Strategic behavior in the constant retrial queue with a single vacation

Donlinks School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China

^* Corresponding author: yuzhang@ustb.edu.cn; yuzhang9006@163.com

Received: 26 November 2018
Accepted: 23 January 2019

Abstract

We study customers’ joining strategies in an M/M/1 constant retrial queue with a single vacation. There is no waiting space in front of the server and a vacation is triggered when the system is empty. If an arriving customer finds the server idle, he occupies the server immediately. Otherwise, if the server is found unavailable, the customer enters a retrial pool called orbit with infinite capacity and becomes a repeated customer. According to the different information provided for customers, we consider two situations, where we investigate system characteristics and customers’ joining or balk decisions based on a linear reward-cost structure. Furthermore, we establish the social welfare of the system and make comparisons between the two information levels. It is found that there exist thresholds of system parameters such that the social planner would prefer revealing more information when the system parameter is greater than or less than the corresponding threshold.