Strategic Behavior and Optimization in an Unobservable Constant Retrial Queue with Balking and Set-Up Time

An M/M/1 constant retrial queue with balking customers and set-up time is considered.Once the system becomes empty, the server will be turned down to reduce operating costs, and it will be activated only when there is a customers arrives. In this paper, the almost unobservable case is studied, in which the information of the queue length is unavailable, whereas the state of the server can be obtained. Firstly, the steady state solutions are derived and the individual equilibrium strategies are analyzed. In addition, social optimization problems, including cost analysis and social welfare maximization are investigated by using the PSO algorithm. Finally, by appropriate numerical examples, the sensitivity of some main system parameters is shown.