Queues with random back-offs

Abstract

We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation periods may be initiated after each service completion, and can be randomly terminated with certain probabilities that depend on the queue length. We examine the scaled queue length and delay in a heavy-traffic regime, and demonstrate a sharp trichotomy, depending on how the activation rate and vacation probability behave as function of the queue length. In particular, the effect of the vacation periods may either (i) completely vanish in heavy-traffic conditions, (ii) contribute an additional term to the queue lengths and delays of similar magnitude, or even (iii) give rise to an order-of-magnitude increase. The heavy-traffic asymptotics are obtained by combining stochastic lower and upper bounds with exact results for some specific cases. The heavy-traffic trichotomy provides valuable insight in the impact of the back-off algorithms on the delay performance in wireless random-access networks.

Optimal Activation Rates in Ultra-Dense Wireless Networks with Intermittent Traffic Sources

“…Intuitively, in the variation of the CSMA network an exponential back-off clock is associated with every packet, while in the original CSMA network only with those packets at the head of their queue. This corresponds to a 1-limited vacation queueing model analyzed in [6], where vacations are interrupted at the instants of a time-inhomogeneous Poisson process with a rate that is νf (N ) times the number of packets in the queue.…”

“…Let L A,(N ) be the stationary number of waiting packets and L A,(N ) the stationary total number of packets (including the one in service) in the auxiliary model. In [6,Cor. 3.5] the probability generating function ofL A,(N ) is shown to be…”

Delays and mixing times in random-access networks

“…Unfortunately, however, simulation experiments demonstrate that such activation rules can induce excessive queues and delays, which has sparked a strong interest in developing approaches for improving the delay performance, see for instance Ghaderi & Srikant [12], Lotfinezhad & Marbach [19], Ni et al [21] and Shah & Shin [23]. In particular, it has been shown that more aggressive schemes, where the transmission durations grow faster as function of the queue lengths, can reduce the delays, see for instance Bouman et al [3].…”