An Algorithmic Solution to the GI/M/C Queue with Group Arrivals.

摘要

The c-server queue is studied with general interarrival times, exponential service times and bounded group arrivals. It is shown that the stationary density of the queue length before arrivals is of a matrix-geometric form, provided that the queue is stable. The essential step in the computation of that stationary density is the evaluation of a positive square matrix R as the unique solution to a nonlinear matrix equation. The order of the matrix R is given by the upper bound K on the sizes of the arrival groups. Various other stationary distributions of waiting times, times in system and the queue length at an arbitrary time can be expressed in terms of the matrix R by means of formulas, which may readily be computationally implemented.