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Ferreira, M. A. M. (2002). Mean sojourn time in state k, k=0,1,..., for the M|G|∞ queueing system (Exact and approximated expressions). In Magáthová, V. (Ed.), Proceedings of the International Conference Quantitative Methods in Economics (Multiple Criteria Decision Making XI). (pp. 57-61). Nitra, Slovakia: Slovak Society for Operations Research.

M. A. Ferreira,  "Mean sojourn time in state k, k=0,1,..., for the M|G|∞ queueing system (Exact and approximated expressions)", in Proc. of the Int. Conf. Quantitative Methods in Economics (Multiple Criteria Decision Making XI), Magáthová, V., Ed., Nitra, Slovakia, Slovak Society for Operations Research, 2002, pp. 57-61

@inproceedings{ferreira2002_1734956839662,
	author = "Ferreira, M. A. M.",
	title = "Mean sojourn time in state k, k=0,1,..., for the M|G|∞ queueing system (Exact and approximated expressions)",
	booktitle = "Proceedings of the International Conference Quantitative Methods in Economics (Multiple Criteria Decision Making XI)",
	year = "2002",
	editor = "Magáthová, V.",
	volume = "",
	number = "",
	series = "",
	pages = "57-61",
	publisher = "Slovak Society for Operations Research",
	address = "Nitra, Slovakia",
	organization = "Faculty of Economics and Management; Slovak Agricultural University in Nitra; Slovak Society for Operations Research",
	url = "http://www.fhi.sk/en/katedry-fakulty/kove/ssov/papers/"
}

TY  - CPAPER
TI  - Mean sojourn time in state k, k=0,1,..., for the M|G|∞ queueing system (Exact and approximated expressions)
T2  - Proceedings of the International Conference Quantitative Methods in Economics (Multiple Criteria Decision Making XI)
AU  - Ferreira, M. A. M.
PY  - 2002
SP  - 57-61
CY  - Nitra, Slovakia
UR  - http://www.fhi.sk/en/katedry-fakulty/kove/ssov/papers/
AB  - In a M|G|∞ queue system ? is the Poisson process arrival rate, ? is the mean service
time, G(.) is the service time distribution function and there are infinite servers.
When we consider practical situations to apply this model we do not want necessarily
the physical presence of infinite servers. But we only guarantee that when a customer arrives
at the system it always finds immediately a server available. Other situations occur when there
is no distinction between a customer and its server.
So, often, it is very important to manage a group of servers, in order to guarantee that
the system works as an infinite server queueing system as it was designed. For this purpose it
is important to know the mean sojourn time in state k , k=0,1,.... Here, by state k , we mean
that there are k customers in the system, or, that is the same, k servers occupied.
Unhappily, only for M|M|∞ (exponential service time) queueing systems we know that
mean. But as it was proposed in (Ramalhoto and Girmes, 1977) we will consider that M|G|∞
systems are well approximated by a Markov Renewal Process. And so we will consider the
mean sojourn time in state k , k=0,1,... for that process as a good approximation to the ones
of the M|G|∞ queueing systems.
Then we are going to show some results to the mean sojourn time in state k , k=0,1,...
distribution function for the Markov Renewal Process considered.
ER  -