Game-Based Models And Strategy Analysis For Economics Of Queues

Customers in queueing systems act independently in order to maximize their own wel-fare. Yet, each customer's optimal behavior is affected by acts taken by both the system managers and the other customers. The result is an aggregate "equilibrium" pattern of behavior which may not be optimal from the point of view of society as a whole. Similar observations have been known to economists and researchers of queueing theory for a long time so that they began to solve this economic problem based on game and queueing theory. Then it gradually developed into a cross-subject of Economics, Game Theory and Queueing Theory named as Economics of Queues, which will be studied in the dissertation.Based on the previous literatures on the subject of Economics of Queues, equilibrium and socially optimal strategies are analyzed in several types of models, where customers' and server's strategies are both considered, and system performance measures under Nash equilibrium are compared with those under social optimization. Moreover, the main results obtained are verified by appropriate numerical examples visually.Firstly in the queues with two complementary services, customers have to purchase a product in addition to a service in order to enjoy a benefit. Customers'equilibrium behavior and price strategies of the two servers in the two kinds of Nash equilibria under competition are presented, which are compared with the equilibrium strategies under monopoly. The competition set of prices is higher than that of the monopolist, which is just caused by competition between the two servers. Moreover, the orientations of likes and dislikes of both customers and servers are compared under three types of payment structures.Secondly, two models with double relative priority parameters are discussed. In the first model, customers'equilibrium behavior as well as server's profit-maximizing strategies based on specific system parameters is analyzed in different types of equilibria. In the other one, the use of relative priority policies for minimizing the queueing system cost is illustrated and the conditions under which relative priorities outperform absolute priorities are presented. Besides the linear and maximum cost functions, much more attention is focused on the quadratic bivariable and exponential cost functions.Besides the queues with double relative priority parameters, the model with N parame- ters is also considered. First, for a job given its class, the mean remaining queueing times starting from the service commencement of an arbitrary job are obtained. Then the mean queueing times upon arrival are also derived.Subsequently, queues with three types of setup/closdown policies-interruptible, skip-pable and insusceptible-are considered, respectively. For the observable case, the equilib-rium threshold strategies of customers are derived and the stationary behavior of the sys-tems is analyzed. For the unobservable case, both the equilibrium and socially optimal mixed strategies of customers are found. Furthermore, the appropriate pricing strategy that maximizes both the social welfare and the monopolistic profit is obtained.Then, two unobservable queues with partial information on service times are analyzed. Given several service time distributions and various partial information, risk-neutral and risk-averse customers'equilibrium and socially optimal strategies are all derived based on maximum entropy principle. Moreover, the profit-maximizing strategies of the server under each type of partial information are also described. The rule is observed that more informa-tion encourages customers to join the queue, which is beneficial for the server's profit.Besides the setup/closedown vacation policies, queueing model with classical multiple vacations is studied. The equilibrium and socially optimal joining strategies of customers, both in vacation and busy period, have been derived and contrasted. The conclusion is summarized that individual optimization leads to excessive congestion without regulation.Finally, the allocation problem of customers in a discrete-time multi-server queueing system is discussed and customers'equilibrium and socially optimal strategies are obtained. Comparisons shows that the servers used in equilibrium are no more than those used in the socially optimal outcome, which is also verified by numerical examples.