Regeneration in tandem queues with multiserver stations
- 1 June 1988
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (2) , 391-403
- https://doi.org/10.2307/3214447
Abstract
A tandem queue with a FIFO multiserver system at each stage, i.i.d. service times and a renewal process of external arrivals is shown to be regenerative by modeling it as a Harris-ergodic Markov chain. In addition, some explicit regeneration points are found. This generalizes the results of Nummelin (1981) in which a single server system is at each stage and the result of Charlot et al. (1978) in which the FIFO GI/GI/c queue is modeled as a Harris chain. In preparing for our result, we study the random assignment queue and use it to give a new proof of Harris ergodicity of the FIFO queue.Keywords
This publication has 19 references indexed in Scilit:
- Certain optimality properties of the first-come first-served discipline for G/G/s queuesStochastic Processes and their Applications, 1987
- The Uniqueness of Stationary Distributions for the GI/G/S QueueMathematics of Operations Research, 1986
- Existence of Limiting Distributions in the GI/G/s QueueMathematics of Operations Research, 1982
- Approximation of multichannel queueing systemsSiberian Mathematical Journal, 1981
- Irr ductibilit et r currence au sens de Harris des Temps d'attente? des files GI/G/qProbability Theory and Related Fields, 1978
- A splitting technique for Harris recurrent Markov chainsProbability Theory and Related Fields, 1978
- A new approach to the limit theory of recurrent Markov chainsTransactions of the American Mathematical Society, 1978
- A critical remark on a system approximation in queueing theoryMathematische Operationsforschung und Statistik, 1976
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962
- On the theory of queues with many serversTransactions of the American Mathematical Society, 1955