A Correlated Queue
- 1 April 1969
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 6 (1) , 122-136
- https://doi.org/10.2307/3212280
Abstract
A “correlated queue” is defined to be a queueing model in which the arrival pattern influences the service pattern or vice versa. A particular model of this nature is considered in this paper. It is such that the service time of a customer is directly proportional to the interval between his own arrival and that of his predecessor. The initial busy period, state and output processes are analyzed in detail. For completeness, a sketch is also given of the analysis of the waiting time process which forms the subject of another paper. The results are used in the analysis of the state and output processes.Keywords
This publication has 5 references indexed in Scilit:
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- Queues with State-Dependent Stochastic Service RatesOperations Research, 1967
- Single Server Queues with Dependent Service and Inter-Arrival TimesJournal of the Society for Industrial and Applied Mathematics, 1963
- Some Results for the Queue with Poisson ArrivalsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1960
- The theory of queues with a single serverMathematical Proceedings of the Cambridge Philosophical Society, 1952