Strategic behavior and social optimization in a clearing queueing system with N-policy and stochastic restarting scheme

Abstract

Considering the power consumption and delay performance, we propose a clearing queueing system with N-policy and stochastic restarting scheme. At the service completion epoch, the server switches to the dormant state to save energy if there are no customers waiting for services, otherwise initiates a new clearing service. After a dormant period, the server will be activated if there are at least N waiting customers, and be activated stochastically with less than N waiting customers. We derive the stationary distribution of system states with the closed form and an effective algorithm is designed to obtain the distribution of the sojourn time. In addition, a reward-cost structure is introduced in the queueing system. We analyze customers’ equilibrium strategic behaviours based on the optimistic value and provide a comparison between the criteria of using average and optimistic value by numerical examples. Finally, we discuss the social optimization problems and present some numerical experiences to illustrate impacts of system parameters on the socially optimal strategies and social optimal welfare.