We consider assignment policies that allocate resources to users, where both resources and users are located on a one-dimensional line. First, we consider unidirectional assignment policies that allocate resources only to users located to their left. We propose the Move to Right (MTR) policy, which scans from left to right assigning nearest rightmost available resource to a user, and contrast it to the Unidirectional Gale-Shapley (UGS) matching policy. While both policies among all unidirectional policies, minimize the expected distance traveled by a request (request distance), MTR is fairer. Moreover, we show that when user and resource locations are modeled by statistical point processes, and resources are allowed to satisfy more than one user, the spatial system under unidirectional policies can be mapped into bulk service queueing systems, thus allowing the application of many queueing theory results that yield closed form expressions. As we consider a case where different resources can satisfy different numbers of users, we also generate new results for bulk service queues. We also consider bidirectional policies where there are no directional restrictions on resource allocation and develop an algorithm for computing the optimal assignment which is more efficient than known algorithms in the literature when there are more resources than users. Numerical evaluation of performance of unidirectional and bidirectional allocation schemes yields design guidelines beneficial for resource placement. \np{Finally, we present a heuristic algorithm, which leverages the optimal dynamic programming scheme for one-dimensional inputs to obtain approximate solutions to the optimal assignment problem for the two-dimensional scenario and empirically yields request distances within a constant factor of the optimal solution.

中文翻译：

---

具有应用的一维分布式服务网络中的资源分配

我们考虑将资源分配给用户的分配策略，其中资源和用户都位于一维线上。首先，我们考虑仅将资源分配给位于其左侧的用户的单向分配策略。我们提出向右移动 (MTR) 策略，该策略从左到右扫描，将最近的最右侧可用资源分配给用户，并将其与单向 Gale-Shapley (UGS) 匹配策略进行对比。虽然在所有单向策略中，这两种策略都尽量减少请求的预期行进距离（请求距离），但 MTR 更公平。此外，我们表明，当用户和资源位置通过统计点过程建模，并且允许资源满足多个用户时，单向策略下的空间系统可以映射到批量服务排队系统，因此允许应用许多排队理论结果，产生封闭形式的表达式。当我们考虑不同资源可以满足不同用户数量的情况时，我们也为批量服务队列生成了新的结果。我们还考虑了对资源分配没有方向限制的双向策略，并开发了一种计算最优分配的算法，当资源多于用户时，该算法比文献中的已知算法更有效。单向和双向分配方案性能的数值评估产生有利于资源放置的设计指南。\np{最后，我们提出了一个启发式算法，