Research On Equilibrium Strategies And Optimization Problems Of Queueing Models WITN Vacations

Queueing models with vacations have been extensively studied and applied to manyservice systems such as flexible manufacturing systems, inventory managements, callcenters, and electronic commerce. However, most problems are often studied from theclassical viewpoint of queueing theory, where customers do not make decisions. Arrivingcustomers decide whether to enter the system or balk by maximizing their individualwelfare. The server’s vacations may affect the sojourn time of a customer and hiswillingness to join. In recent years, queueing models with vacations get more and moreattentions. In this paper, some queueing models with vacations are considered from aneconomic viewpoint, and customers’ equilibrium and socially optimal strategies arestudied. The main work of this dissertation is summarized as follows:Firstly, the M/M/1queueing model with a single vacation and the M/M/1queueingmodel with setup time and a single vacation are studied. Both the steady-state probabilitiesand the expcted soujourn time are obtained under some levels of information regarding thesystem state. For the case where each customer observes the queue length before hisdecision, equilibrium threshold strategies are obtained. For the unobservable case,equilibrium and socially optimal balking strategies are derived. Furthermore, effects of theinformation level on the strategies are also illustrated via numerical experiments.Secondly, the M/G/1queueing model with N-policy is studied. For the unobservablecase, equilibrium strategies of customers are obtained and compared with the overalloptimal behavior. Moreover, the number N is taken as a decision variable and the optimaloperations policy is discussed in equilibrium states. For the partially observable case, thestationary behavior of the system is analyzed, and the equilibrium and socially optimalmixed strategies are derived.Finally, the discrete-time Geo/Geo/1queueing system with vacations is considered.For the queues with multiple vacations and a single vacation, equilibrium and sociallyoptimal balking strategies are obtained and compared. Furthermore, the appropriatepricing strategy that maximizes the monopolistic profit is obtained. For the queue with working vacations, equilibrium threshold strategies of customers are obtained in the fullyobservable case, and the Nash equilibrium balking strategies are derived both in thepartially observable case and fully unobservable case. Moreover, the effect of theinformation levels as well as several parameters on the equilibrium joining probabilities isillustrated by numerical examples.In a word, equilibrium strategies are analyzed in some queueing models withvacations using game theory and compared with socially optimal strategies which areobtained by using optimization theory. The results may provide the theoretical basis toproblems of optimization and control in practical queues.h...