Asymptotically optimal policies for controlled queues in heavy traffic

This paper studies a controlled queueing system in which the decisionmaker may change servers according to rules which depend only on the queue length. It is proved that for a given control policy a properly normalised sequence of these controlled queue length processes converges weakly to a controlled diffusion process as the queueing systems approach a state of heavy traffic.

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Controlled queues in heavy traffic

Advances in Applied Probability ◽

10.1017/s0001867800040854 ◽

1975 ◽

Vol 7 (03) ◽

pp. 656-671 ◽

Cited By ~ 1

Author(s):

John H. Rath

Keyword(s):

Diffusion Process ◽

Queue Length ◽

Queueing System ◽

Systems Approach ◽

Heavy Traffic ◽

Queueing Systems ◽

Control Policy ◽

Controlled Diffusion ◽

Controlled Queues

This paper studies a controlled queueing system in which the decisionmaker may change servers according to rules which depend only on the queue length. It is proved that for a given control policy a properly normalised sequence of these controlled queue length processes converges weakly to a controlled diffusion process as the queueing systems approach a state of heavy traffic.

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Optimal and Asymptotically Optimal Policies for Assemble-to-Order N- and W-Systems

SSRN Electronic Journal ◽

10.2139/ssrn.2507854 ◽

2014 ◽

Cited By ~ 4

Author(s):

Lijian Lu ◽

Jeannette Song ◽

Hanqin Zhang

Keyword(s):

Asymptotically Optimal ◽

Optimal Policies

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A Fluid-Diffusion-Hybrid Limiting Approximation for Priority Systems with Fast and Slow Customers

Operations Research ◽

10.1287/opre.2021.2154 ◽

2021 ◽

Author(s):

Lun Yu ◽

Seyed Iravani ◽

Ohad Perry

Keyword(s):

Heavy Traffic ◽

Priority Queue ◽

Costs And Benefits ◽

Fluid Limit ◽

Asymptotically Optimal ◽

Asymptotic Regime ◽

Limit Process ◽

Priority Systems ◽

Pool System ◽

Fluid Diffusion

The paper “Fluid-Diffusion-Hybrid (FDH) Approximation” proposes a new heavy-traffic asymptotic regime for a two-class priority system in which the high-priority customers require substantially larger service times than the low-priority customers. In the FDH limit, the high-priority queue is a diffusion, whereas the low-priority queue operates as a (random) fluid limit, whose dynamics are driven by the former diffusion. A characterizing property of our limit process is that, unlike other asymptotic regimes, a non-negligible proportion of the customers from both classes must wait for service. This property allows us to study the costs and benefits of de-pooling, and prove that a two-pool system is often the asymptotically optimal design of the system.

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