Analysis Of Customer Balking Strategies In The M/M/1Repairable Queues

Queuing theory, also called stochastic service system theory, is another branch of op-erational research. Repairable queuing system is the extension and expansion of classical queuing system, which is broader and more complex. Whether classical queueing system or repairable queueing system, to study strategy behavior from the customer’s perspective not only can help customers make wise decisions, but provide managers with adequate theoret-ical basis of the pricing issues on queueing system, which is of great practical significance and become a new hot spot in the research of experts and scholars. At present, the vast majority of customers strategy study is based on the classical queue model and vacation queue model, few articles involves the repairable queueing model. Based on the background, this article study the customer decision problems of M/M/1repairable queueing system from perspective of economics.The article assumes queuing system with a single unreliable server, in which the failure frequency follows Possion process. When a failure occurs, the server begins to repair and the repair time obey exponential distribution. Once the repair is finished, the server comes back to the state before the failure and provides arriving customers with service, so again and again. Based on two different levels of information-observable and partially observable, the paper introduces a linear "reward-cost" structure, constructs the overall profit function about the individual customer, whole society and single-server, and analyzes and determines the customer equilibrium balking strategies, socially optimal balking strategies and server profit maximization strategies. Finally the paper illustrates the effects of the system parameters and economic parameters on the strategy behavior via numerical experiments and derives the inequality, established respectively under the two levels of information, nprof≤nsoc≤ne and qprof≤qsoc≤qe.The economic explanation is that when customers make decisions to maximize their benefits, they tend to ignore the negative external influences, and when it comes to the socially optimal and profit maximization, the overall utility will be considered.