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A queueing system with non-recurrent input and batch servicing

Published online by Cambridge University Press:  14 July 2016

C. Pearce
C. Pearce*
Affiliation:
Australian National University
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Extract

We consider a queueing system in which arrivals occur at times , and after every kth arrival a servicing of k arrivals is begun. We assume that the number of servers is infinite. Initially, at t0= 0, the system is empty and the arrival process {tn} is about to start. The batch service times are independently and identically distributed with distribution function No assumption is made about the process {tn}.

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 2 , December 1965 , pp. 442 - 448
Copyright
Copyright © Applied Probability Trust 

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References

[1] Finch, P. D. (1961) Some probability problems in inventory control. Publ. Math. Debrecen 8, 3–4, 241-261.Google Scholar
[2] Finch, P. D. (1963) A coincidence problem in telephone traffic with non-recurrent arrival process. J. Aust. Math. Soc. 3, 237–240.Google Scholar