An experimental evaluation of the matrix-geometric method for the GI/PH/1 queue

A GI/PH/1 queue is a single server queueing model with general interarrival time distribution and phase type service time distribution. It provides a unified framework to include a large number of special cases of single server models that are commonly used. A class of algorithms for computing the performance measures for such queues goes under the name ‘matrix-geometric solution’ and has been implemented as a FORTRAN package by V. Ramaswami. Reported here are the results of a numerical experiment with that package. Using a carefully selected set of examples, the authors address many issues related to the computational complexity and numerical accuracy of the matrix-geometric method. Among other things, some insights into modeling service times using two moment approximations are also obtained. The examples reflect a wide variety of characteristics in the interarrival and service time distributions and may therefore be of independent interest as possible test problems to evaluate the performance of algorithms for single server queues.