Non-Cooperative Scheduling of Multiple Bag-of-Task Applications

TL;DR

This paper analyzes how multiple non-cooperative schedulers compete for resources in heterogeneous platforms, deriving equilibrium behaviors and assessing their efficiency and fairness.

Contribution

It provides a closed-form characterization of Nash equilibria in non-cooperative scheduling of bag-of-task applications on master-worker platforms.

Findings

Nash equilibrium formulas for non-cooperative schedulers

Conditions where equilibrium is Pareto optimal

Equilibrium can be arbitrarily inefficient for performance measures

Abstract

Multiple applications that execute concurrently on heterogeneous platforms compete for CPU and network resources. In this paper we analyze the behavior of $K$ non-cooperative schedulers using the optimal strategy that maximize their efficiency while fairness is ensured at a system level ignoring applications characteristics. We limit our study to simple single-level master-worker platforms and to the case where each scheduler is in charge of a single application consisting of a large number of independent tasks. The tasks of a given application all have the same computation and communication requirements, but these requirements can vary from one application to another. In this context, we assume that each scheduler aims at maximizing its throughput. We give closed-form formula of the equilibrium reached by such a system and study its performance. We characterize the situations where this Nash equilibrium is optimal (in the Pareto sense) and show that even though no catastrophic situation (Braess-like paradox) can occur, such an equilibrium can be arbitrarily bad for any classical performance measure.