Strategy Analysis of Retrial Queue with Parallel Customer and Standby Server

The objective of this study is devoted to studying the equilibrium strategy of an unreliable M/M/1+1 retrial queue model, which contains two types of parallel customers and batch service provided by a standby server. Two kinds of customers in this queuing system enter the system in parallel and follow the exponential distribution with different parameters. If the server stays idle, an arrival obtains service immediately; Otherwise, he enters the retrial space and waits for service. When a failure occurs, new customers will not be allowed to enter and the customer who is being served will be excluded from the system. Meanwhile, the system enables the standby server to serve customers in the retrial space with batch service mode. Based on the revenue-cost theory, we propose a benefit function and perform the equilibrium analysis for two types of parallel customers in both fully observable and almost observable cases. In addition, the average social benefits of this particular system are detailed analyzed by using symbolic calculation. Finally, the numerical illustrations that aid in visualizing the changes in customer behavior strategies and social benefits as the different system parameters.