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

2016/03/11 by Dongyuan Zhan, Zhan, Dongyuan, Gideon Weiss +1
Mathematics · #60J28 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J28

paper · pdf · doi:10.48550/arxiv.1603.03571

arxiv created 2016/03/11 · arxiv updated 2016/03/14

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.

Related

• Law of Large Numbers Limits for Many Server Queues
• Validity of heavy-traffic steady-state approximations in many-server queues with abandonment
• Fluid Models of Parallel Service Systems under FCFS
• Design Heuristic for Parallel Many Server Systems under FCFS-ALIS
• Fluid limits of many-server queues with state dependent service rates