Minimizing Slowdown in Heterogeneous Size-Aware Dispatching Systems (full version)

TL;DR

This paper develops and analyzes size-aware dispatching policies for heterogeneous queue systems to minimize mean slowdown, demonstrating the optimality of SPTP scheduling and proposing improved dispatching strategies.

Contribution

It proves the optimality of SPTP scheduling for slowdown in single-server queues and derives size-aware value functions for various queue disciplines, leading to better dispatching policies.

Findings

SPTP minimizes slowdown in single-server queues.

Derived size-aware value functions for multiple queue disciplines.

Proposed dispatching policies outperform existing methods.

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 so-called size-aware value functions for M/G/1-FIFO/LIFO/SPTP/SPT/SRPT 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.