Equilibrium Balking Strategies In The Markovian Queues With Vacation Times

No matter in the classic queueing system or in the vacation queueing system, customers always want to have a good service. In the past, researches have only paid attention to the server in which service rate and service quality are controlled by the server and customers do not make decisions. Even when there exists some kind of dynamic control, the decisions are made by the server and customers are forced to follow them. However, based on the given information about the queueing system, customers in fact have the right to decide whether to join or to balk themselves. In order to simulate the real queueing system better, it is necessary to take into account the customers’strategic responses for maximizing their own benefits.In this paper, we explore the equilibrium customer strategies in observable Markovian queues under single vacation policy from both continuous and discrete time aspects. Based on the reward-cost structure, we obtain the stationary distribution of the system and the mean sojourn time of an arriving customer. Then by introducing appropriate functions, we provide an algorithm to identify the equilibrium balking strategies. Furthermore, the resulting stationary system behavior is explored and the equilibrium social benefit is derived. Finally, we illustrate the effects of the parameters on the equilibrium behavior via numerical experiments. The results show the following conclusions. The threshold increases with the service reward, arrival rate and vacation rate. When the parameters vary in a certain range, the threshold remains the same. The entrance; probability fluctuates with the service reward, arrival rate and vacation rate. When the threshold gets an inflection point value, the corresponding entrance probability has an extreme value. The increase; trend of social benefits with respect to various parameters is similar to the trend of thresholds, however, it is less influenced by the entrance probability.