Economics And Game Strategy Analysis Of Strategic Customers In Queueing Service Systems

During the last few decades, there has been an emerging interest in the economic analysis of queueing service systems. In such an economic analysis, a certain reward-cost structure is imposed on a queueing system, incorporating customers' desire for service as well as their unwillingness to wait. The customers are allowed to take their own decisions and act individually and independently in order to maximize their wel-fare. Inevitably, each customer's decision affects and is affected by the decisions of the other customers, the servers and the administrator of the system. Therefore the sys-tem can be modeled as a game between the customers or between the customers and the servers or between the customers and the manager of the system. And the result is an equilibrium scheme where no one has incentive to deviate from this. The central problem in the economic study of queueing service systems is the computation of Nash equilibrium and socially optimal strategies.This thesis mainly investigates strategic customers' queueing behavior in various queueing service systems. The goal is to derive the Nash equilibrium and socially opti-mal strategies under different levels of system information and compare these strategies with each other.Firstly, we study the equilibrium behavior of customers in the queueing system with server's delayed repair process. Specifically, the equilibrium threshold balking strategies are investigated for the unreliable server queues with single-stage and multi-stage delayed repairs respectively in observable cases. It is shown in numerical exam-ples that the information about the system is not always helpful for increasing social benefit in equilibrium. In some cases more accurate information improves the equilib-rium social benefit, but in other cases can hurt the customers.Secondly, two different queueing systems with server vacations are discussed. The first one is concerned with the single-server queue with working vacations, where the server undertakes the workload with a lower service rate rather than completely stops to work during the vacation period. Four cases with respect to different levels of infor-mation are studied. The corresponding Nash equilibria are derived. In the other model, a queueing system with general service and setup times is studied. For the fully observ-able and almost observable cases, the equilibrium joining strategies of customers who wish to maximize their expected net benefit are obtained. Two numerical examples are presented to illustrate the equilibrium joining probabilities for these cases under some specific distribution functions of service and setup times.Then, we investigate the equilibrium and socially optimal balking behavior for the single-server classical retrial queues. Unobservable and observable cases are studied and the corresponding Nash equilibrium and social optimization balking strategies for all customers are derived, and are compared regarding these two information level-s through numerical examples. Additionally, we consider a single-server retrial queue with two types of customers in which the server is subject to vacations along with break-downs and repairs. By assuming both types of customers face linear costs for waiting and retrials, we discuss and compare the optimal and equilibrium retrial rates regarding the situations in which the customers are cooperative or noncooperative, respectively.Finally, the game between the customers and the service provider is studied. We consider a retrial queue in which the server will take vacations after a reserved time when a service is completed. Customers have to pay the announced price charged by the server if they decide to enter the system and receive service from the server. The decision about whether to give up the service (balk) or to enter the system is based on their full price, which consists of the service fee plus the cost of waiting in the orbit. By knowing the customers' Nash equilibrium strategies for joining when they are informed about whether the server is idle or not (either busy or on vacation) upon arrival for any posted price, the server will choose what value for the price to charge in order to maximize its own revenue. We further study how the social planner, whose goal is to maximize the overall welfare of the customers and the server, determines the price to charge a joining customer.