Individual versus Social Optimization in Exponential Congestion Systems
Individual versus Social Optimization in Exponential Congestion Systems
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DOI：
10.1287/opre.25.2.233
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发表时间：
1977-04
期刊：
影响因子：
--
通讯作者：
S. Lippman;S. Stidham
中科院分区：
文献类型：
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作者：
S. Lippman;S. Stidham
我们考虑一个被建模为生灭过程的随机拥塞系统。顾客按照泊松过程到达。当系统中有\(i\)个顾客时，离开率在\(i\)上是非递减的、凹的且有上界。成本结构由线性持有成本和顾客进入系统时获得的随机奖励组成。系统可以通过决定哪些顾客将进入来进行控制。我们扩展了瑙尔（Naor）、耶恰利（Yechiali）和克努森（Knudsen）的主要结果是，无论是否有折扣，以及对于有限或无限的时间范围，个体最优规则要求顾客在社会最优规则要求其进入系统时进入系统。我们还研究了最优拥塞收费的性质，它促使顾客为自身利益行事时遵循社会最优规则。
We consider a stochastic congestion system modeled as a birth-death process. Customers arrive from a Poisson process. The departure rate when i customers are in the system is non-decreasing, concave, and bounded above in i. The cost structure consists of a linear holding cost and a random reward received when a customer enters the system. The system can be controlled by deciding which customers will enter. Our main result extending those of Naor, Yechiali, and Knudsen is that, with or without discounting and for a finite or infinite time horizon, the individually optimal rule calls for the customer to enter the system whenever the socially optimal rule does. We also study the properties of the optimal congestion toll, which induces customers acting in their own interest to follow a socially optimal rule.