TY - GEN

T1 - On Achieving Zero Delay with Power-of-d-Choices Load Balancing

AU - Liu, Xin

AU - Ying, Lei

N1 - Funding Information:
This work was supported in part by NSF ECCS-1547294, ECCS-1609202, ECCS-1739344 and the U.S. Office of Naval Research (ONR Grant No. N00014-15-1-2169).

PY - 2018/10/8

Y1 - 2018/10/8

N2 - Power-of-d-choices is a popular load balancing algorithm for many-server systems such as large-scale data centers. For each incoming job, the algorithm probes d servers, chosen uniformly at random from a total of N servers, and routes the job to the least loaded one. It is well known that power-of-d-choices reduces queueing delays by orders of magnitude compared to the policy that routes each incoming job to a randomly selected server. The question to be addressed in this paper is how large d needs to be so that power-of-d-choices achieves asymptotic zero delay like the join-the-shortest-queue (JSQ) algorithm, which is a special case of power-of-d-choices with d=N. We are interested in the heavy-traffic regime where the load of the system, denoted by lambda, approaches to one as N increases, and assume lambda=1-gamma N-{-alpha} for 0 < gamma < 1 and 0leqalpha < 1/6. This paper establishes that when d=omega-left(frac{1}{1-lambda}right), the probability that an incoming job is routed to a busy server is asymptotically zero, i.e. a job experiences zero queueing delay with probability one asymptotically; and when d=Oleft(frac{1}{1-lambda}right)' the probability that a job is routed to a busy server is lower bounded by a positive constant independent of N. Therefore, our results show that d=omega(frac{1}{1-lambda}) is sufficient and almost necessary for achieving zero delay with the power-of-d-choices load balancing policy.

AB - Power-of-d-choices is a popular load balancing algorithm for many-server systems such as large-scale data centers. For each incoming job, the algorithm probes d servers, chosen uniformly at random from a total of N servers, and routes the job to the least loaded one. It is well known that power-of-d-choices reduces queueing delays by orders of magnitude compared to the policy that routes each incoming job to a randomly selected server. The question to be addressed in this paper is how large d needs to be so that power-of-d-choices achieves asymptotic zero delay like the join-the-shortest-queue (JSQ) algorithm, which is a special case of power-of-d-choices with d=N. We are interested in the heavy-traffic regime where the load of the system, denoted by lambda, approaches to one as N increases, and assume lambda=1-gamma N-{-alpha} for 0 < gamma < 1 and 0leqalpha < 1/6. This paper establishes that when d=omega-left(frac{1}{1-lambda}right), the probability that an incoming job is routed to a busy server is asymptotically zero, i.e. a job experiences zero queueing delay with probability one asymptotically; and when d=Oleft(frac{1}{1-lambda}right)' the probability that a job is routed to a busy server is lower bounded by a positive constant independent of N. Therefore, our results show that d=omega(frac{1}{1-lambda}) is sufficient and almost necessary for achieving zero delay with the power-of-d-choices load balancing policy.

UR - http://www.scopus.com/inward/record.url?scp=85056152577&partnerID=8YFLogxK

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U2 - 10.1109/INFOCOM.2018.8485827

DO - 10.1109/INFOCOM.2018.8485827

M3 - Conference contribution

AN - SCOPUS:85056152577

T3 - Proceedings - IEEE INFOCOM

SP - 297

EP - 305

BT - INFOCOM 2018 - IEEE Conference on Computer Communications

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2018 IEEE Conference on Computer Communications, INFOCOM 2018

Y2 - 15 April 2018 through 19 April 2018

ER -