Open AccessAnalysis of a single server serving three queues m[x 1 ] /g1/1, m[x 2 ] /g2/1 , m[x 3 ] /g3/1 with priority services, working breakdown, modified bernoulli vacation
Author(s) -
GEETHA PRIYA K,
FRANCIS RAJ L
Publication year - 2022
Publication title -
journal of computational mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-8686
DOI - 10.26524/cm130
Subject(s) - poisson distribution , bernoulli's principle , queue , poisson process , laplace transform , service (business) , computer science , queueing theory , queueing system , mathematics , discrete mathematics , operations research , computer network , statistics , engineering , business , mathematical analysis , marketing , aerospace engineering
In this paper considers M[X1]/G1/1, M[X2]/G2/1 , M[X3]/G3/1 general queueing system with priority services . Three types of customers from different classes arrive at the system in different independent Poisson process. The server follows the non preemptive priority rule subject to working breakdown, and modified Bernoulli vacation with general (arbitrary) vacation periods. After completing the service, if there is no high priority customers present in the system. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained. Also the average number of customer in the priority and non priority, preemptive priority queue and the average waiting time are derived.