Queuing System with Two Types of Customers and Dynamic Change of a Priority

Valentina Klimenok, Alexander Dudin, Olga Dudina and Irina Kochetkova
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Valentina Klimenok: Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Ave., 220030 Minsk, Belarus
Alexander Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Ave., 220030 Minsk, Belarus
Olga Dudina: Department of Applied Mathematics and Computer Science, Belarusian State University, 4 Nezavisimosti Ave., 220030 Minsk, Belarus
Irina Kochetkova: Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russia

Mathematics, 2020, vol. 8, issue 5, 1-25

Abstract: The use of priorities allows us to improve the quality of service of inhomogeneous customers in telecommunication networks, inventory and health-care systems. An important modern direction of research is to analyze systems in which priority of a customer can be changed during his/her stay in the system. We considered a single-server queuing system with a finite buffer, where two types of customers arrive according to a batch marked Markov arrival process. Type 1 customers have non-preemptive priority over type 2 customers. Low priority customers are able to receive high priority after the random amount of time. For each non-priority customer accepted into the buffer, a timer, which counts a random time having a phase type distribution, is switched-on. When the timer expires, the customer with some probability leaves the system unserved and with the complimentary probability gains the high priority. Such a type of queues is typical in many health-care systems, contact centers, perishable inventory, etc. We describe the behavior of the system by a multi-dimensional continuous-time Markov chain and calculate a number of the stationary performance measures of the system including the various loss probabilities as well as the distribution function of the waiting time of priority customers. The illustrative numerical examples giving insights into the system behavior are presented.

Keywords: changing priority queue; batch marked Markov arrival process; phase-type time distribution; waiting time (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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