A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities

Seokjun Lee, Sergei Dudin, Olga Dudina, Chesoong Kim and Valentina Klimenok
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Seokjun Lee: Department of Management Information Systems, Sangji University, Wonju 26339, Korea
Sergei Dudin: Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Olga Dudina: Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Chesoong Kim: Department of Business Administration, Sangji University, Wonju 26339, Korea
Valentina Klimenok: Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus

Mathematics, 2020, vol. 8, issue 8, 1-20

Abstract: A single-server queueing system with a finite buffer, several types of impatient customers, and non-preemptive priorities is analyzed. The initial priority of a customer can increase during its waiting time in the queue. The behavior of the system is described by a multi-dimensional Markov chain. The generator of this chain, having essential dependencies between the components, is derived and formulas for computation of the most important performance indicators of the system are presented. The dependence of some of these indicators on the capacity of the buffer space is illustrated. The profound effect of the phenomenon of correlation of successive inter-arrival times and variance of the service time is numerically demonstrated. Results can be used for the optimization of dispatching various types of customers in information transmission systems, emergency departments and first aid stations, perishable foods supply chains, etc.

Keywords: priority system; marked Markov arrival process; phase-type distribution; change of the priority; dispatching (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 (3)

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