Batch Input to a Multiserver Queue with Constant Service Times

Delay probability formulas for batch input to a finite number of constant-holding-time servers are derived under the assumption of statistical equilibrium. The service-delay distribution (delay until a first request from the batch enters service) is given in terms of the roots of a transcendental equation, while the probability of no service-delay and the average delay are expressed directly in terms of the number of servers, the holding time, and the parameters of the input process. A numerical example with a fixed batch size is discussed.