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A Queueing system with general moving average input and negative exponential service time

Published online by Cambridge University Press:  09 April 2009

C. Pearce
C. Pearce
Affiliation:
The Australian National University Canberra
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If we think of the input to a queueing system as arising from some process and depending on the history of that process, we might well expect the duration of inter-arrival intervals to depend mostly on the recent history and to a much smaller extent on that which is more remote.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 6 , Issue 2 , May 1966 , pp. 223 - 236
Copyright
Copyright © Australian Mathematical Society 1966

References

[1]Finch, P. D., The single server queueing system with non-recurrent input process and Erlang service time, J. Aust. Math. Soc. 3 (1963), 220–36.CrossRefGoogle Scholar
[2]Finch, P. D. and Pearce, C., ‘A second look at a queueing system with moving average input process’, J. Aust. Math. Soc. 5 (1965), 100–6.CrossRefGoogle Scholar
[3]Loynes, R. M., ‘Stationary waiting time distributions for single server queues, Ann. of Math. Statist. 33 (1962), 1323–39.CrossRefGoogle Scholar
[4]Loynes, R. M., ‘The stability of a queue with non-independent inter-arrival and service times’, Proc. Camb. Phil. Soc. 58 (1962), 497–520.CrossRefGoogle Scholar
[5]Kendall, D. G. ‘Stochastic processes occurring in the theory of queues and their analysis by means of the imbedded Markov chain’, Ann. of Math. Statist., 24 (1954), 338–54.CrossRefGoogle Scholar
[6]Smith, W. L., ‘On the distribution of queueing times, Proc. Camb. Phil. Soc. 49 (1953), 449–61.CrossRefGoogle Scholar