Open AccessMulti-server queueing system with reserve servers
Author(s) -
Valentina Klimenok
Publication year - 2019
Publication title -
žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika/žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika
Language(s) - English
Resource type - Journals
eISSN - 2617-3956
pISSN - 2520-6508
DOI - 10.33581/2520-6508-2019-3-57-70
Subject(s) - server , computer science , markov process , markovian arrival process , queueing theory , computer network , service (business) , process (computing) , server farm , set (abstract data type) , stationary distribution , markov chain , distributed computing , real time computing , client–server model , operating system , mathematics , business , statistics , marketing , machine learning , programming language
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.