Erlang loss queueing system with batch arrivals operating in a random environment

Authors:
Che Soong Kim;Alexander Dudin;Valentina Klimenok;Valentina Khramova
Affiliations:
Sangji University, Wonju, Kangwon 220-702, Republic of Korea;Belarusian State University, 4, Nezavisimosti Ave., Minsk 220030, Belarus;Belarusian State University, 4, Nezavisimosti Ave., Minsk 220030, Belarus;Belarusian State University, 4, Nezavisimosti Ave., Minsk 220030, Belarus
Venue:
Computers and Operations Research
Year:
2009

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Abstract

We consider the BMAP/PH/N/0 queueing system operating in a finite state space Markovian random environment. Disciplines of partial admission, complete rejection and complete admission are analyzed. The stationary distribution of the system states is calculated. The loss probability and other main performance measures of the system are derived. The Laplace-Stieltjes transform of the sojourn time distribution of accepted customers is obtained. Illustrative numerical examples are presented. They show effect of an admission strategy, a correlation in an arrival process, a variation of a service process. Poor quality of the loss probability approximation by means of more simple models utilization is illustrated.