Equilibrium Balking Strategies In The Queueing System With Different Service Mechanism

In the queueing system, customers make their decisions after they trade off be-tween the waiting cost and their reward. The customer’s decision is affected by other customer’s behavior, the customer want to maximize their surplus as possible as they can and they are unwillingness to wait. The studies on different service mechanism systems have attracted increasing attentions in recent years.In this paper, we mainly focus on two queueing models with different service mechanism systems. The main achievements are as follows:1. The equilibrium customer strategies in the observable M/M/l queue with an unreliable server has been considered in Economou and Kanta (Oper. Res. Lett.36:696-699,2008). The server has two states:on and off. The corresponding unobservable cases are investigated in our paper. Namely,(1) Fully unobservable case:Customers are not informed about the queue length nor the server state.(2) Almost unobservable case: Customers are informed only about the server state. We identify the equilibrium balking strategies in these two unobservable information cases.2. The customers’behavior and the Nash equilibrium joining strategies are in-vestigated in a single-server constant retrial queue with a Poisson arrival process and exponential service and retrial times in which the server is subjected to Poisson gener-ated supplementary services. Whenever a supplementary services occurs, all customers are served to abandon the system at the same time. There is no waiting space in front of the server. It is assumed that the arriving customers that find the server busy de-cide whether to leave their contact details or to balk the system based on a natural reward-cost structure. We study the balking behavior of the customers and derive the corresponding Nash equilibrium strategies under different levels of information. We consider separately the unobservable case where an arriving customer does not get in-formed about the exact number of customers waiting for service and the observable case where the customers get informed not only about the state of the server but also the exact number of customers in the orbit.