# American Institute of Mathematical Sciences

October  2012, 8(4): 861-875. doi: 10.3934/jimo.2012.8.861

## On the optimal and equilibrium retrial rates in an unreliable retrial queue with vacations

 1 Department of Mathematics, Beijing Jiaotong University, 100044 Beijing 2 Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506, United States

Received  September 2011 Revised  July 2012 Published  September 2012

A single-server retrial queue with two types of customers in which the server is subject to vacations along with breakdowns and repairs is studied. Two types of customers arrive to the system in accordance with two different independent Poisson flows. The service times of the two types of customers have two different independent general distributions. We assume that when a service is completed, the server will take vacations after an exponentially distributed reserved time. It is assumed that the server has an exponentially distributed lifetime, a generally distributed vacation time and a generally distributed repair time. There is no waiting space in front of the server, therefore, if the server is found busy, or on vacation, or down, the blocked two types of customers form two sources of repeated customers. Explicit expressions are derived for the expected number of retrial customers of each type. Additionally, by assuming both types of customers face linear costs for waiting and retrial, we discuss and compare the optimal and equilibrium retrial rates regarding the situations in which the customers are cooperative or noncooperative, respectively.
Citation: Feng Zhang, Jinting Wang, Bin Liu. On the optimal and equilibrium retrial rates in an unreliable retrial queue with vacations. Journal of Industrial & Management Optimization, 2012, 8 (4) : 861-875. doi: 10.3934/jimo.2012.8.861
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##### References:
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