scholarly journals Instability of the Join-the-Shortest-Queue and FCFS Policies in Queueing Systems and Their Stabilization

1997 ◽  
Vol 45 (2) ◽  
pp. 309-314 ◽  
Author(s):  
Ali Sharifnia
Keyword(s):  
Queueing Systems ◽  
Join The Shortest Queue ◽  
Shortest Queue

Subdiffusive Load Balancing in Time-Varying Queueing Systems

2019 ◽  
Vol 67 (6) ◽  
pp. 1678-1698
Author(s):  
Rami Atar ◽  
Isaac Keslassy ◽  
Gal Mendelson
Keyword(s):  
Load Balancing ◽  
Queue Length ◽  
Queueing Systems ◽  
Load Condition ◽  
Service Rates ◽  
Queue Lengths ◽  
Join The Shortest Queue ◽  
The Difference ◽  
Shortest Queue ◽  
Diffusion Scale

The degree to which delays or queue lengths equalize under load-balancing algorithms gives a good indication of their performance. Some of the most well-known results in this context are concerned with the asymptotic behavior of the delay or queue length at the diffusion scale under a critical load condition, where arrival and service rates do not vary with time. For example, under the join-the-shortest-queue policy, the queue length deviation process, defined as the difference between the greatest and smallest queue length as it varies over time, is at a smaller scale (subdiffusive) than that of queue lengths (diffusive).

scholarly journals Steady-State Analysis of the Join-the-Shortest-Queue Model in the Halfin–Whitt Regime

2020 ◽  
Vol 45 (3) ◽  
pp. 1069-1103
Author(s):  
Anton Braverman
Keyword(s):  
Steady State ◽  
Diffusion Limit ◽  
Fluid Limit ◽  
Time Intervals ◽  
Dimensional Diffusion ◽  
Queue Model ◽  
Join The Shortest Queue ◽  
Shortest Queue ◽  
Process Level ◽  
General Tool

This paper studies the steady-state properties of the join-the-shortest-queue model in the Halfin–Whitt regime. We focus on the process tracking the number of idle servers and the number of servers with nonempty buffers. Recently, Eschenfeldt and Gamarnik proved that a scaled version of this process converges, over finite time intervals, to a two-dimensional diffusion limit as the number of servers goes to infinity. In this paper, we prove that the diffusion limit is exponentially ergodic and that the diffusion scaled sequence of the steady-state number of idle servers and nonempty buffers is tight. Combined with the process-level convergence proved by Eschenfeldt and Gamarnik, our results imply convergence of steady-state distributions. The methodology used is the generator expansion framework based on Stein’s method, also referred to as the drift-based fluid limit Lyapunov function approach in Stolyar. One technical contribution to the framework is to show how it can be used as a general tool to establish exponential ergodicity.

scholarly journals Multiple-server system with flexible arrivals

2011 ◽  
Vol 43 (4) ◽  
pp. 985-1004 ◽  
Author(s):  
Osman T. Akgun ◽  
Rhonda Righter ◽  
Ronald Wolff
Keyword(s):  
Finite Buffers ◽  
Service Production ◽  
Weak Majorization ◽  
Service Rates ◽  
Join The Shortest Queue ◽  
Traffic Systems ◽  
Shortest Queue ◽  
Performance Gains ◽  
Number Of Customers ◽  
Server System

In many service, production, and traffic systems there are multiple types of customers requiring different types of ‘servers’, i.e. different services, products, or routes. Often, however, a proportion of the customers are flexible, i.e. they are willing to change their type in order to achieve faster service, and even if this proportion is small, it has the potential of achieving large performance gains. We generalize earlier results on the optimality of ‘join the shortest queue’ (JSQ) for flexible arrivals to the following: arbitrary arrivals where only a subset are flexible, multiple-server stations, and abandonments. Surprisingly, with abandonments, the optimality of JSQ for minimizing the number of customers in the system depends on the relative abandonment and service rates. We extend our model to finite buffers and resequencing. We assume exponential service. Our optimality results are very strong; we minimize the queue length process in the weak majorization sense.

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