Multi-server Markovian heterogeneous arrivals queue with two kinds of working vacations and impatient customers

Abstract

This paper deals with multi-server queueing system with two kinds of Working Vacations (WVs) and impatient customers. A random timer is started whenever a customer comes into the system. The customer may abandon the system if the service is not completed before the impatience timer expires. Each time after serving all the customers, the system becomes empty and then the server begins 1st kind of vacation. On returning from 1st kind of WV, the server begins 2nd kind of WV whenever a system has no customers. When the server comes back from either 1st kind or 2nd kind of WV, if there is at least one customer in the system, the server switches to busy period. The steady state probabilities have been derived using the Probability Generating Functions (PGFs) method. Various measures of performance are presented and numerical illustrations are also provided.

Heterogeneous Server Retrial Queueing Model With Feedback and Working Vacation Using Artificial Bee Colony Optimization Algorithm

“…Laxmi et al [23] examined a queuing system with several working vacations, incorporating elements of renewal input, balking, reneging, and heterogeneous servers. Two types of Working Vacations (WVs) and impatient clients were handled with in a multi-server queueing system by Yohapriyadharsini et al [25]. Kumar et al [10] examined a unreliable Markovian queueing model with two stage service, incorporating hybrid vacation.…”