Many Server Scaling of the N-System Under FCFS-ALIS

TL;DR

This paper investigates the behavior of a multi-server N-System under FCFS-ALIS policy when both arrivals and servers are scaled up, providing fluid and diffusion approximations for its steady state, advancing understanding of large-scale service systems.

Contribution

It introduces the first analysis of the many-server limit behavior of the N-System with explicit steady state distribution under simultaneous scaling.

Findings

Derived fluid and central limit approximations for the scaled system

Established the first step towards understanding large-scale parallel service systems

Provided explicit steady state distribution for the N-System

Abstract

The N-System with independent Poisson arrivals and exponential server-dependent service times under first come first served and assign to longest idle server policy has explicit steady state distribution. We scale the arrival and the number of servers simultaneously, and obtain the fluid and central limit approximation for the steady state. This is the first step towards exploring the many server scaling limit behavior of general parallel service systems.