Abstract
This paper deals with an M x / G/1 queueing system with two phases of heterogeneous service under N-policy, where the server remains idle till the queue size becomes N(⩾1). As soon as the queue size becomes N, the server immediately starts first `essential service' for all the units. After completion of the essential service of a unit, it may leave the system with probability (1− θ) or may immediately go for a second phase of service in an additional service channel with probability θ (0⩽ θ⩽1). For this model, we derive the queue size distribution at a random epoch as well as at a departure epoch. Further, we derive some important performance measures of this model. This is a generalization of recent papers considered by Medhi [Queueing Systems 42 (2002) 239] and Lee et al. [Queueing Systems 15 (1994) 387].
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