On The Optimal Policies Of Several Economic Queueing Systems

Queueing systems are very useful stochastic service models,which provides a research tool for many service systems with congestion problems when the resources are limited.How to optimize different performance evaluations of the queueing systems is a very important direction in research work.This doctoral dissertation mainly studies the optimal policies for several types of queueing systems from the perspective of system administrators and customers.First,under the background of systems with random failures,we analyze the control problems of a stationary repairable queueing system and a non-stationary repairable queueing system.We give some properties of the bias of the canonical policies and prove that the optimal control policy has a simple structure.Based on these properties,we also discuss the corresponding algorithm problems.Second,we study a finite double-sided queue with several customer types.Assuming no matching time between the two-sided customers,we show that the optimal admission control policy for maximizing the long-run average net profit per unit time has a threshold structure.Furthermore,we prove that there exists a bias optimal policy having a threshold form with the largest optimal control level for each customer type,which is also the unique n-bias optimal policy for any n ? 1.Using the above results,we then provide an efficient iterative algorithm to produce the optimal control policy.Third,we study the information policy of the servers in the tandem queueing system with two servers.An illustration was given by an earlier paper of Hassin,which considers two gas stations located one after the other on a main road.A driver who needs to fill the gas can see the queue length upon arriving at the first station,but not the second one.The driver decides which station to enter based only on this partial information for minimizing the expected waiting time.Via extensive numerical experiments,Hassin showed that the first server enjoys a larger market share,which led him to making a number of conjectures.Here,we prove that all the numerical observations and conjectures are true so that the advantage of being the first server is assured.Finally,inspired by the impact of emerging technologies on(toll)parks,we study a problem of equilibrium,social welfare,and revenue for an infinite-server queue.More specifically,we approximate the park as an infinite-server queue and assume that a tourist’s utility consists of a positive reward for receiving service minus a cost caused by the expected internal congestion.In the observable setting,we show the existence,the uniqueness,and the expressions of the individual threshold,the socially optimal threshold,and the optimal revenue threshold.Then,we prove that the optimal revenue threshold is smaller than the socially optimal threshold,which is smaller than the individual one.Furthermore,we also find that using the same method,the cost structures in some theorems can be generalized to any finite polynomial function with non-negative coefficients.In the unobservable setting,we derive the joining probabilities of the individual and the optimal revenue.We also complement our results with numerical experiments and provide managerial insights on whether to release the real-time information.