Waiting time dynamics of priority-queue networks

TL;DR

This paper investigates the dynamics of priority-queue networks, revealing how different interaction protocols and network topologies influence waiting time distributions, which often follow power-law behaviors with model-dependent exponents.

Contribution

It introduces a scalable OR-type interaction protocol for priority-queue networks and analyzes how network structure and synchronization affect waiting time distributions.

Findings

Waiting time distributions follow power-law tails with model-dependent exponents.

The OR-type protocol overcomes the scalability issues of the original protocol.

Synchronization in task execution influences the power-law exponent of waiting times.

Abstract

We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A {\bf 388}, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.