Optimal Decisions And Equilibrium Analysis In Queueing Systems With Differentiated Services

Queueing systems,also known as stochastic service systems,arise from stochastic arrival processes and uncertain service times.While congestion is a common phe-nomenon in daily life,queueing scenarios have found widespread use in models of tickets systems,call centers and network service centers,etc.In order to reduce the con-gestion of service systems,managers need to design different service disciplines,such as first-come first-served,last-come first-served,random order,etc,based on different queueing regimes.Notice that in most queueing systems,customers queue for their own good,thus their decisions can significantly affect the system performance,which cannot be ignored.Different from traditional queueing systems,when the customer be-havior is added into account,customers can make optimal decisions to maximize their expected utilities,and the service provider has to adopt a corresponding pricing strat-egy or queueing mechanism to maximize his own profit.Therefore,a non-cooperative game between customers and the service provider is formed.This dissertation studies the optimal design of queueing systems with differentiated service policies,and consid-ers the equilibrium strategy as well as the optimal pricing strategy from the perspective of customers and the service provider,respectively.Firstly,in the framework of the communication networks,this dissertation propos-es a simultaneous service-and-retrial differentiation(SSRD)policy in a retrial queueing system,and the optimal allocation policy is derived.Queueing literature often sug-gests that higher service variability results in a larger delay,however,this dissertation presents a counterintuitive finding that the benefits of the simultaneous service-and-retrial differentiation policy outweigh the risk of increased service variability.Also,it reveals that the minimum customer delay can be achieved by differentiating customers into exactly two grades.Furthermore,by quantifying the asymptotic performance gain when the system is in heavy traffic,this dissertation gives the upper bound of reduced delay.These results imply that when the differentiation of the intervals of retrials is large enough,the expected delay of the system can be minimized.Thus,under such optimal allocation policy,the retrial queueing system with differentiated services can theoretically degenerate into a retrial queueing system with priorities.Secondly,the issue of information heterogeneity in retrial queueing systems is in-vestigated.In the retrial queue,customers are divided into two streams,one are in-formed about the server's state(idle or busy)upon arrival and the other are uninformed.Both streams of customers decide whether to join the system or not at arrival instants,and an asymmetric game is form among them.The equilibrium strategies for the cus-tomers are derived,and the impact of information heterogeneity on the system through-put and social welfare is studied.It shows that the social welfare is increasing in the fraction of informed customers,thus the maximum social welfare is reached when al-1 customers are informed about the state of the server.On the other hand,when the workload is low(or high),the throughput-maximizing server should conceal(or dis-close)his state to customers.When the workload falls within an intermediate range,information heterogeneity in the population(i.e.,revealing the information to a certain portion of customers)leads to more efficient outcomes.Furthermore,it shows that the service provider can induce the optimal fraction of informed customers that maximizes throughput,by charging a unique information fee.Lastly,in the priority queue with two classes of customers,the information disclo-sure policies and optimal pricing issues under two information levels are considered.One is the unobservable case,in which all customers do not know the state of the sys-tem,thus they have to make decisions based on evaluating their expected waiting times from the system parameters.The mixed equilibrium strategy(both joining and priority-purchasing strategy)is considered.By contrast,in the observable case,customers can make rational decisions based on the real-time system state upon arrival.This disserta-tion proves that the equilibrium form in observable case must be a two-threshold form.The unique Pareto-dominant equilibrium strategy and the optimal pricing strategies are derived under two cases.By comparing the revenues of service provider under different information levels,it discloses that the service provider is better off in the observable setting no matter the system load is low or high,but medium system load is relative-ly more beneficial in the unobservable setting.Some further managerial insights are presented from the service provider's point of view.