A queueing system with batch arrival of customers in sessions

Authors:
Chesoong Kim;Alexander Dudin;Sergey Dudin;Valentina Klimenok
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 Industrial Engineering
Year:
2012

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Abstract

This paper describes and analyzes a single-server queueing model with a finite buffer and session arrivals. Generation of the sessions is described by the Markov Arrival Process (MAP). Arrival of the groups of the requests within any admitted session is described by the Terminating Batch Markov Arrival Process (TBMAP). Service time of the request has Phase (PH) type distribution. The number of the sessions that can be simultaneously admitted to the system is under control. Analysis of the joint distribution of the number of sessions and requests in the system is implemented by means of the matrix technique. Analysis of the sojourn time of an arbitrary and admitted session is performed by means of the extension of the method of catastrophes. Effect of control on the main performance measures of the system is numerically demonstrated.