Equilibrium analysis of cloud user request based on the Markov queue with variable vacation and vacation interruption

This paper considers the equilibrium balking behavior of customers in a single-server Markovian queue with variable vacation and vacation interruption, where the server can switch across four states: vacation, working vacation, idle period, and busy period. Once the queue becomes empty, the server commences a working vacation and slows down its service rate. However, this period may be interrupted anytime by the vacation interruption. Upon the completion of a working vacation, the server takes a vacation in a probability-based manner and stops service if the system is empty. The system stays idle after a vacation until a new customer arrives. The comparisons between the equilibrium balking strategy of customers and the optimal expected social benefit per time unit for each type of queue are elucidated and the inconsistency between the individual optimization and the social optimization is revealed. Moreover, the sensitivity of the expected social benefit and the equilibrium threshold with respect to the several parameters as well as diverse precision levels is illustrated through numerical examples in a competitive cloud environment.