This paper introduces non-cooperative games on a network of single server queues with fixed routes. A player has a set of routes available and has to decide which route(s) to use for its customers. Each player’s goal is to minimize the expected sojourn time of its customers. We consider two cases: a continuous strategy space, where each player is allowed to divide its customers over multiple routes, and a discrete strategy space, where each player selects a single route for all its customers. For the continuous strategy space, we show that a unique pure-strategy Nash equilibrium exists that can be found using a best-response algorithm. For the discrete strategy space, we show that the game has a Nash equilibrium in mixed strategies, but need not have a pure-strategy Nash equilibrium. We show the existence of pure-strategy Nash equilibria for four subclasses: (i) N -player games with equal arrival rates for the players, (ii) 2-player games with identical service rates for all nodes, (iii) 2-player games on a $$2\times 2$$ 2 × 2 -grid, and (iv) 2-player games on an $$A\times B$$ A × B -grid with small differences in the service rates.

中文翻译：

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单服务器队列网络上的非合作队列游戏

本文介绍了具有固定路由的单服务器队列网络上的非合作博弈。玩家有一组可用的路线，并且必须决定为其客户使用哪条路线。每个参与者的目标是最小化其客户的预期逗留时间。我们考虑两种情况：一个连续的策略空间，其中每个参与者都可以将其客户划分为多条路线，以及一个离散的策略空间，其中每个参与者为其所有客户选择一条路线。对于连续策略空间，我们表明存在唯一的纯策略纳什均衡，可以使用最佳响应算法找到该均衡。对于离散策略空间，我们证明博弈在混合策略中具有纳什均衡，但不需要具有纯策略纳什均衡。