Abstract
A parallel server system with n identical servers is considered. The service time distribution has a finite mean 1/μ, but otherwise is arbitrary. Arriving customers are to be routed to one of the servers immediately upon arrival. Join-Idle-Queue routing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where n → ∞ and the customer input flow rate is λn. Under the condition λ/μ < 1/2, we prove that, as n → ∞, the sequence of (appropriately scaled) stationary distributions concentrates at the natural equilibrium point, with the fraction of occupied servers being constant equal λ/μ. In particular, this implies that the steady-state probability of an arriving customer having to wait for service vanishes.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 45-47 |
| Number of pages | 3 |
| Journal | Performance Evaluation Review |
| Volume | 45 |
| Issue number | 2 |
| DOIs | |
| State | Published - Sep 1 2017 |
| Event | Workshop on MAthematical Performance Modeling and Analysis, MAMA 2017, 2017 Greenmetrics Workshop and Workshop on Critical Infrastructure Network Security, CINS 2017 - Urbana-Champaign, United States Duration: Jun 1 2017 → … |
ASJC Scopus subject areas
- Software
- Hardware and Architecture
- Computer Networks and Communications