Introduction to queueing theory (2nd ed)
Introduction to queueing theory (2nd ed)
Calculation of the Steady State Waiting Time Distribution in GI/PH/c and MAP/PH/c Queues
Queueing Systems: Theory and Applications
Exact Buffer Overflow Calculations for Queues via Martingales
Queueing Systems: Theory and Applications
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The time τ(n) of first passage from queue length x to queue length nx in a many-server queue with both the arrival process and service intensities governed by a finite Markov process is considered. The mean and the Laplace transform are computed as solutions of systems of linear equations coming out by optional stopping of a martingale obtained as a stochastic integral of the exponential Wald martingale for Markov additive processes. Compared to existing techniques for QBD's, the approach has the advantage of being far more efficient for large n.