Discrete-time batch service GI/Geo#47;1#47;N queue with accessible and non-accessible batches

Veena Goswami and K. Sikdar

International Journal of Mathematics in Operational Research, 2010, vol. 2, issue 2, 233-257

Abstract: Discrete-time queues are extensively used in modelling the asynchronous transfer mode environment at cell level. In this paper, we consider a discrete-time single-server finite-buffer queue with general inter-arrival and geometric service times where the services are performed in accessible or non-accessible batches of maximum size b with a minimum threshold value a. We provide a recursive method, using the supplementary variable technique and treating the remaining inter-arrival time as the supplementary variable, to develop the steady-state queue/system length distributions at pre-arrival and arbitrary epochs under the early arrival system. The method is depicted analytically for geometrical and deterministic inter-arrival time distributions, respectively. Various performance measures and outside observer's observation epochs are also discussed. Finally, some computational results have been presented.

Keywords: accessible batches; discrete-time queues; finite buffers; non-accessible batches; supplementary variables; asynchronous transfer mode; single-server queues. (search for similar items in EconPapers)
Date: 2010
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