Equilibrium Analysis In The Model For Economics Of Queues With Variable System Rates

In this paper, we mainly investigate the equilibrium analysis of Markovi-an queuing system with variable system rates,"system rates" is the service rates of system there. In the queuing system with a single server, the service rate of system is mainly caused by the change of single-server’s service rate. We primarily discuss a single-server queuing model with partial breakdowns. The system may become defective, instead of stopping service completely, the service continues at a slower rate. We assume queuing system has an infinite waiting room where customers arrive according to a Poisson process with rate λ, the service time of a single-server is exponentially distributed at rate μ with normal working state, the customers are served at a lower rate of μ0with partial breakdowns state. The service discipline is first-come first served. Based on the reward-cost structure, customers can decide whether to join or balk according to different information levels upon their arrival. The paper mainly studies information in fully observable case and fully unobservable case. Customers are informed both the number of the customers present and the state of the server upon arrival in the fully observable case, but customers do not observe customers’number of system or the server state. Using the knowledge of queuing theory, the process of state change in the system can be simulated by Markov chain, then we compute the steady state equation with mathematical method and obtain the expected queue length equilibrium entrance probability and so on, show the economical analysis of customers’ optimal strategies combined with game theory. This model primarily explores equilibri-um customer strategies in an M/M/1queue with partial breakdowns. In actual life, many service systems generally operate under random environments, the server is influenced to serve customers at a slower rate with partial breakdowns state by many factors, such as congestion, viruses and so on. Chapter two gives equilibrium threshold strategy for fully observable case and equilibrium mixed strategy for fully unobservable case. Finally, corresponding numerical examples are presented to more visually illustrate the effects of several parameters in the system.