On Stability and Sojourn Time of Peer-to-Peer Queuing Systems

TL;DR

This paper investigates the stability and sojourn time of peer-to-peer queuing systems with randomly arriving and departing jobs and servers, extending analysis beyond exponential workloads and providing bounds on job sojourn time.

Contribution

It extends stability analysis to general workload distributions and derives bounds for job sojourn time in P2P queue systems.

Findings

Stability conditions are established for general workload distributions.

Upper and lower bounds for job sojourn time are derived.

Numerical analysis shows bounds' tightness.

Abstract

Recent development of peer-to-peer (P2P) services (e.g. streaming, file sharing, and storage) systems introduces a new type of queue systems that receive little attention before, where both job and server arrive and depart randomly. Current study on these models focuses on the stability condition, under exponential workload assumption. This paper extends existing result in two aspects. In the first part of the paper we relax the exponential workload assumption, and study the stability of systems with general workload distribution. The second part of the paper focuses on the job sojourn time. An upper bound and a lower bound for job sojourn time are investigated. We evaluate tightness of the bounds by numerical analysis.