Random Fluid Limit of an Overloaded Polling Model

Frolkova, Maria; Foss, Sergey; Zwart, Bert

doi:10.1017/s0001867800006947

Cited by 6 publications

(26 citation statements)

References 16 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark. Remerova et al [25,Lemma 3] discuss the finiteness of E[f (B)] for the M/G/1 busy period B for a quite general class of functions f (•). They obtain bounds on moments of B that are more general but less sharp than Theorem 5.4.…”

Section: Fractional Moments Of Busy Periodsmentioning

confidence: 99%

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

Scully

Kreveld

Boxma

et al. 2020

SIGMETRICS Perform. Eval. Rev.

View full text Add to dashboard Cite

We consider the tail behavior of the response time distribution in an M/G/1 queue with heavy-tailed job sizes, specifically those with intermediately regularly varying tails. In this setting, the response time tail of many individual policies has been characterized, and it is known that policies such as Shortest Remaining Processing Time (SRPT) and Foreground-Background (FB) have response time tails of the same order as the job size tail, and thus such policies are tail-optimal. Our goal in this work is to move beyond individual policies and characterize the set of policies that are tail-optimal. Toward that end, we use the recently introduced SOAP framework to derive sufficient conditions on the form of prioritization used by a scheduling policy that ensure the policy is tail-optimal. These conditions are general and lead to new results for important policies that have previously resisted analysis, including the Gittins policy, which minimizes mean response time among policies that do not have access to job size information. As a by-product of our analysis, we derive a general upper bound for fractional moments of M/G/1 busy periods, which is of independent interest. CCS Concepts: • General and reference → Performance; • Mathematics of computing → Queueing theory; • Networks → Network performance modeling; • Computing methodologies → Model development and analysis; • Software and its engineering → Scheduling.

show abstract

Section: Fractional Moments Of Busy Periodsmentioning

confidence: 99%

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

Scully

Kreveld

Boxma

et al. 2020

SIGMETRICS Perform. Eval. Rev.

View full text Add to dashboard Cite

show abstract

“…However, hardly any attention has been given to the overloaded polling system. The few literature refers to [11][12][13][14]. By using measure-valued state descriptor, Puha et al [11] proved that the overloaded GI/GI/ processor sharing queues converge in distribution to supercritical uid models and a uid limit result is proved as rst order approximations to overloaded processor sharing queues.…”

Section: Introductionmentioning

confidence: 99%

“…Using both uid and di usion limits, Jennings et al [13] showed that the virtual waiting time process of an overloaded Multi-class FIFO( rstin-rst-out) queue with abandonments converges to a limiting deterministic uid process. Instead Remerova et al [14] showed the uid asymptotic process for the joint queue length process on an overloaded branchingtype cyclic polling system by using the asymptotic properties of multi-type branching processes.…”

Section: Introductionmentioning

confidence: 99%

“…Second, by considering the polling system with re-routing policy, we aim to study how the strikingly simple overloaded uid limit depends on the system parameters and in particular, on the routing probabilities p i,j . Actually, the work carried out here is a natural progression from [9] and a natural extension of [14] due to the exhaustiveness. Our resulting expressions are very insightful, simple to implement and suitable for optimization purposes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An asymptotic property of branching-type overloaded polling networks

et al. 2019

View full text Add to dashboard Cite

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 cyclic polling system with multigated service discipline by exploiting the connection with multi-type branching processes. In contrast to the heavy traffic behaviors, the cycle time of the overloaded polling system increases by a deterministic times over times under passage to the fluid dynamics and the fluid limit preserves some randomness. The present paper aims to extend the overloaded asymptotics in Remerova et al. [Random fluid limit of an overloaded polling model, Adv. Appl. Probab., 2014, 46, 76–101] to the corresponding polling system with general branching-type service disciplines and customer re-routing policy. A unifying overloaded asymptotic property is derived. Due to the exhaustiveness, the property is a natural extension of the classical polling model with multigated service discipline in Remerova et al. [Random fluid limit of an overloaded polling model, Adv. Appl. Probab., 2014, 46, 76–101] and provides new exact results that have not been observed before for rerouting policy. Additionally, a stochastic simulation is undertaken for the validation of the fluid limit and the optimization of the gating indexes to minimize the total population is considered as an example to demonstrate the usefulness of the random fluid limit.

show abstract

“…It is highly unusual for such random dynamics to occur, as in queueing networks typically the random characteristics vanish and deterministic limits emerge on the fluid scale. A few exceptions are known for various polling-type models as considered in [13,21,14].…”

mentioning

confidence: 99%

Queue-based Random-access Algorithms: Fluid Limits and Stability Issues

2014

View full text Add to dashboard Cite

We use fluid limits to explore the (in)stability properties of wireless networks with queue-based random-access algorithms. Queuebased random-access schemes are simple and inherently distributed in nature, yet provide the capability to match the optimal throughput performance of centralized scheduling mechanisms in a wide range of scenarios. Unfortunately, the type of activation rules for which throughput optimality has been established, may result in excessive queue lengths and delays. The use of more aggressive/persistent access schemes can improve the delay performance, but does not offer any universal maximum-stability guarantees.In order to gain qualitative insight and investigate the (in)stability properties of more aggressive/persistent activation rules, we examine fluid limits where the dynamics are scaled in space and time. In some situations, the fluid limits have smooth deterministic features and maximum stability is maintained, while in other scenarios they exhibit random oscillatory characteristics, giving rise to major technical challenges. In the latter regime, more aggressive access schemes continue to provide maximum stability in some networks, but may cause instability in others. In order to prove that, we focus on a particular network example and conduct a detailed analysis of the fluid limit process for the associated Markov chain. Specifically, we develop a novel approach based on stopping time sequences to deal with the switching probabilities governing the sample paths of the fluid limit process. Simulation experiments are conducted to illustrate and validate the analytical results.

show abstract

Random Fluid Limit of an Overloaded Polling Model

Cited by 6 publications

References 16 publications

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

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

An asymptotic property of branching-type overloaded polling networks

Queue-based Random-access Algorithms: Fluid Limits and Stability Issues

Contact Info

Product

Resources

About