Steady-state analysis of load-balancing algorithms in the sub-Halfin–Whitt regime

We study a class of load-balancing algorithms for many-server systems (N servers). Each server has a buffer of size $b-1$ with $b=O(\sqrt{\log N})$, i.e. a server can have at most one job in service and $b-1$ jobs queued. We focus on the steady-state performance of load-balancing algorithms in the h...

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Vydané v:Journal of applied probability Ročník 57; číslo 2; s. 578 - 596
Hlavní autori: Liu, Xin, Ying, Lei
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cambridge, UK Cambridge University Press 01.06.2020
Applied Probability Trust
Predmet:
Algorithms
Approximation
Employment
Load balancing
Queues
Random variables
Research Papers
Servers
Steady state
steady state
Stein’s method
load balancing
mean-field model
asymptotic zero delay
90B15
heavy traffic
state space collapse
68M20
60K25
Many-server systems
ISSN:0021-9002, 1475-6072
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Shrnutí:We study a class of load-balancing algorithms for many-server systems (N servers). Each server has a buffer of size $b-1$ with $b=O(\sqrt{\log N})$, i.e. a server can have at most one job in service and $b-1$ jobs queued. We focus on the steady-state performance of load-balancing algorithms in the heavy traffic regime such that the load of the system is $\lambda = 1 - \gamma N^{-\alpha}$ for $0<\alpha<0.5$ and $\gamma > 0,$ which we call the sub-Halfin–Whitt regime ($\alpha=0.5$ is the so-called Halfin–Whitt regime). We establish a sufficient condition under which the probability that an incoming job is routed to an idle server is 1 asymptotically (as $N \to \infty$) at steady state. The class of load-balancing algorithms that satisfy the condition includes join-the-shortest-queue, idle-one-first, join-the-idle-queue, and power-of-d-choices with $d\geq \frac{r}{\gamma}N^\alpha\log N$ (r a positive integer). The proof of the main result is based on the framework of Stein’s method. A key contribution is to use a simple generator approximation based on state space collapse.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2020.13