The field of stochastic scheduling is motivated by the design and operational problems arising in systems where scarce service resources must be allocated over time to jobs with random features vying for their attention. Important examples include manufacturing and computer-communication systems. Consider, e.g., the case of a manufacturing workstation processing different part types, where part arrival and processing times are subject to random variability. The performance of such systems, as measured by a criterion such as the average time jobs stay in the system (flowtime), may be significantly affected by the policy employed to prioritize over time jobs awaiting service (scheduling policy). The impact of scheduling policies, together with the high degree of discretionality in the decisions they involve, explain the importance and difficulty of the fundamental problem of stochastic scheduling: to design relatively simple scheduling policies that (nearly) achieve given performance objectives. The theory of stochastic scheduling addresses this problem in a variety of stochastic service system models. Random features such as job processing times are thus modeled by specifying their probability distributions, which are assumed to be known by the system manager. Model assumptions vary across several dimensions, including the class of scheduling policies considered admissible, job arrival and processing time distributions, type and arrangement of service resources and performance objective to be optimized. Regarding methods and techniques, it seems fair to say that no unified and practical approach has been developed to design and analyze (nearly) optimal policies across the range of stochastic scheduling models. Although many such models can be cast in the framework of dynamic programming, straightforward application of this technique has not proven very
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