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We introduce a new approximation procedure to improve the accuracy of matrix analytic methods when using truncated queueing models to analyse infinite buffer systems. This is accomplished through emulating the presence of unobserved waiting customers beyond the finite buffer that are able to immediately enter the system following an observed customer's departure. We show that this procedure results in exact steady-state probabilities at queue lengths below the buffer for truncated versions of the classic M/M/1, M / M / 1 + M , M / M / ∞ , and M/PH/1 queues. We also present two variants of the basic procedure for use within a M / P H / 1 + M queue and a N-queue polling system with exhaustive service, phase-type service and switch-in times, and exponential impatience timers. The accuracy of these two variants in the context of the polling model are compared through several numerical examples. [ABSTRACT FROM AUTHOR]

This paper analyzes a 2-class, single-server polling model operating under a ki-limited service discipline with class-dependent switchover times. Arrivals to each class are assumed to follow a Poisson process with phase-type distributed service times. Within each queue, customers are impatient and renege (i.e., abandon the queue) if the time before entry into service exceeds an exponentially distributed patience time. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the per-class waiting time distributions are computed via the use of matrix analytic techniques. The impacts of reneging and choice of service time distribution are investigated through a series of numerical experiments, with a particular focus on the determination of (k1,k2) which minimizes a cost function involving the expected time a customer spends waiting in the queue and an additional penalty cost should reneging take place. [ABSTRACT FROM AUTHOR]