Priority Service Pricing With Heterogeneous Customer Delay Costs

As an important part of the national economy and an industry closely related to peo-ple's lives,the service industry has already accounted for half of the national economy and has become the largest industry in the national economy.The service industry is the main driving force of economic growth.When there is a temporary mismatch between service demand and supply,queues is formed.Queues are a common phenomenon in most service offerings.In reality,each customer's delay cost rate is different,that is,customers are heterogeneous.Some customers may incur a larger cost due to the op-portunities lost during waiting.Some customers may have enough time to wait and the waiting cost is lower.Based on this,service providers often introduce a fee-based "pri-ority" options when the system is congested and heterogeneity of customers' waiting costs.Customers can use these options to self-segment themselves.This approach has been widely used in healthcare,amusement parks,government(consular services)and transportation.Therefore,in order to improve the efficiency of queueing system and make service operations more efficient,it is necessary to design a pricing strategy that maximizes the service system's revenue or maximizes the social welfare,taking into account the heterogeneity of customers.The main research contents and conclusions of this thesis include the following three aspects:First,Chapter 3 of this thesis studies the priority pricing problem for a single-server queueing system with two priority classes in which customers have different sensitivities to delay.The system makes a fixed-delay announcement to inform arriv-ing customers of the expected delay for each class,whereupon each customer must decide which class to join.Any customer who joins the priority class is charged a fixed priority price.Our examination of customers' joining behavior under any given prior-ity prices reveals that there can be multiple equilibrium delays and that the number of those delays depends on the structure of customers' delay cost distribution.We charac-terize the stability of these equilibria and show that the system can reach the largest or smallest equilibrium by making a proper initial delay announcement.In addition,we consider two pricing problems to maximize the system's long-run average revenue and social welfare respectively.The results derived here establish that both the revenue-maximizing price and the social welfare-maximizing price are quite sensitive to the delay cost distribution.Secondly,Chapter 4 of this thesis studies the priority pricing problem for a single-server queueing system with multiple priority classes in which customers have different sensitivities to delay.The system makes a fixed-delay announcement to inform arriving customers of the expected delay for each class.We employ a transformation of vari-ables to establish the existence of the equilibrium delay and then analyze the the prior-ity pricing problem that maximizes the service system's revenue and maximizes social welfare respectively.The corresponding pricing strategy is given when the customer's delay cost rate follows some special distributions.At the same time,the influence of the number of priorities classes in the service system on the service system's revenue and social welfare is discussed.Our numerical studies show that the service system's revenue and social welfare both increase with the number of priority classes and that the most of the benefit the service system can gain from a complex pricing scheme(or an infinite number of priority classes in the extreme case)can be gained by offering a relatively small number of priority classes.Finally,Chapter 5 of this thesis studies the priority pricing problem for a single-server queueing system with two priority classes and customers can upgrade their priori-ties.Because there is a time interval between purchasing services and joining the service system,and customers are uncertain about the future system's states when purchasing services.Therefore,when a customer arrives at the service system and observes the system's states,the customer who previously purchased ordinary service can choose to purchase the priority again to join the priority queue.The equilibrium joining behavior of heterogeneous customers is analyzed when the priority price is known.Then,based on the customers'joining behavior,the pricing strategy that maximizes the revenue of the service system or maximizes social welfare is studied.The main contributions of this thesis are:(1)Our work explores customers' be-havioral equilibrium under the fixed-delay announcement.We find that the equilibrium delay may not be unique and that the number of equilibria depends on the delay cost distribution structure.(2)This thesis analyzes the priority prices that maximize the system's long-run average revenue and the ones that maximize social welfare.We fo-cus in particular on examining the effect of delay cost distributions on these optimal prices.Our results indicate that the optimal prices are sensitive to the specific delay cost distribution family considered.(3)we investigate the influence of the number of priority classes on the service system's revenue and social welfare by analyzing the ser-vice system with multiple priority classes.(4)Our work is a rare research that considers priority upgrades in the context of queueing games.We assume that customers are het-erogeneous and analyze the equilibrium joining behavior of customers,as well as the pricing strategies of service systems and social managers.