基于累积前景理论的M/M/1排队模型

M/M/1 queuing model under cumulative prospect theory

基于Kahneman和Tversky提出的累积前景理论(Cumulative Prospect Theory,简称CPT),分析了M/M/1排队模型中顾客的最优到达率问题,此模型包含参照点、S-型价值函数、损失厌恶以及概率的权重函数.分析了模型的适定性问题,并在适定性的基础上对顾客最优到达率进行了分析.基于累积前景理论,商家服务速率越高,最优顾客到达率越高.商品价格和顾客的边际等待成本对最优顾客到达率的影响与服务收益对最优到达率的影响相反.在数值案例中,各要素对顾客最优到达率的影响与期望效用理论(Expected Utility Theory,简称EU)的分析结果是类似的.并指出累积前景理论求出的顾客最优到达率总是比期望效用理论下求出的顾客最优到达率低.

This paper formulated the M/M/1 model featuring a reference point in wealth,S-shape utility functions with loss aversion,and a probability weighting function under Kahahm and Tversky’s cumulative prospect theory(CPT).It highlighted the well-posedness issue of the model and analyzed the optimal arrival rate of customers.The results showed that the higher the rate at which the firm can process orders,the higher the rate at which customers will place orders.The impact of commodity prices and customers’marginal waiting costs was opposite to the service revenue on the optimal arrival rate under CPT.As a comparison,it presented the M/M/1 model under expected utility theory(EU),where the influence of each factor on the optimal queuing rate was easy to analyze because the utility function was globally concave.In the numerical case,the results of CPT and EU are similar,but the optimal customer arrival rate calculated by CPT was always lower than that under EU.