Consider a population of customers, each of which needs to decide independently when to arrive to a facility that provides a service during a fixed period of time, say a day. This is a common scenario in many service systems such as a bank, lunch at a cafeteria, music concert, flight check-in and many others. High demand for service at a specific time leads to congestion that comes at a cost, for examlple, for waiting, earliness or tardiness. Queueing theory provides tools for the analysis of the waiting times and associated costs. If customers have the option of deciding when to join the queue, they will face a decision dilemma of when to arrive. The level of congestion one suffers from depends on others, behavior and not only that of the individual under consideration. This fact leads customers to make strategic decisions regarding their time of arrival. In addition, multiple decision makers that affect each other’s expected congestion call for noncooperative game-theoretical analysis of this strategic interaction. This common daily scenario has prompted a research stream pioneered by the ?/M/1 model of Glazer and Hassin (Eur J Oper Res 13(2):146–150, 1983) that first characterized an arrival process to a queue as a Nash equilibrium solution of a game. This survey provides an overview of the main results and developments in the literature on queueing systems with strategic timing of arrivals. Another issue is that of social optimality, namely the strategy profile used by customers that optimizes their aggregate utility. In particular, we review results concerning the price of anarchy (PoA), which is the ratio between the socially optimal and the equilibrium utilities.

考虑一群客户，每个客户都需要独立决定何时到达在固定时间段（例如一天）内提供服务的设施。这是许多服务系统中的常见场景，例如银行、自助餐厅的午餐、音乐会、航班值机等。在特定时间对服务的高需求会导致拥堵，而这种拥堵是有代价的，例如，等待、提早或迟到。排队理论为分析等待时间和相关成本提供了工具。如果客户可以选择何时加入队列，他们将面临何时到达的决策困境。一个人遭受的拥堵程度取决于其他人的行为，而不仅仅是所考虑的个人的行为。这一事实引导客户就他们的到达时间做出战略决策。此外，影响彼此预期拥塞的多个决策者要求对这种战略互动进行非合作博弈论分析。这种常见的日常场景引发了由 Glazer 和 Hassin 的 ?/M/1 模型（Eur J Oper Res 13(2):146–150, 1983）开创的研究流，该流首先将到达队列的过程描述为 Nash博弈的均衡解。本调查概述了有关具有战略到达时间的排队系统的文献中的主要结果和发展。另一个问题是社会最优性的问题，即客户使用的优化其总效用的策略配置文件。特别是，我们审查了有关无政府状态（PoA）价格的结果，