无限服务台排队的均衡、社会福利和收入
Equilibrium, social welfare, and revenue in an infinite-server queue
摘要：
受新兴技术对收费停车场的影响，本文研究了无限服务员排队的均衡、社会福利和收入问题。更具体地说，我们假设一个客户的效用包括一个积极的奖励接收服务减去成本所造成的其他客户在系统中。在可观察的设置，我们显示的存在性，唯一性，以及个人的阈值，社会最优阈值，最优收入阈值的表达式，分别。然后，我们证明了最优收入阈值是小于社会最优阈值，这是小于个人的。此外，我们还将费用函数推广到任何非负系数的有限多项式函数。在不可观测的设置，我们得到了个人和最优收入的加入概率。最后，通过数值实验，我们补充了我们的结果，并比较了这两个信息水平下的社会福利和收入。
英文摘要：
Motivated by the impact of emerging technologies on toll parks, this paper studies a problem of equilibrium, social welfare, and revenue for an infinite-server queue. More specifically, we assume that a customer's utility consists of a positive reward for receiving service minus a cost caused by the other customers in the system. In the observable setting, we show the existence, uniqueness, and expressions of the individual threshold, the socially optimal threshold, and the optimal revenue threshold, respectively. Then, we prove that the optimal revenue threshold is smaller than the socially optimal threshold, which is smaller than the individual one. Furthermore, we also extend the cost functions to any finite polynomial function with non-negative coefficients. In the unobservable setting, we derive the joining probabilities of individual and optimal revenue. Finally, using numerical experiments, we complement our results and compare the social welfare and the revenue under these two information levels.
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