We consider a discrete-time queueing system with the discrete autoregressive process of order 1 (DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distribution. As shown in the analysis, our approach provides a natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distributions. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the virtual waiting time in the heavy traffic case.

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We consider a discrete-time queueing system with the discrete autoregressive process of order 1 (DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distribution. As shown in the analysis, our approach provides a natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distributions. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the virtual waiting time in the heavy traffic case.

No abstract

We analyze a multiserver queue with a discrete autoregressive process of order 1 (DAR (1)) as an input. DAR(1) is a good mathematical model for VBR-coded teleconference traffic.Based on matrix analytic methods and the theory of Markov regenerative processes, we obtain the stationary distributions of the system size and the waiting time of an arbitrary packet. Numerical examples illustrate the quantitative effect of the stationary distribution and the autocorrelation function of input traffics on system performance.keywords DAR(1), multiserver queue, Teleconference traffic, multiserver ATM multiplexer, matrix analytic methods, Markov regenerative theory, performance analysis