Abstract: Because service processing takes time, customers who participate in queuing need to wait for service. According to previous experience in waiting in line for services and consulting using artificial intelligence, customers can know a waiting time (waiting time includes waiting time in queuing and time served.) before participating in queuing, which forms a reference point. Customers like to receive service at their scheduled time, but affected by external environmental factors and service rate, waiting time often exceeds their expectations:delayed service or advanced service. Although the advanced service benefits and the probability of participating in queuing next time increases, the delayed service will affect the praise of service quality. Under the condition that the loss of delayed service is the same as the gain of advanced service, customers loathe the loss of service waiting. In a queuing system, the length of the waiting time is closely related to the price and service rate: the lower the price (the higher the arrival rate) and the slower the service rate, the longer the waiting time; vice versa. Then, under the condition of aversion to service waiting loss, how to configure price and service rate, as well as the relationship between price and service rate and related parameters, has been the main research subject.
This study adopts the utility function of the loss and gain due to service waiting to describe the behavior of customers participating in queuing. On this basis, the M/M/1 queuing model and the double M/M/1 queuing model are built. The analyses of the models show that: (1)Whether they are in the M/M/1 queuing model or the dual M/M/1 queuing model, their optimal prices have an increasing relationship with demand potential and a decreasing relationship with aversion to service waiting loss. Their optimal service rate is in an increasing relationship with aversion to service waiting loss. (2)For the double M/M/1 queuing model, the optimal price increases with the channel preference. If the optimal price of one side of the two queues is higher, it decreases with a price change in a customer transfer rate, otherwise it increases with a price change in a customer transfer rate. Profits are maximized when customers prefer one queue over the other; profits are minimized when customers have the same preference for both queues. A price change in a customer transfer rate and aversion to service waiting loss are not good for profit. At the same time, the application of the model is illustrated by two cases of providing medical services (One is the offline single channel mode, and the other is the online and offline dual channel mode) through a certain medical institution.
This study assumes that each M/M/1 queuing in the double M/M/1 queuing model has homogeneity: utility, service waiting unit cost, aversion to service waiting loss and unit cost of service rate remain the same. In practice, there are many heterogeneities (utility, service waiting unit cost, aversion to service waiting loss and unit cost of service rate do not remain the same.). On the basis of this study, we can set different values for utility, service waiting unit cost, aversion to service waiting loss, and unit cost of service rate in the future research.
When constructing the utility function, this study only considers the utility of participating in the queuing, but does not consider the utility of not participating in the queuing, which is the shortcoming of this study. Therefore, in the future, based on this study, all utilities (including the utility of not participating in the queuing) can be considered to study price and service rate decision-making.
The price and service rate in the decision-making of a single service provider is the subject in this paper. In reality, there are also decision-makings of the price and service rate in the competitive relationship between two or among more service providers. Therefore, in the future, we can study the decision-making of the price and service rate for the multi-service provider game relationship with aversion to service waiting loss.

Key words: aversion to service waiting loss, price, service rate, queuing

摘要： 考虑参加排队的客户厌恶服务等待损失,针对价格、服务速率与服务等待密切相关,如何配置价格与服务速率的问题。采用服务等待损失和收益效用函数刻画客户参加排队的行为,在此基础上,建立M/M/1排队模型和双M/M/1排队模型。通过模型的分析表明,无论是M/M/1排队模型,还是双M/M/1排队模型,最优价格与厌恶服务等待损失为递减关系,最优服务速率与厌恶服务等待损失为递增关系。对于双M/M/1排队模型,当客户偏好某一队列时,获利最多;当客户对两个队列有相同偏好时,获利最少;厌恶服务等待损失增加不利于企业的利润。最后,通过某一医疗机构的两种方式(一种是线下的单渠道方式,一种是线上和线下双渠道方式)提供医疗服务的案例说明模型的应用。

关键词: 厌恶服务等待损失, 价格, 服务速率, 排队