# Random Fluid Limit of an Overloaded Polling Model

@article{Remerova2014RandomFL, title={Random Fluid Limit of an Overloaded Polling Model}, author={Maria Remerova and Sergey Foss and Bert Zwart}, journal={Advances in Applied Probability}, year={2014}, volume={46}, pages={76 - 101} }

In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the joint queue length process. Under passage to the fluid dynamics, the server switches between the queues infinitely many times in any finite time interval causing frequent oscillatory behavior of the fluid limit in the neighborhood of zero. Moreover, the fluid limit is random. In addition, we suggest…

## 12 Citations

### Asymptotic Properties of a Branching-type Overloaded Polling Network

- Mathematics
- 2017

In this paper, we consider an $N$-queue overloaded polling network attended by a single cyclically roving server. Upon the completion of his service, a customer is either routed to another queue or…

### Workload analysis of a two-queue fluid polling model

- Mathematics, Computer Science
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This paper analyzes a two-queue random time-limited Markov modulated polling model, and investigates the transient process-limit of the joint workload in heavy traffic, implying that in this case the two limits (stationarity and heavy traffic) commute.

### An asymptotic property of branching-type overloaded polling networks

- Mathematics
- 2019

Abstract Remerova et al. [Random fluid limit of an overloaded polling model, Adv. Appl. Probab., 2014, 46, 76–101] studied the fluid asymptotics of the joint queue length process for an overloaded…

### Queue-Based Random-Access Algorithms: Fluid Limits and Stability Issues

- Computer ScienceArXiv
- 2013

Flood limits are examined to explore the (in)stability properties of wireless networks with queue-based random-access algorithms and find that in some situations the fluid limits have smooth deterministic features and maximum stability is maintained, while in other scenarios they exhibit random oscillatory features.

### Polling Systems and Their Application to Telecommunication Networks

- BusinessMathematics
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A review of papers on stochastic polling systems published in 2007–2020 and an investigation of how the customer service order within a queue affects the performance characteristics are presented.

### Heavy-traffic behaviour of scheduling policies in queues

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- 2018

The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.

### Characterizing Policies with Optimal Response Time Tails under Heavy-Tailed Job Sizes

- Computer ScienceProc. ACM Meas. Anal. Comput. Syst.
- 2020

The recently introduced SOAP framework is used to derive sufficient conditions on the form of prioritization used by a scheduling policy that ensure the policy is tail-optimal, and this work derives a general upper bound for fractional moments of M/G/1 busy periods.

### Characterizing Policies with Optimal Response Time Tails under Heavy-Tailed Job Sizes

- Computer ScienceAbstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems
- 2020

The recently introduced SOAP framework is used to derive sufficient conditions on the form of prioritization used by a scheduling policy that ensure the policy is tail-optimal, and this work derives a general upper bound for fractional moments of M/G/1 busy periods.

### Achievable Performance of Blind Policies in Heavy Traffic

- Computer Science, MathematicsMath. Oper. Res.
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For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm…

### Comments on: Polling: past, present and perspective

- ArtTOP
- 2018

We like to say that Sem Borst and Onno Boxma have given a nice survey of the literature and trends in the studies of stochastic polling systems. The authors are good experts who are working in the…

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