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On the Steady-State Solution of the M/G/2 Queue

Per Hokstad
Advances in Applied Probability
Vol. 11, No. 1 (Mar., 1979), pp. 240-255
DOI: 10.2307/1426776
Stable URL: http://www.jstor.org/stable/1426776
Page Count: 16
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On the Steady-State Solution of the M/G/2 Queue
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Abstract

The asymptotic behaviour of the M/G/2 queue is studied. The difference-differential equations for the joint distribution of the number of customers present and of the remaining holding times for services in progress were obtained in Hokstad (1978a) (for M/G/m). In the present paper it is found that the general solution of these equations involves an arbitrary function. In order to decide which of the possible solutions is the answer to the queueing problem one has to consider the singularities of the Laplace transforms involved. When the service time has a rational Laplace transform, a method of obtaining the queue length distribution is outlined. For a couple of examples the explicit form of the generating function of the queue length is obtained.

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