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We study scheduling control of parallel processing networks in which someresources need to simultaneously collaborate to perform some activities andsome resources multitask. Resource collaboration and multitasking give rise tosynchronization constraints in resource scheduling when the resources are notdivisible, that is, when the resources cannot be split. The synchronizationconstraints affect the system performance significantly. For example, becauseof those constraints, the system capacity can be strictly less than thecapacity of the bottleneck resource. Furthermore, the resource schedulingdecisions are not trivial under those constraints. For example, not all staticprioritization policies retain the maximum system capacity and the ones thatretain the maximum system capacity do not necessarily minimize the delay (or ingeneral the holding cost). We study optimal scheduling control of a class ofparallel networks and propose a dynamic prioritization policy that retains themaximum system capacity and is asymptotically optimal in diffusion scale andconventional heavy-traffic regime with respect to the expected discounted totalholding cost objective.

On the Optimal Control of Parallel Processing Networks with Resource Collaboration and Multitasking