On the retrial queue with imperfect coverage and delay reboot

¹ Department of Finance, Chaoyang University of Technology, Taichung, Taiwan, ROC
² Department of Applied Statistics, National Taichung University of Science and Technology, Taichung, Taiwan, ROC

^* Corresponding author: jauchuan@nutc.edu.tw

Received: 17 February 2020
Accepted: 18 September 2020

Abstract

Retrial systems have been used extensively to model many practical problems in call center, data center, cloud service computing center and computer network system. This paper deals with a multi-server retrial system with the features of imperfect coverage and delay reboot. In the investigated system, arrivals may not be detected because of some fault issues. When this situation happened, the system is cleared by a reboot operation. Once arrivals are detected and located, they are attended to when a server is available; otherwise, they join a retrial orbit and generate repeated attempts till a free server is found. We analyze the presented model as a quasi-birth-and-death process and develop various performance indices. The optimal number of servers and optimal service rate are searched by constructing an average cost function. A heuristic search technique is employed to obtain the optimization approximate solution at a minimum cost. Numerical illustrations are given to demonstrate the optimization procedure and the effects of varying parameters on performance indices. We also present an application example to demonstrate the applicability of investigated model.