Discrete-time GeoX/G(a,b)/1/N queues with single and multiple vacations

Discrete-time GeoX/G(a,b)/1/N queues with single and multiple vacations

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Article ID: iaor20071508
Country: Netherlands
Volume: 45
Issue: 1/2
Start Page Number: 93
End Page Number: 108
Publication Date: Jan 2007
Journal: Mathematical and Computer Modelling
Authors: , ,
Keywords: GI/G/1 queues, vacation models, batch processes
Abstract:

In this paper, we consider a discrete-time single-server finite-buffer batch arrival queue in which customers are served in batches according to a general bulk-service rule, that is, at least ‘a’ customers are needed to start a service with a maximum serving capacity of ‘b’ customers. The server takes a (single and multiple) vacation as soon as the queue length falls below ‘a’ at the completion of service. The interarrival times of batches are assumed to be independent and geometrically distributed. The service times of the batches and vacation times of the server are generally distributed and their durations are integral multiples of slot duration. We obtain queue length distributions at service completion, vacation termination, arbitrary, and prearrival epochs. Finally, we discuss various performance measures and numerical results.

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