Individual versus Social Optimization in the Allocation of Customers to Alternative Servers
研究顾客到达多个服务台时，个体自私选择与社会整体最优的差异，发现个体倾向于过度使用等待成本与平均服务时间比值最小的服务台，并针对指数服务情形提出收费方案来纠正这种偏差。
Customers arrive at a service area according to a Poisson process. An arriving customer must choose one of K servers without observing present congestion levels. The only available information about the kth server is the service time distribution (with expected duration μ k −1 ) and the cost per unit time of waiting at the kth server (h k ). Although service distributions may differ from server to server and need not be exponential, it is assumed that they share the same coefficient of variation. Individuals acting in self-interest induce an arrival rate pattern (λ̂ 1 , λ̂ 2 , …, λ̂ k ). In contrast, the social optimum is the arrival rate pattern (λ 1 *, λ 2 *, …, λ k *) which minimizes long-run average cost per unit time for the entire system. The main result is that λ̂ k 's and λ̂ k *'s differ systematically. Individuals overload the servers with the smallest h k /μ k values. For an exponential service case with pre-emptive LIFO service an alternative charging scheme is presented which confirms that differences between individual and social optima occur precisely because individuals fail to consider the inconvenience that they cause to others.