Analysis Of Customer Equilibrium Strategies And Stochastic Process Limits In Queueing Systems

Queueing theory models many practical phenomena in daily life,examples include consumer checkout lines in supermarkets,on-hold calls waiting to be answered in call centers,and patients waiting lines for triage,tests,and treatment in healthcare systems.Motivated by the aforementioned service systems,queueing theory applies stochastic modeling and probability theory to study desired performance functions such as the waiting time,queue length,and probability of delay,which is also called the stochastic service system.These performance functions can help service providers to make better operational decisions.Besides the stochastic nature of the arrival process and service times,another important factor that can potentially impact system performance is customers’ strategic behavior.Queueing models that consider customers’ behavior are called “queueing economics model”,where customers are modeled by utility maximizing entities who make decisions rationally based on information available to them.Customers decisions usually include to join or not to join the service system,to purchase or not to purchase priority service,etc.Taking into account customers’ strategic behavior,service providers aim to select proper rules and system parameters to improve the revenue.Since all participants are selfish,there exist non-cooperative game among customers,or between customers and service providers.This study aim to investigate customers’ equilibrium joining behavior and determine the optimal design of the queueing systems driven by various applications in service systems,including communication network,call center,online service system,and healthcare.Firstly,in order to investigate how service disruptions influence the normal operations and system performance in communication networks,we study a queueing model with so-called “negative customers”.Upon the arrival of a negative customer,the system breaks down with some customers removed from the system.To capture customers’ strategic behavior,we allow regular customers(called positive customers)to maximize their expected utility by deciding on whether or not to join the queue system.The equilibrium strategy and revenue-and socially optimal joining strategy as well as the order of them are studied under two information revelation policies: observable queue length and unobservable queue length.A careful analysis of these results reveals an interesting observation: when the queue length information is unobservable,increasing the arrival rate of negative customers may improve the social welfare and customers’ willingness to join.In the interest of having a further study of queueing model with server vacation,the second part of this study considers a Bernoulli vacation queue model with applications to call centers.There are no customer waiting line in this model,where the blocked arrivals join the orbit and retry for service at later times.This study considers the constant retrial queueing system with Bernoulli vacations,where service providers reveal or hide the server state information but show customers the queue length information.To maximize their utilities,blocked customers decide on whether to join the system or not upon arriving.The steady-state distribution and customers’ equilibrium joining strategy are derived;and the comparison of joining threshold under different information levels is reported.Subsequently,to boost the volume of customer participantes and improve the system throughput in online service system,service providers often offer free service experience to first-time customers(e.g.,Amazon,Thunder).To capture the aforemention features,we develop a new queueing model.Our new queueing model facilitates the characterization of customer behavior as well as the corresponding optimal design of the system with exogenous and endogenous service capacities.There exists uncertainty of the system parameters these customers observed after experience(bounded rationality).Results include the equilibrium behavior of first-time customers,and optimal decisions for the service provider and social planners.In contrast to the conventional wisdom,this study shows that the service provider’s optimal revenue decreases as customers become less rational.Finally,to improve the performance analysis and design of heathcare and other relevant large-scale service systems,we develop a novel queueing model,where customers’ service times waiting times exhibits significant correlation.Such an assumption has practical relevance: For example,in healthcare system,prolonged patient delay before treatment usually induces a worse health condition,which in turn will overcomplicate the treatment process,leading to a longer treatment time,while in conventional queueing systems,service times are usually assumed exogenous(independent with the waiting times).We resort the heavy-traffic fluid approximation of the aforementioned queueing system due to the difficulty to achieve solutions by conventional method.Fluid approximation has been proven effective especially for large-scale systems(when arrival rate and number of servers are large).To analyze the fluid model,we develop dynamic equations for relevant system functions,and devise efficient algorithms that converges geometrically fast.The effectiveness of the fluid solutions are verified by(i)a heavy-traffic weak law of large number(WLLN)limit theorem which shows that,as the system scale increase,all scaled queueing functions converge to their fluid counterparts,and(ii)engineering confirmations via simulations.In addition,we also provide discussions on how to set appropriate staffing levels so as to control delay-based performance functions at designated targets.