Game-theoretic Analysis Of Queueing Systems Based On Quality Of Service

In queueing systems, the quality of service (QoS) is regarded as a key factor reflect-ing customer satisfaction. Both server breakdowns and vacations can impact the quality of service. This thesis focuses on game-theoretic analysis of some QoS based queue-ing systems like repairable queueing systems, vacation queueing systems and health-care systems. Firstly, the homogeneous and heterogeneous customers' strategic behav-ior are investigated in the retrial queueing system with server breakdowns and repairs.Secondly, under different information levels, customers' strategic behavior is explored in the discrete-time queueing system with working vacation and in the double-ended queueing system with gated policy, respectively. Finally, both the game-theoretic anal-ysis and the optimal allocation policy are derived in the healthcare system. This thesis consists of five chapters.Chapter 1 introduces game-theoretic analysis along with its background in queue-ing systems and summarizes some recent works. And then some basic concepts and essential theories are presented.Chapter 2 investigates the game-theoretic analysis of retrial queueing systems with server breakdowns and repairs. In Section 2.1, a single-server constant retrial queue with individual removal is studied. Customers, equilibrium strategies and social opti-mization strategies are obtained under the observable and unobservable cases. It seems that server breakdowns would lower customers' quality of service and then less cus-tomers would join the queueing system. However, numerical examples demonstrate that customers have difference preferences on the expected times of breakdowns per time unit under different information levels. In Section 2.2, the retrial queueing system with server breakdowns and repairs, which can be applied to secondary users' dynamic spectrum sharing in cognitive radio system, is analyzed. Server breakdowns can be re-garded as the arrival of primary users. Sensing failures caused by secondary users will degrade the quality of service of the system. This section concentrates on the impact of sensing failures on strategic behaviors of secondary users. Since the socially optimal strategy improves efficiency in the utilization of the cognitive radio system, an admis-sion fee is imposed on secondary users to make the equilibrium strategy coincide with the socially optimal strategy. In Section 2.3, when all the customers have heterogeneous delay cost, the effect of different parameters on the behavior of customers is investigated via numerical examples. It is interesting to find that the maximum profit does not equal to the optimal social welfare any more. The main reason is the heterogeneity increases tthe negative externalities among all customers in the system.Chapter 3 considers the game-theoretic analysis of both continuous-time and discrete-time vacation queueing systems. In Section 3.1, the customers' equilibrium behavior of discrete-time queueing system with single working vacation is explored in the fully ob-servable and fully unobservable cases respectively. Furthermore, the impact of server's vacation time on customers' strategic behavior is analyzed through numerical examples.Section 3.2 is concerned with a double-ended queueing system which is motivated by the passenger-taxi problem under a gated policy. This policy makes taxis start to balk when the taxi queue length reaches an upper limit and to join again when the taxi queue length is reduced to a lower limit. The strategic behaviors of arriving passengers under three information scenarios, i.e., the fully unobservable, almost unobservable, and fully observable queue cases, are investigated. Numerical analysis shows that the equilibrium threshold strategy in the fully observable case not only relies on the gated policy, but also depends on the difference between the arrival rate of customers and taxis. It also illustrates that the gated policy can further improve the social welfare of such a service system in several situations.Chapter 4 focuses on the game-theoretic analysis of speed-quality trade-off in allo-cating budget for public service. For both two-tier and three-tier healthcare systems, the patients' equilibrium behavior and the optimal allocation policy are discussed. More-over, such a result is quite robust for two-tier and three-tier healthcare systems using the budgets allocated for speed-quality trade-off. The analysis generates managerial insights for social planner (government) in making its budget policy in supporting the public service system such as healthcare.Finally, Chapter 5 highlights the innovations of our work and some future works that we will be engaged in.