On queues in discrete regenerative environments, with application to the second of two queues in series
- 1 March 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 11 (04) , 851-869
- https://doi.org/10.1017/s0001867800033073
Abstract
Let Un be the time between the nth and (n + 1)th arrivals to a single-server queuing system, and Vn the nth arrival's service time. There are quite a few models in which {Un, Vn , n ≥ 1} is a regenerative sequence. In this paper, some light and heavy traffic limit theorems are proved solely under this assumption; some of the light traffic results, and all the heavy traffic results, are new for two such models treated earlier by the author; and all the results are new for the semi-Markov queuing model. In the last three sections, the results are applied to a single-server queue whose input is the output of a G/G/1 queue functioning in light traffic.Keywords
This publication has 18 references indexed in Scilit:
- A queue with poisson input and semi-Markov service times: busy period analysisJournal of Applied Probability, 1975
- Queues with random service output: the case of Poisson arrivalsJournal of Applied Probability, 1974
- The M/M/1 Queue in a Markovian EnvironmentOperations Research, 1974
- A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov ChainOperations Research, 1973
- Regenerative processes in the theory of queues, with applications to the alternating-priority queueAdvances in Applied Probability, 1972
- A queue subject to extraneous phase changesAdvances in Applied Probability, 1971
- Functional limit theorems for the queue GI/G/1 in light trafficAdvances in Applied Probability, 1971
- On some limit theorems for the GI/G/1 queueJournal of Applied Probability, 1970
- The single server queue with Poisson input and semi-Markov service timesJournal of Applied Probability, 1966
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962