Optimal Scheduling of Parallel Queues with Stochastic Flow Models: The cμ-rule Revisited*

Performance Bounds and Suboptimal Policies for Multi-Class Queue

“…While jobs depend on service time then the order of serving impress on quantities such average queue length. There are many policies which minimizes an average queue length for finite multi-class M/M/1 queuing system where one can find in [3]. There are some differences between multi-classes queue rather than single class queue which, for instance, are (1) the frequently of the job arrival of some classes is more than some other classes, (2) the service time of some classes is longer than other classes.…”

“…Indeed it is known (see for example [3,4]) that the cµ-rule is the optimal control in two main settings: (i) generally distributed service requirements among all nonpreemptive disciplines and (ii) exponentially distributed service requirements among all preemptive disciplines. In the preemptive case cµ-rule is only optimal if the service times are exponentially distributed.…”

“…Finding an optimal control policy for a Markov decision process is one of the highlighted topics for infinite (or even very large) state space systems where computing it often is intractable [3]. It is not easy to run even the known general form of the optimal control policy due to some difficulties since at each time there is a slot in the discrete time process.…”

Real-Time Optimization in Complex Stochastic Environments

“…Based on this new framework, we studied optimization problems for Stochastic Flow Models (SFMs) capturing the essential features of underlying resource contention problems with event-driven dynamics. We established unbiased IPA estimates for multiclass, multiobjective SFMs [4] and revisited a classic stochastic scheduling problem solution known as the "c-mu-rule" in a SFM setting to support the long-standing conjecture that this solution is independent of stochastic modeling assumptions [19], [7].…”