System Stability Under Adversarial Injection of Dependent Tasks

TL;DR

This paper analyzes the stability of distributed systems with dependent tasks under adversarial job arrivals, exploring conditions for system stability or instability based on scheduling policies and task dependencies.

Contribution

It extends adversarial queuing theory to systems with dependent tasks, providing new stability and instability results under various conditions.

Findings

Identifies conditions for system stability under different scheduling policies.

Demonstrates scenarios leading to system instability with dependent tasks.

Generalizes previous models to include task dependencies and adversarial arrivals.

Abstract

In this work, we consider a computational model of a distributed system formed by a set of servers in which jobs, that are continuously arriving, have to be executed. Every job is formed by a set of dependent tasks (i.~e., each task may have to wait for others to be completed before it can be started), each of which has to be executed in one of the servers. The arrival of jobs and their properties is assumed to be controlled by a bounded adversary, whose only restriction is that it cannot overload any server. This model is a non-trivial generalization of the Adversarial Queuing Theory model of Borodin et al., and, like that model, focuses on the stability of the system: whether the number of jobs pending to be completed is bounded at all times. We show multiple results of stability and instability for this adversarial model under different combinations of the scheduling policy used at the servers, the arrival rate, and the dependence between tasks in the jobs.