In this paper, we study an optimal online resource reservation problem in a simple communication network. The network is composed of two compute nodes linked by a local communication link. The system operates in discrete time; at each time slot, the administrator reserves resources for servers before the actual job requests are known. A cost is incurred for the reservations made. Then, after the client requests are observed, jobs may be transferred from one server to the other to best accommodate the demands by incurring an additional transport cost. If certain job requests cannot be satisfied, there is a violation that engenders a cost to pay for each of the blocked jobs. The goal is to minimize the overall reservation cost over finite horizons while maintaining the cumulative violation and transport costs under a certain budget limit. To study this problem, we first formalize it as a repeated game against nature where the reservations are drawn randomly according to a sequence of probability distributions that are derived from an online optimization problem over the space of allowable reservations. We then propose an online saddle-point algorithm for which we present an upper bound for the associated K-benchmark regret together with an upper bound for the cumulative constraint violations. Finally, we present numerical experiments where we compare the performance of our algorithm with those of simple deterministic resource allocation policies.

翻译：本文研究简单通信网络中的最优在线资源预留问题。该网络由两个通过本地通信链路连接的计算节点组成。系统以离散时间方式运行；在每个时隙，管理员在实际作业请求到达之前预留服务器资源。预留操作会产生相应成本。随后，在观察到客户端请求后，作业可在两个服务器之间转移以最好地满足需求，但会产生额外传输成本。若某些作业请求无法满足，则会产生违规行为，每个被阻塞的作业需支付违约成本。目标是在有限时间范围内最小化总预留成本，同时将累积违规成本和传输成本控制在预算限额内。为研究该问题，我们首先将其形式化为一个对抗自然的重复博弈，其中预留量按照从允许预留空间上的在线优化问题推导出的概率分布序列随机抽取。接着，我们提出一种在线鞍点算法，并给出其关联的K基准遗憾的上界以及累积约束违规的上界。最后，通过数值实验比较所提算法与简单确定性资源分配策略的性能表现。