Research output: Contribution to journal › Article › peer-review
Large-scale join-idle-queue system with general service times. / Foss, S.; Stolyar, A. L.
In: Journal of Applied Probability, Vol. 54, No. 4, 01.12.2017, p. 995-1007.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Large-scale join-idle-queue system with general service times
AU - Foss, S.
AU - Stolyar, A. L.
PY - 2017/12/1
Y1 - 2017/12/1
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 routed to one of the servers immediately upon arrival. The join-idle-queue routeing 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 at λ / μ. In particular, this implies that the steady-state probability of an arriving customer waiting 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 routed to one of the servers immediately upon arrival. The join-idle-queue routeing 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 at λ / μ. In particular, this implies that the steady-state probability of an arriving customer waiting for service vanishes.
KW - asymptotic optimality
KW - fluid limit
KW - join-idle-queue
KW - Large-scale service system
KW - load balancing
KW - pull-based load distribution
KW - stationary distribution
KW - LOAD DISTRIBUTION
KW - SERVERS
UR - http://www.scopus.com/inward/record.url?scp=85041353326&partnerID=8YFLogxK
U2 - 10.1017/jpr.2017.49
DO - 10.1017/jpr.2017.49
M3 - Article
AN - SCOPUS:85041353326
VL - 54
SP - 995
EP - 1007
JO - Journal of Applied Probability
JF - Journal of Applied Probability
SN - 0021-9002
IS - 4
ER -
ID: 9445322