Equilibrium Analysis For Economics-Based Queues With Bernoulli Vacation

During the last decades, there is an emerging tendency to study customers’strategic behavior in different queueing systems from an economic viewpoint, where a reward-cost structure is imposed on the system that characterizes the customers’ desire for service and cost for delays. Customers are allowed to make their own decisions in a decentralized manner and therefore the system can be modeled as a game among the customers. The focus of these studies is to find equilibrium individual strategies and socially optimal strategies, and useful managerial policies can be implemented based on these strategies which are related to pricing issues closely.The strategic joining behavior of customers in a single-server Markovian queueing system with Bernoulli vacation is studied. It is assumed that the server begins a vacation period if the queue is empty upon completion of a service, and if the queue is not empty, the server will take a Bernoulli type vacation.The Bernoulli vacation policy is described as follows. That is, if the queue is empty after a service completion then the server begins a vacation period; otherwise, a vacation period begins with specified probability p (0≤ p≤1) or the system serve another customer with probability 1-p. At the end of a vacation period, if a customer is present in the queue then service begins; otherwise, the server waits for the first customer to arrive. It is worthwhile to point out that the existence of a control parameter p in the system is an important merit of the Bernoulli vacation scheduling service, which is clearly applicable to queueing systems involving communication systems. Assuming that arriving customers can observe various levels of the system information, we study strategic customers’ decision on whether to join or balk the queue based on a linear reward-cost structure. The Nash equilibrium strategies in the fully observable case and the unobservable cases are investigated. The effect of the information level as well as several parameters on the equilibrium behavior is illustrated via numerical examples.