TY - JOUR

T1 - Join-Idle-Queue system with general service times

T2 - Large-scale limit of stationary distributions

AU - Foss, Sergey

AU - Stolyar, Alexander L.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85041422385&partnerID=8YFLogxK

U2 - 10.1145/3152042.3152058

DO - 10.1145/3152042.3152058

M3 - Article

AN - SCOPUS:85041422385

VL - 45

SP - 45

EP - 47

JO - Performance Evaluation Review

JF - Performance Evaluation Review

SN - 0163-5999

IS - 2

ER -