Abstract
We present an analysis of the number of losses, caused by the buffer overflows, in a finite‐buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.
Highlights
In a finite-buffer queueing system i.e., a system with the finite waiting room, we should expect losses
We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times
The purpose of this paper is to find formulas describing the loss process in a finitebuffer queueing model that enables fitting all of characteristics 1 – 6
Summary
In a finite-buffer queueing system i.e., a system with the finite waiting room , we should expect losses. The influence of the system load, buffer size, and service time variance on the number of losses is studied in several classic queueing theory textbooks. Other known methods for finding loss characteristics in BMAP queues e.g., 9, 12 are devoted to the stationary case only It is an open question whether they can be extended to cover the transient case as well. It starts with the definition of the main characteristic of interest, which is the average number of losses in interval 0, t. The dependence of the loss ratio on the autocorrelation structure, on the batch size distribution, and on the buffer size in the steadystate, as well as the transient intensity of the loss process, are investigated.
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