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Advances in Operations Research
Volume 2016 (2016), Article ID 4024950, 17 pages
Research Article

Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations

Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781 039, India

Received 27 October 2015; Accepted 14 February 2016

Academic Editor: Viliam Makis

Copyright © 2016 Cosmika Goswami and N. Selvaraju. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a PH/M/c queue with multiple working vacations where the customers waiting in queue for service are impatient. The working vacation policy is the one in which the servers serve at a lower rate during the vacation period rather than completely ceasing the service. Customer’s impatience is due to its arrival during the period where all the servers are in working vacations and the arriving customer has to join the queue. We formulate the system as a nonhomogeneous quasi-birth-death process and use finite truncation method to find the stationary probability vector. Various performance measures like the average number of busy servers in the system during a vacation as well as during a nonvacation period, server availability, blocking probability, and average number of lost customers are given. Numerical examples are provided to illustrate the effects of various parameters and interarrival distributions on system performance.