Impact of time-correlated arrivals on the performance of backpressure-based stochastic network control

In this paper, we consider the backpressure-based control for wireless multihop networks with time-correlated arrivals. The arrival process considered in this work is fairly general in the sense that it may exhibit long-range dependence depending on the asymptotic shape of the autocorrelation function. We first show that the original backpressure policy is still throughput-optimal even with correlated arrivals if the autocorrelation functions are monotonically decreasing. The resulting upper bound on average network delay is expressed in terms of the autocorrelation parameters. After that, we extend our model to include the case where the arrival rate vector is possibly outside the stability region and take the method of joint flow control and backpressure policy that is known to perform arbitrarily close to the utility-optimal throughput point with a corresponding tradeoff in average network delay. The effect of correlated arrivals appears again in the tradeoff in terms of the autocorrelation parameters.