Abstract
We consider a discrete-time queueing system and its application to related models. The model is defined byX n+1=Xn+An-Dn+1 with discrete states, whereX n is the queue-length at the nth time epoch,A n is the number of arrivals at the start of the nth slot andD n+1 is the number of outputs at the end of the nth slot. In this model, the arrival process {A n} is described as a sequence of independently and identically distributed random variables. The departureD n+1 depends only on the system sizeX n+An at the beginning of the time slot.
We study the reversibility for the model. The departure discipline in which the system has quasi-reversibility is determined. Models with special arrival processes were studied by Walrand [8] and Ōsawa [7]. In this paper, we generalize their results. Moreover, we consider discrete-time queueing networks with some reversible nodes. We then obtain the product-form solution for these networks.
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Ōsawa, H. Quasi-reversibility of a discrete-time queue and related models. Queueing Syst 18, 133–148 (1994). https://doi.org/10.1007/BF01158778
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DOI: https://doi.org/10.1007/BF01158778