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An M\(^{[x]}\)/G/1 system with startup server and \(J\) additional options for service. (English) Zbl 1162.90399
Summary: We consider an M\(^{[x]}\)/G/1 queueing system with a startup time, where all arriving customers demand first the essential service and some of them may further demand one of other optional services: Type 1, Type 2,\( \cdots \) , and Type \(J\) service. The service times of the essential service and of the Type \(i (i=1,2,\cdots ,J)\) service are assumed to be random variables with arbitrary distributions. The server is turned off each time when the system is empty. As soon as a customer or a batch of customers arrives, the server immediately performs a startup which is needed before starting each busy period. We derive the steady-state results, including system size distribution at a random epoch and at a departure epoch, the distributions of idle and busy periods, and waiting time distribution in the queue. Some special cases are also presented.

MSC:
90B22 Queues and service in operations research
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