关键词: 排队, 均衡策略, 违约, 社会收益

Abstract: In the e-commerce supply chain system,the delay in information transmission between supply chains or the complexity of user needs can slow down the logistics process of goods,thereby increasing the waiting time required for customers to receive services. Therefore,customers often face a dilemma of whether to renege. Since the logistics of goods does not completely stop when a node in the supply chain system fails,but rather proceeds at a slower rate,this paper considers a queuing system with partial system failure. There is a significant amount of literature focusing on the study of strategic behavior in service or supply chain systems,but these papers share a common assumption: once customers choose to join the system,they are not allowed to renege. Under the assumption of no-reneging situation,the decision to join or balk will be made when the customers arrive at the system,and once the customers choose to join the system,the customer will not renege before the end of service. However,customers are usually faced with the dilemma of whether to renege,especially when server fails,making it seemingly unavoidable for customers to choose to renege.
In this paper,we consider the equilibrium strategy of the M/M/1 queuing system with customer reneging and partial breakdowns. Based on the “reward-cost” structure,we derive the equilibrium threshold strategy and show that the threshold strategy is double-threshold strategy. Moreover,we construct the balance equations and derive the steady-state distributions of the system under the equilibrium strategy in the reneging case and no-reneging case,respectively. Using the steady-state distributions,we compute the equilibrium throughput and the equilibrium social welfare of the system in the reneging case and no-reneging case,respectively. At last,we illustrate the impact on equilibrium throughput and equilibrium social welfare by numerical examples.
The research results show that: (1)the equilibrium strategy of customers is double-threshold strategy,and customers will be more willing to join the system when customer reneging is allowed; (2)the impact of customer reneging on equilibrium throughput is relatively small; (3)when the service intensity is small,the difference in equilibrium social welfare between the reneging situation and no-reneging situation will be relatively small,and it is not meaningful for the social manager to provide the reneging option; (4)when the service intensity is large,the social benefit in reneging situation will be better than that in no-reneging situation,and allowing customers to reneging can bring better social welfare.
The discussion in this paper deepens the research on the queues with strategic customers,thus offering a theoretical basis with practical implications for decision-making social managers. Based on this study,future research can explore the value of reneging under different information environments. Specifically,researchers can examine how customers' decisions regarding reneging will be influenced when the system information is incomplete,and how these influences alter their attitudes and behavioral strategies. This type of research is crucial to understanding customers' responses to uncertainty and information asymmetry. Another interesting direction would be the pricing of reneging choices from the perspective of maximizing social planner's welfare.

Key words: queue, equilibrium strategy, reneging, social welfare