Achievable region with impatient customers

Kavitha, Veeraruna; Sinha, Raman Kumar

doi:10.1145/3150928.3150953

Cited by 4 publications

(8 citation statements)

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“…The achievable region is well understood in such a 'homogeneous' multi-class setting [9,10]. Interestingly, in this case, it is known that the static and dynamic achievable regions coincide (see [2]), in contrast with the 'heterogeneous' multi-class setting considered here, where we see that the static achievable region is a strict subset of the dynamic achievable region. Moreover, the achievable region in the homogeneous setting is its own Pareto frontier (i.e., all points of the achievable region are efficient) under work conserving policies, also in contrast with the heterogeneous setting considered here.…”

Section: Introductionmentioning

confidence: 75%

“…The tolerant queue in turn utilizes the service capacity left unused by the eager class in a work-conserving manner. As a result, the service processes of the two classes are interdependent (unlike in the case of static scheduling as considered in [2,3]). Our dynamic schedulers are of nested type: a top-level policy chooses the sub-policy used for scheduling the -class based on the occupancy (state) of the τ -class.…”

Section: Dynamic Schedulersmentioning

confidence: 99%

“…We formally define the dynamic achievable region in Section 5, and demonstrate the Pareto-complete family of dynamic schedulers in Section 6. Related literature: The present paper is a follow-up of our prior work [2,3], which analyses the same hererogenous queueing system under the SFJ limit for a class of (partially) static scheduling policies. Under this class of policies, the scheduling of the eager class is oblivious to the state of the tolerant queue, with the tolerant queue simply utilizing the service capacity left unused by the eager class.…”

Section: Introductionmentioning

confidence: 99%

“…This generalization, which requires a non-trivial analysis, results is a substantial expansion of the achievable region of feasible performance vectors (as is shown in Sections 5,6). Moreover, the generalization to dynamic policies necessitates the identification of a Pareto-complete family of schedulers (which is the goal of Section 6); in the restricted class of static schedulers analysed in [2,3], it turns out that all policies are efficient.…”

Section: Introductionmentioning

confidence: 99%

“…Aside from [2,3], the only prior work we are aware of that analyses a part-queueing, part-loss service system is [4]. In this paper, the authors obtain the performance metrics for all classes in closed form, assuming exponential inter-arrival and service times for all classes, under a certain static priority scheduling discipline.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Dynamic scheduling in a partially fluid, partially lossy queueing system

Chaudhary¹,

Kavitha²,

Nair³

2019

Preprint

Self Cite

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We consider a single server queueing system with two classes of jobs: eager jobs with small sizes that require service to begin almost immediately upon arrival, and tolerant jobs with larger sizes that can wait for service. While blocking probability is the relevant performance metric for the eager class, the tolerant class seeks to minimize its mean sojourn time. In this paper, we discuss the performance of each class under dynamic scheduling policies, where the scheduling of both classes depends on the instantaneous state of the system. This analysis is carried out under a certain fluid limit, where the arrival rate and service rate of the eager class are scaled to infinity, holding the offered load constant. Our performance characterizations reveal a (dynamic) pseudo-conservation law that ties the performance of both the classes to the standalone blocking probabilities of the eager class. Further, the performance is robust to other specifics of the scheduling policies. We also characterize the Pareto frontier of the achievable region of performance vectors under the same fluid limit, and identify a (two-parameter) class of Pareto-complete scheduling policies.

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Section: Introductionmentioning

confidence: 75%

Section: Dynamic Schedulersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic scheduling in a partially fluid, partially lossy queueing system

Chaudhary¹,

Kavitha²,

Nair³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Pseudo conservation for partially fluid, partially lossy queueing systems

2018

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Dynamic Scheduling in a Partially Fluid, Partially Lossy Queueing System

Chaudhary

Kavitha

Nair

2023

ACM Trans. Model. Perform. Eval. Comput. Syst.

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We consider a single server queueing system with two classes of jobs: eager jobs with small sizes that require service to begin almost immediately upon arrival, and tolerant jobs with larger sizes that can wait for service. While blocking probability is the relevant performance metric for the eager class, the tolerant class seeks to minimize its mean sojourn time. In this paper, we analyse the performance of each class under dynamic scheduling policies, where the scheduling of both classes depends on the instantaneous state of the system. This analysis is carried out under a certain fluid limit, where the arrival rate and service rate of the eager class are scaled to infinity, holding the offered load constant. Our performance characterizations reveal a (dynamic) pseudo-conservation law that ties the performance of both the classes to the standalone blocking probabilities associated with the scheduling policies for the eager class. Further, the performance is robust to other specifics of the scheduling policies. We also characterize the Pareto frontier of the achievable region of performance vectors under the same fluid limit, and identify a (two-parameter) class of Pareto-complete scheduling policies.

show abstract

Achievable region with impatient customers

Cited by 4 publications

References 4 publications

Dynamic scheduling in a partially fluid, partially lossy queueing system

Dynamic scheduling in a partially fluid, partially lossy queueing system

Pseudo conservation for partially fluid, partially lossy queueing systems

Dynamic Scheduling in a Partially Fluid, Partially Lossy Queueing System

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