Minimizing slowdown in heterogeneous size-aware dispatching systems

Abstract

We consider a system of parallel queues where tasks are assigned (dispatched) to one of the available servers upon arrival. The dispatching decision is based on the full state information, i.e., on the sizes of the new and existing jobs. We are interested in minimizing the so-called mean slowdown criterion corresponding to the mean of the sojourn time divided by the processing time. Assuming no new jobs arrive, the shortest-processing-time-product (SPTP) schedule is known to minimize the slowdown of the existing jobs. The main contribution of this paper is three-fold: 1) To show the optimality of SPTP with respect to slowdown in a single server queue under Poisson arrivals; 2) to derive the socalled size-aware value functions for M/G/1-FIFO/LIFO/ SPTP with general holding costs of which the slowdown criterion is a special case; and 3) to utilize the value functions to derive efficient dispatching policies so as to minimize the mean slowdown in a heterogeneous server system. The derived policies offer a significantly better performance than e.g., the size-aware-task-assignment with equal load (SITA-E) and least-work-left (LWL) policies.

Task assignment in a heterogeneous server farm with switching delays and general energy-aware cost structure

“…In this paper, we extend earlier results [4,5] for the M/G/1 queue in several respects. First, we include a switching delay, which is an important system characteristic when, e.g., a server in a data center is switched off in order to save energy.…”

“…See also Aalto and Virtamo [26]. Recently, FCFS, LCFS, SPT and SRPT queues were analyzed in [4,5] with a general service time distribution. Similarly, PS is considered in [27,28].…”

Load balancing of elastic data traffic in heterogeneous wireless networks

“…In this chapter, we consider some of the important existing task assignment policies for distributed systems based on [9,19,8,20,21,22,23,24,25]. In the first section, a distributed server system is introduced.…”

“…A third performance goal is fairness where all kinds of jobs, whether short or long, should experience the same expected slowdown. The dispatching problem is a joint-optimization problem of two interacting policies: (i) A dispatching policy assigning a queue for each job immediately upon arrival, and (ii) an internal scheduling policy of the queues, i.e., queuing discipline or service order [19]. It is assumed that the job sizes are independently and identically distributed according to a general job size distribution and that the arrival process of jobs to the servers is a Poisson process.…”

Lookahead actions in dispatching to parallel queues

“…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.)…”