E. Hyytiä, S. Aalto and A. Penttinen, Minimizing Slowdown in Heterogeneous Size-Aware Dispatching Systems (full version), technical report, Aalto University, Department of Communications and Networking, 2012, This is a full version of the paper appearing in SIGMETRICS'12..
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.
Links:
BibTeX entry:
@techreport{hyytia-slowdown-tr-2012,
title = {Minimizing Slowdown in Heterogeneous Size-Aware Dispatching Systems (full version)},
author = {Esa Hyyti{\"a} and Samuli Aalto and Aleksi Penttinen},
institution = {Aalto University, Department of Communications and Networking},
type = {technical report},
note = {This is a full version of the paper appearing in SIGMETRICS'12.},
year = {2012},
month = {Mar.}
}