Fluid Models of Parallel Service Systems under FCFS

TL;DR

This paper develops fluid models for parallel service systems under FCFS, identifying conditions for resource pooling and throughput optimality, and analyzing how service time distributions affect matching rates through simulations.

Contribution

It introduces deterministic fluid approximations for FCFS parallel systems and links system structure and service times to resource pooling and throughput performance.

Findings

Resource pooling conditions depend on system structure and service times.

FCFS with the compatibility tree achieves throughput optimality.

Matching rates vary with service time distribution, confirmed by simulations.

Abstract

We study deterministic fluid approximations of parallel service systems operating under first come first served policy (FCFS). The condition for complete resource pooling is identified in terms of the system structure and the customer service times. The static planning linear programming approach (Harrison and Lopez \cite{harrison-lopez:99}) is used to obtain a maximum throughput compatibility tree and to show that FCFS using this compatibility tree is throughput optimal. We investigate matching rates and show by Hotelling's $T^2$-test and simulation that they are dependent on the service time distribution.