Abstract
We study scheduling control of parallel processing networks in which some resources need to simultaneously collaborate to perform some activities and some resources multitask. Resource collaboration and multitasking give rise to synchronization constraints in resource scheduling when the resources are not divisible, that is, when the resources cannot be split. The synchronization constraints affect the system performance significantly. For example, because of those constraints, the system capacity can be strictly less than the capacity of the bottleneck resource. Furthermore, the resource scheduling decisions are not trivial under those constraints. For example, not all static prioritization policies retain the maximum system capacity, and the ones that retain the maximum system capacity do not necessarily minimize the delay (or, in general, the holding cost). We study optimal scheduling control of a class of parallel networks and propose a dynamic prioritization policy that retains the maximum system capacity and is asymptotically optimal in diffusion scale and a conventional heavy-traffic regime with respect to the expected discounted total holding cost objective.
Highlights
We study control of processing networks in which some resources need to collaborate to perform some activities and some resources multitask
We propose a dynamic prioritization policy which is asymptotically optimal in diffusion scale in the conventional heavy-traffic regime
An linear program (LP) is solved at discrete time epochs, and the resource allocation decisions are done with respect to an index rule that depends on the optimal LP solution
Summary
We study control of processing networks in which some resources need to collaborate to perform some activities and some resources multitask. Harrison et al (2014) consider the control of a very general processing network with resource collaboration and multitasking They present an open problem of devising a dynamic resource-allocation policy that achieves what they call hierarchical greedy ideal (HGI) performance in the heavy-traffic limit. A very recent study considering cost minimization in parallel networks with resource collaboration and multitasking is Zychlinski et al (2019) In their setting, the resources are identical, and a service process can require the collaboration of multiple resources. The resources are identical, and a service process can require the collaboration of multiple resources They prove asymptotic optimality of a static policy and a state-dependent policy in a many-server heavy-traffic regime in a parallel network in fluid scale. We assume that all the random variables and stochastic processes are defined in the same complete probability space (Ω, F , P), E denotes expectation under P, and P(A, B) : P(A ∩ B)
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