Second-order performance analysis of discrete-time queues fed by DAR(2) sources with a focus on the marginal effect of the additional traffic parameter


Correspondence to: Daniel Wei-Chung Miao, Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei, Taiwan.



Discrete autoregressive process of order 1 (DAR(1)) has been used as a popular stochastic model for correlated traffic sources because it parsimoniously uses a single parameter to capture the desirable correlation structure. In contrast with DAR(1), discrete autoregressive process of order 2 (DAR(2)) uses one more parameter to provide a much richer pattern in the autocorrelation function and is able to capture slower decay rate and longer memory. To investigate how the additional traffic parameter in DAR(2) influences the queueing performance, this paper provides an analysis of the discrete-time DAR(2)/D/1 queue. The performance measures concerned are the mean and second-order statistics of queue size, which are both important in the queueing systems seen in telecommunication networks. Under a mild condition, these performance indices are derived in closed form that allows for efficient computing. An approximate version of these results is also developed to relax the condition and cover more general sources, and both versions serve as a simple tool set for performance evaluation. The numerical examples use this tool to demonstrate that the DAR(2) source may cause up to 30% poorer performance than DAR(1) when the traffic is heavy, bursty, and highly correlated. This indicates that the effect from slower decay rate in autocorrelation is not negligible and using the extra parameter is necessary particularly when the queue is heavily loaded with correlated traffic. Copyright © 2012 John Wiley & Sons, Ltd.