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The M/G/1 queue with several types of customers and change-over times

We study an M/G/1 queue with m types of customer, operating under the first-come, first-served discipline. It is assumed that the server expends a random length of time in change-over from one type of customer to another. Various priority rules have been proposed to reduce the amount of time spent in change-over. These queue disciplines generally require a separate monitoring, whose cost is frequently non-negligible. As a basis for evaluating the merits of alternate queue disciplines, it is important to have information on the M/G/1 queue with m customer types when service is first-come, first-served. By appealing to general methods for the M/SM/1 queue, a large number of detailed and explicit results are obtained. In addition, algorithmic solutions are given for the steady-state distributions which are analytically intractable.