Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-27T17:23:25.145Z Has data issue: false hasContentIssue false

The M/G/k group-arrival group-departure loss system

Published online by Cambridge University Press:  14 July 2016

D. Fakinos*
Affiliation:
Air Force General Staff, Athens
*
Postal address: 45 Trivonianou St., T.T. 407, Mets, Athens, Greece.

Abstract

This paper considers the equilibrium behaviour of the M/G/k group-arrival group-departure loss system. Such a system has k servers whose customers arrive in groups, the arrival epochs of groups being points of a Poisson process. The duration of a service can be characteristic of the group size; however, customers who belong to the same group have equal service times. The customers of a group start being served immediately upon their arrival, unless their number is greater than the number of idle servers. In this case the whole group leaves and does not return later (i.e. is lost). Among other things, a generalization of the Erlang B-formula is given and it is shown that the arrival and departure processes are statistically indistinguishable.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1982 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Kelly, F. P. (1976) The departure process from a queueing system. Math. Proc. Camb. Phil. Soc. 80, 283285.Google Scholar
Natvig, B. (1975) On the input and output processes for a general birth-and-death queueing model. Adv. Appl. Prob. 7, 576592.CrossRefGoogle Scholar
Shanbhag, D. N. and Tambouratzis, D. G. (1973) Erlang's formula and some results on the departure process from a loss system. J. Appl. Prob. 10, 233240.Google Scholar
Takács, L. (1969) On Erlang's formula. Ann. Math. Statist. 40, 7178.Google Scholar