Batch Input to a Multiserver Queue With Constant Service Times

Batch arrivals constitute an important class of input processes in the theory of queues. The investigation of the problem of batch input to a group of constant-holding-time servers was motivated by the existence of installations with multiple Automatic Calling Units (ACU). Customer-based computer equipment controlling the ACU's is capable of originating simultaneous requests. The dial-tone markers, the first common control equipment in a No. 5 Crossbar central office to serve the requests, can be modeled as a group of constant-holdingtime servers. Another example comes from an information transmission system. Messages containing a (small) random number of characters (a batch of characters) arrive according to a Poisson process and must be transmitted to some destination. Delayed messages are stored in a buffer. Since the transmission time per character is usually fixed, this system provides another example of the model studied. In Section II, the mathematical model used in this study is described and the input process defined; the state equations are written and used to derive the generating function for the equilibrium state probabilities. The probability of no service-delay is found in Section 83