Goswami, Veena; Sikdar, K. Discrete-time batch service \(GI/Geo/1/N\) queue with accessible and non-accessible batches. (English) Zbl 1183.90114 Int. J. Math. Oper. Res. 2, No. 2, 233-257 (2010). Summary: 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. Cited in 1 Document MSC: 90B22 Queues and service in operations research Keywords:accessible batches; discrete-time queues; finite buffers; non-accessible batches; supplementary variables; asynchronous transfer mode; single-server queues PDFBibTeX XMLCite \textit{V. Goswami} and \textit{K. Sikdar}, Int. J. Math. Oper. Res. 2, No. 2, 233--257 (2010; Zbl 1183.90114) Full Text: DOI