Abstract
A generalization of theD [X]/D/1 queue is investigated, where independent and identically distributed (i.i.d) batches of customers arrive at a single-server queue periodically. The service requirement of a customer is a fixed constant equal for all the customers. In the time between two successive arrivals, the server can accommodate exactlyK≥1 customers. The queue size and the waiting time distributions for the infinite buffer queue are derived. Important numerical aspects are addressed and simple approximations for light and heavy traffic for various values ofK and Poisson distributed batches are proposed. Finally, the analysis for the finite queue is highlighted and its blocking probability derived.
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Bisdikian, C., Lew, J.S. & Tantawi, A.N. The generalizedD [X]/D/1 queue: A flexible computer communications model. Telecommunication Systems 6, 127–146 (1996). https://doi.org/10.1007/BF02114290
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DOI: https://doi.org/10.1007/BF02114290