Analysis And Optimization Of Queueing Systems With Loss Aversion

Pricing is a control mechanism for queueing service systems.It has crucial applications in congestion control,revenue management,and quality-of-service control,etc.For pricing control problems in queueing models,customers are generally assumed to be fully rational decision-markers who maximize their utility.However,customers often need to make decisions in an uncertain environment of queueing systems in real life.Customers make their satisfactory decisions based on the different information about the system and their characteristics.Thus,customers are often not fully rational.Reference-dependent preference is an effective portrayal of customers’ bounded rationality.The important manifestation of reference-dependent preference is loss aversion.Loss aversion refers to the fact that customers are concerned not only with the actual outcome of the decision but also with the change in outcomes when people make decisions in uncertain realities.Moreover,the customer perceives losses more strongly than she does equally sized gains.This paper focuses on the impact of loss aversion on queueing service systems based on prospect theory and queueing game theory.This paper systematically explores the impacts of loss aversion on customers as well as on the optimal pricing of the system from three perspectives:loss aversion structure(stochastic reference points and state-dependent reference points),preference types(bundled and unbundled preferences),and operational environment(risky and riskless environments).In order to highlight the importance of understanding loss aversion with bundled preference in customers’ decisions and queueing service system’s pricing under the riskless environment,we consider a queueing system with uncertain service rates,where the system manager(firm or social planner)commits performance-based prices to loss-averse customers.The riskless environment means that customers can learn the current state of the server upon arrival.The bundled preference means that gains and losses are perceived through the price,the service reward,and the waiting cost as a whole.Then,we investigate the optimal pricing problem and perform the impacts of loss aversion on the firm’s revenue-optimal price and social planner’s socially optimal price in two scenarios:the stochastic reference point model and the state-dependent reference point model.We find that loss aversion with bundled preference only has the effect on the socially optimal price in the stochastic reference point model,i.e.,loss aversion with bundled preference causes the socially optimal price in the low state to fall and causes the socially optimal price in the high state to rise.There is no effect on the revenue-optimal and socially optimal prices in other cases.Subsequently,to understand the impact of loss aversion with unbundled preference on customer decisions and the pricing of queueing service systems under a riskless environment,we explore the optimal pricing problem based on a similar queueing model and a similar structure of reference-point model as described above.The unbundled preference means that gains and losses with regard to price are perceived separately from the other two components.In terms of the effect of loss aversion with unbundled preference on optimal prices,we find that loss aversion with unbundled preference has effects on all types of optimal prices.More precisely,loss aversion with unbundled preference causes the socially optimal price in the low state to fall and causes the socially optimal price in the high state to rise for the stochastic reference point model.However,the prices in other cases are decreasing in loss aversion with unbundled preference.Further,the sensitivity of socially optimal price to loss aversion with unbundled preference differs dramatically between the stochastic reference point model and the state-dependent reference point model.But the sensitivity of revenue-optimal price to loss aversion with unbundled preference remains unchanged from the stochastic reference point model to the state-dependent reference point model.In addition,we find that the effect of loss aversion on the revenue-optimal prices varies significantly across preferences,except for the socially optimal prices under the stochastic reference point model.Finally,to understand the impact of loss aversion with bundled preference on customer decisions and the pricing of queueing service systems under a risky environment,we explore the optimal pricing problem based on a similar queueing model and a similar structure of the reference-point model as described above.The risky environment means that customers cannot learn the current state of the server upon arrival.Interestingly,for the state-dependent reference point model,loss aversion has no effect on the customers’ decision and the revenue-optimal price in a risky environment or riskless environment.We also find that in the stochastic reference point model under the risky environment,loss aversion restrains customers from joining the queue and leads to a higher revenue-optimal price,which is inconsistent with the effect of loss aversion with bundled preference on the customers’ decision and revenue-optimal price under the riskless environment.