Equilibrium pricing in an M/G/1 retrial queue with reserved idle time and setup time

Power consumption is a ubiquitous and challenging problem in modern society. To save energy, one should turn off an idle device which still consumes about 60% of its peak consumption and switch it on again when some jobs arrive. However, it is not tolerate for delay sensitive applications. Therefore, there is a trade-off between power consumption and delay performance. In this paper we study an M/G/1 retrial queueing system with setup times in which the server keeps idle for a reserved idle time after completion of a service. If there are arrivals during this reserved idle time, these customers can be served immediately. Otherwise, the server will be turned off for saving energy until a new customer comes to activate the server. The setup time follows an exponential distribution. Based on the reward-cost function and the expected payoff, all customers will make decisions on whether to join or balk the system upon arrival. Given these strategic behaviors we study the optimal pricing strategies from the perspective of the server and social planner, respectively. The optimization of the reserved idle time for maximizing the server's profit is also studied. Finally, numerical experiments are presented to illustrate the impact of system parameters on the customers' equilibrium behavior and profit maximization solutions.