Theory of probability and Mathematical statistics

Multi-server queueing system with reserve servers

V. I. Klimenok

Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Abstract: In this paper, we investigate a multi-server queueing system with an unlimited buffer, which can be used in the design of energy consumption schemes and as a mathematical model of unreliable real stochastic systems. Customers arrive to the system in a batch Markovian arrival process, the service times are distributed according to the phase law. If the service time of the customer by the server exceeds a certain random value distributed according to the phase law, this server receives assistance from the reserve server from a finite set of reserve servers. In the paper, we calculate the stationary distribution and performance characteristics of the system.

Keywords: queueing system; reserve servers; batch Markovian arrival process; phase type distribution; stationary distribution; performance characteristics.

UDC: 519.872

Received: 01.11.2019

DOI: 10.33581/2520-6508-2019-3-57-70