follows from Eq. (2) and (3) …”

“…Given a path L \ {n} of links with independent and non-identically distributed service processes, with kernel K L\{n} ; then K L can be obtained in terms of K L\{n} as 3 In the following ⊗ denotes the convolution in (min, ×) algebra.…”

Wireless digital control of continuous passive plants over token ring networks

“…TDMA typically achieves a greater capacity than random access protocols such as ALOHA; however, for correlated flows such as those under a CBR source, ALOHA can obtain greater capacity than TDMA [14]. In addition, in [15] the time-varying delay statistics can be computed for TDMA and ALOHA MACs subject to various sources such as a CBR source. These papers do not characterize the delay characteristics for round trip communication patterns, which will be seen in the l 2 -stable passive networks introduced in [1].…”

Cross-Layer Analysis of the End-to-End Delay Distribution in Wireless Sensor Networks

“…Hence, the resulting delay distribution model does not consider the uncertainty due to random backoffs of CSMA/CA protocols. In [23], the end-to-end delay distribution in a linear network is derived for homogeneous networks. However, this model assumes infinite queue lengths at each node, which may not be practical considering the resource constraints of sensor nodes.…”