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Stationary sojourn times in $\mathrm{MAP}/\mathrm{PH}/1/r$ queue with bi-level hysteretic control of arrivals
R. V. Razumchikab a Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences,
44-2 Vavilov Str., Moscow 119333, Russian Federation
b Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
Abstract:
This paper reports some new results concerning the
analysis of the time-related stationary characteristics
of a finite-capacity queueing system
operating in a random environment
with the bi-level hysteretic control of arrivals.
The topic of the paper is motivated by
the overload problem in networks of SIP (session initiation protocol) servers
and the viewpoint that multilevel hysteretic control
of arrivals in SIP servers
can be used to mitigate signalling network congestion.
The considered mathematical model of SIP server is the
single server queueing system with Markovian arrival processes (MAP), PH (phase-type)
service,
and bi-level hysteretic control policy.
According to this policy, a system may be in one
of the three operation modes: normal, overload, or blocking.
The switching between modes occurs at
instants whenever the total number of customers in the
system changes.
The analytical method for the computation of the
stationary sojourn times in different operation modes (in terms of
Laplace–Stieltjes transforms (LST)),
which utilizes the knowledge about the presence of
hysteretic loops, is given. It is also applicable
in the case when, in addition to the sojourn times,
one needs to account for the number of lost customers.
Keywords:
queueing system; random environment; first passage times; hysteretic control.
Received: 19.09.2017
Citation:
R. V. Razumchik, “Stationary sojourn times in $\mathrm{MAP}/\mathrm{PH}/1/r$ queue with bi-level hysteretic control of arrivals”, Inform. Primen., 11:4 (2017), 19–25
Linking options:
https://www.mathnet.ru/eng/ia497 https://www.mathnet.ru/eng/ia/v11/i4/p19
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Abstract page: | 159 | Full-text PDF : | 59 | References: | 26 |
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