Utility Optimal Scheduling in Processing Networks

TL;DR

This paper introduces the Perturbed Max-Weight algorithm (PMW) for scheduling in processing networks, effectively balancing utility optimization and backlog management despite the underflow problem.

Contribution

It develops a novel perturbation-based Max-Weight algorithm that achieves near-optimal utility while controlling network backlog in processing networks.

Findings

PMW achieves utility within O(1/V) of optimal for any V ≥ 1.

PMW maintains an average backlog of O(V).

The algorithm effectively avoids underflows in queue levels.

Abstract

We consider the problem of utility optimal scheduling in general \emph{processing networks} with random arrivals and network conditions. These are generalizations of traditional data networks where commodities in one or more queues can be combined to produce new commodities that are delivered to other parts of the network. This can be used to model problems such as in-network data fusion, stream processing, and grid computing. Scheduling actions are complicated by the \emph{underflow problem} that arises when some queues with required components go empty. In this paper, we develop the Perturbed Max-Weight algorithm (PMW) to achieve optimal utility. The idea of PMW is to perturb the weights used by the usual Max-Weight algorithm to ``push'' queue levels towards non-zero values (avoiding underflows). We show that when the perturbations are carefully chosen, PMW is able to achieve a utility that is within $O(1/V)$ of the optimal value for any $V\geq1$, while ensuring an average network backlog of $O(V)$.