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Erlang's formula and some results on the departure process for a loss system

Published online by Cambridge University Press:  14 July 2016

D. N. Shanbhag  and
D. G. Tambouratzis
D. N. Shanbhag
Affiliation:
University of Sheffield
D. G. Tambouratzis
Affiliation:
Agricultural College, Athens
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Abstract

The present paper investigates the limiting distribution of the number of busy channels (queue size) and the remaining lengths of holding times at an epoch of departure for a loss system with general holding times and exponentially distributed interarrival times. Further, it is established that for this loss system in the limit an interdeparture interval length is independent of the queue size at the end of the interval and is distributed according to an exponential distribution with mean λ–1. It is also seen that in the limit interdeparture times are mutually independent.

Keywords

LOSS SYSTEM WITH POISSON ARRIVALSERLANG'S FORMULALIMITING DEPARTUREPROCESSREMAINING HOLDING TIMESBUSY CHANNELS
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 233 - 240
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Boes, D. C. (1969) Note on the output of a queueing system. J. Appl. Prob. 6, 459–461.Google Scholar
[2] Finch, P. D. (1959) The output process of the queueing system M/G/l. J. R . Statist. Soc. B21, 375–380.Google Scholar
[3] Mirasol, N. M. (1963) The output of an M/G/8 queueing system. Operat. Res. 11, 282–284.Google Scholar
[4] Shanbhag, D. N. (1966) On infinite server queues with batch arrivals. J. Appl. Prob. 3, 274–279.Google Scholar
[5] Takács, L. (1969) On Erlang's formula. Ann. Math. Statist. 40, 71–78.CrossRefGoogle Scholar