Dynamic scheduling of a system with two parallel servers: asymptotic policy in heavy traffic

This paper presents characteristics of optimal routing that assigns each arriving packet to one of two heterogeneous parallel servers, each with its own queue. The characteristics are derived from numerical solutions to an optimization problem, which is to find optimal routing that minimizes the average packet delay under the condition that all of the packets' arrival times as well as all of the packets' sizes are completely known in advance. There are four characteristics: (1) Under light or moderate traffic, the average packet delay of optimal routing is almost the same as that of join the shortest delay (JSD) policy. (2) Under heavier traffic, optimal routing comes to more often use fix queue based on size (FS) policy. (3) Under heavy traffic, optimal routing assigns small packets to the slower server. (4) As the ratio of the slower server's service rate to the faster server's service rate decreases, optimal routing comes to more often use FS policy under light or moderated traffic. These characteristics are verified by the fact that a mimic optimal routing designed based on the four characteristics attains almost the same performance as optimal routing.

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Scheduling multiclass queueing networks on parallel servers: Approximate and heavy-traffic optimality of Klimov's priority rule

Algorithms — ESA '97 - Lecture Notes in Computer Science ◽

10.1007/3-540-63397-9_18 ◽

1997 ◽

pp. 232-245 ◽

Cited By ~ 6

Author(s):

Kevin D. Glazebrook ◽

José Niño-Mora

Keyword(s):

Queueing Networks ◽

Heavy Traffic ◽

Priority Rule ◽

Multiclass Queueing Networks ◽

Parallel Servers ◽

Multiclass Queueing

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Dynamic Scheduling for Parallel Server Systems in Heavy Traffic: Graphical Structure, Decoupled Workload Matrix and some Sufficient Conditions for Solvability of the Brownian Control Problem

Stochastic Systems ◽

10.1287/14-ssy163 ◽

2016 ◽

Vol 6 (1) ◽

pp. 26-89

Author(s):

V. Pesic ◽

R. J. Williams

Keyword(s):

Control Problem ◽

Dynamic Scheduling ◽

Heavy Traffic ◽

Sufficient Conditions ◽

Parallel Server ◽

Server Systems ◽

Brownian Control Problem ◽

Graphical Structure

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Dynamic Scheduling of a Parallel Server System in Heavy Traffic with Complete Resource Pooling: Asymptotic Optimality of a Threshold Policy

Electronic Journal of Probability ◽

10.1214/ejp.v10-281 ◽

2005 ◽

Vol 10 (0) ◽

pp. 1044-1115 ◽

Cited By ~ 38

Author(s):

Steven Bell ◽

Ruth Williams

Keyword(s):

Dynamic Scheduling ◽

Heavy Traffic ◽

Asymptotic Optimality ◽

Threshold Policy ◽

Resource Pooling ◽

Parallel Server ◽

Server System

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Optimal dynamic scheduling of a general class of parallel-processing queueing systems

Advances in Applied Probability ◽

10.1017/s0001867800008831 ◽

1998 ◽

Vol 30 (04) ◽

pp. 1130-1156 ◽

Cited By ~ 1

Author(s):

Noah Gans ◽

Garrett van Ryzin

Keyword(s):

Parallel Processing ◽

Closed Form ◽

General Class ◽

Dynamic Scheduling ◽

Broad Class ◽

Heavy Traffic ◽

Queueing Systems ◽

Optimal System ◽

Call System ◽

Optimal Dynamic

In this paper we develop policies for scheduling dynamically arriving jobs to a broad class of parallel-processing queueing systems. We show that in heavy traffic the policies asymptotically minimize a measure of the expected system backlog, which we call system work. Our results yield succinct, closed-form expressions for optimal system work in heavy traffic.

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