The traditional approach when looking for a symmetric equilibrium behavior in queueing models with strategic customers who arrive according to some stationary arrival process is to look for a strategy which, if used by all, is also a best response of an individual customer under the resulting stochastic steady-state conditions. This description lacks a key component: a proper definition of the set of players. Hence, many of these models cannot be defined as proper noncooperative games. This limitation raises two main concerns. First, it is hard to formulate these models in a canonical way, and hence, results are typically limited to a specific model or to a narrow class of models. Second, game theoretic results cannot be applied directly in the analysis of such models and call for ad hoc adaptations. We suggest a different approach, one that is based on the stationarity of the underlying stochastic processes. In particular, instead of considering a system that is functioning from time immemorial and has already reached stochastic steady-state conditions, we look at the process as a series of isolated, a priori identical, and independent strategic situations with a random, yet finite, set of players. Each of the isolated games can be analyzed using existing tools from the classical game theoretic literature. Moreover, this approach suggests a canonic definition of strategic queueing models as properly defined mathematical objects. A significant advantage of our approach is its compatibility with models in the existing literature. This is exemplified in detail for the famous model of the unobservable “to queue or not to queue” problem and other related models.

在战略客户根据某种固定到达过程排队的模型中寻找对称均衡行为时，传统方法是寻找一种策略，该策略如果被所有人使用，也是随机结果下单个客户的最佳响应稳态条件。该描述缺少关键组成部分：对参与者集合的正确定义。因此，许多模型不能被定义为适当的非合作博弈。此限制引起两个主要问题。首先，很难以规范的方式制定这些模型，因此，结果通常限于特定模型或狭窄类别的模型。其次，博弈论的结果不能直接应用于这种模型的分析中，并要求进行特殊的适应。我们建议采用其他方法，一种基于基础随机过程的平稳性。特别是，我们不考虑某个系统自古以来就一直在运行，并且已经达到了随机的稳态条件，而是将这一过程视为一系列孤立的，先验相同且独立的战略情况，它们具有随机但有限的条件，套球员。每个孤立的游戏都可以使用经典游戏理论文献中的现有工具进行分析。此外，这种方法建议对战略排队模型进行规范定义，作为正确定义的数学对象。我们的方法的一个重要优点是它与现有文献中的模型兼容。对于无法观察到的“排队还是不排队”问题的著名模型和其他相关模型，详细说明了这一点。