We consider single-server scheduling to minimize holding costs where the capacity, or rate of service, depends on the number of jobs in the system, and job sizes become known upon arrival. In general, this is a hard problem, and counter-intuitive behavior can occur. For example, even with linear holding costs the optimal policy may be something other than SRPT or LRPT, it may idle, and it may depend on the arrival rate. We first establish an equivalence between our problem of deciding which jobs to serve when completed jobs immediately leave, and a problem in which we have the option to hold on to completed jobs and can choose when to release them, and in which we always serve jobs according to SRPT. We thus reduce the problem to determining the release times of completed jobs. For the clearing, or transient system, where all jobs are present at time 0, we give a complete characterization of the optimal policy and show that it is fully determined by the cost-to-capacity ratio. With arrivals, the problem is much more complicated, and we can obtain only partial results.

中文翻译：

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在具有状态相关服务费率的单服务器队列中进行调度

我们考虑单服务器调度以最小化持有成本，其中容量或服务率取决于系统中的作业数量，并且作业大小在到达时变得已知。一般来说，这是一个难题，可能会出现违反直觉的行为。例如，即使使用线性持有成本，最优策略也可能不是 SRPT 或 LRPT，它可能是空闲的，并且可能取决于到达率。我们首先在完成的工作立即离开时决定为哪些工作提供服务的问题与我们可以选择保留已完成的工作并可以选择何时释放它们的问题以及我们始终为工作提供服务的问题之间建立等价关系根据 SRPT。因此，我们将问题减少到确定已完成作业的发布时间。对于清算或瞬态系统，在所有工作都在时间 0 出现的情况下，我们给出了最优策略的完整特征，并表明它完全由成本容量比决定。对于到达，问题要复杂得多，我们只能得到部分结果。