On a single-server queue with multiple transaction

Abstract
An algorithm is presented to determine time-dependent as well as several stationary queue length characteristics for single-server queues, in which the service transaction can consist of two components: the normal service time and the post-service time, In particular, a component wise non-preemptive priority discipline is considered, where the customers waiting for receiving their normal service time are preferred in face of the customers waiting for receiving their post-service time. The stationary characteristics of the total number of customers are obtained by solving a system of relationships between them where only one fixed stationary characteristic must be calculated explicitly.

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