In the present paper a two-server queuing process fed by Poisson arrivals and exponential service time distributions has been considered under the bulk-service discipline. Time-dependent probabilities for the queue length have been obtained in terms of Laplace transforms, from which different measures associated with the queuing process could be determined. The mean queue-length and the distributions of the length of busy periods for (i) at least one channel is busy and (ii) both channels being busy, are obtained.

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In this paper the queuing system GI/M/2 has been studied by using the “Phase” method. The Laplace transform of the time-dependent probability generating function and the steady-state solutions have been obtained. When the arrival time distribution is exponential, the results correspond to those obtained by Saaty (Saaty, T. L. 1960. Time-dependent solution of the many-server Poisson queue. Opns Res. 8 755–772.) for the queuing process M/M/2.

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