Size- and state-aware dispatching problem with queue-specific job sizes

Abstract

We consider the dispatching problem in a size-and state-aware multi-queue system with Poisson arrivals and queue-specific job sizes. By size-and state-awareness, we mean that the dispatcher knows the size of an arriving job and the remaining service times of the jobs in each queue. By queue-specific job sizes, we mean that the time to process a job may depend on the chosen server. We focus on minimizing the mean sojourn time (i.e., response time) by an MDP approach. First we derive the so-called size-aware relative values of states with respect to the sojourn time in an M/G/1 queue operating under FIFO, LIFO, SPT or SRPT disciplines. For FIFO and LIFO, the size-aware relative values turn out to be insensitive to the form of the job size distribution. The relative values are then exploited in developing efficient dispatching rules in the spirit of the first policy iteration.

Energy-aware job assignment in server farms with setup delays under LCFS and PS

“…Such simple policies are no longer optimal when there is a setup delay. The job assignment problem has been approached also within the Markov decision problem (MDP) framework, see, e.g., [15]- [17]. The idea is to start with an arbitrary static policy, and then carry out the first policy iteration (FPI) step.…”

Lookahead actions in dispatching to parallel queues

“…In our context, a static basic policy α 0 feeds a Poisson process to each queue and the system decomposes to k independent M/G/1-FCFS queues. The value function of a size-aware M/G/1-FCFS queue is quadratic [22], and for Queue i we have…”

“…Given the so-called value function, one carries out the first policy iteration (FPI) step, which typically yields the greatest improvement towards the optimal policy. In the context of dispatching problems, this approach has been utilized to minimize the blocking probability, see Krishnan [15,16] and Leeuwaarden et al [17], and the sojourn time (i.e., delay or latency) or its generalization by arbitrary holding costs, see, e.g., Krishnan [18], Sassen et al [19], Bhulai et al [20] and Hyytiä et al [21][22][23]. Most dispatching systems considered have a rather complex state space (e.g., infinite number of waiting places, a continuous range of remaining service time, etc.)…”

Optimal Routing of Fixed Size Jobs to Two Parallel Servers

“…Typically the basic policy is static (e.g. RND), as then the system decomposes and the corresponding value function is straightforward to compute (see, e.g., Krishnan, 1990;Bhulai, 2006;Hyytiä et al, 2012b)). The downside is that the static basic policy effectively separates the servers immediately after the decision and dependencies between the queues are not present in the cost estimates.…”