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Meeting Soft Deadlines in Single- and Multi-server Systems

机译：满足单服务器和多服务器系统中的最后期限

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摘要

We consider single-and multi-server systems, where jobs have a maximum waiting time (deadline) defined, e.g., by a service level agreement. A fixed cost is associated with deadline violations and the task is to minimize the long-run cumulative costs. Job sizes (service durations) are observed upon arrival, and current queue backlogs are known. For a single FCFS server, the optimization task is to find the optimal admission policy that may reject a job upon arrival if admitting it would cause in future one or more deadlines to be violated (in expectation). For parallel FCFS servers, the policy must (i) either accept or reject a job upon arrival, and if accepted, (ii) assign it to one of the servers. We derive efficient deadline-aware policies in the MDP framework. For a single server, we obtain the optimal admission policy. For dispatching to parallel servers, we develop efficient heuristic admission and dispatching policies, whose performances are evaluated by means of numerical examples. Additionally, we give some exact closed-form results for heavy-traffic limits.
机译：我们考虑单服务器和多服务器系统，其中作业具有最大等待时间（最后期限），例如通过服务水平协议来定义。固定成本与违反期限有关，任务是使长期累积成本最小化。在到达时会观察到作业大小（服务持续时间），并且当前的队列积压是已知的。对于单个FCFS服务器，优化任务是找到最佳准入策略，该准入策略可能会拒绝一项到达的作业，前提是该作业将导致将来违反一个或多个截止日期（预期）。对于并行FCFS服务器，策略必须（i）在到达时接受或拒绝作业，并且如果被接受，则（ii）将其分配给其中一台服务器。我们在MDP框架中得出有效的期限感知策略。对于单个服务器，我们获得了最佳的准入策略。为了调度到并行服务器，我们开发了有效的启发式许可和调度策略，其性能通过数值示例进行评估。此外，对于交通拥挤的限制，我们给出了一些精确的封闭式结果。

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