Pseudo conservation for partially fluid, partially lossy queueing systems

Kavitha, Veeraruna; Nair, Jayakrishnan; Sinha, Raman Kumar

doi:10.1007/s10479-018-2780-8

Cited by 2 publications

(17 citation statements)

References 20 publications

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“…We would like to refer the equation ( 2) as a pseudo conservation law, as it provides the expected sojourn time in terms of the fraction blocked (lost). This would require an explicit proof which is considered in [15]. For now, we consider two example families of schedulers and illustrate the validity of our conjecture.…”

Section: Conjecture Of a Pseudo Conservation Lawmentioning

confidence: 87%

“…We conjecture that given a probability of blocking, irrespective of the way the -agents are blocked and irrespective of the way the τ -agents are served, the τ -expected sojourn time remains the same 2 . And this could be conjectured only in SFJ limit and when the policies do not depend upon the τ -state (The proof of this conjecture is considered in [15]).…”

Section: Conjecture Of a Pseudo Conservation Lawmentioning

confidence: 96%

“…Performance: Using exactly the same logic as in the previous model, one can show that the expected sojourn time of the CD model can also be obtained as limit of the expected sojourn times of M/G/1 queues with service time moments given by that of Υ0 τ of Theorem 1. To complete the analysis, one also needs to show the ergoidicity of the original system which is considered in [15]. Thus the achievable region in the SFJ limit is given by (Appendix B):…”

Section: Expected Sojourn Time and Achievable Regionmentioning

confidence: 99%

“…To the best of our knowledge we are not aware of a work that directly studies this type of a heterogeneous achievable region. Some variants of queueing systems (e.g., [3], [6], [8], [12], [11], [13], [17] etc) have some connections to few parts of our models, and these are discussed in [15].…”

Section: Introductionmentioning

confidence: 99%

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Queuing with Heterogeneous Users: Block Probability and Sojourn times

Kavitha,

Sinha

2017

Preprint

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Communication networks need to support voice and data calls simultaneously. This results in a queueing system with heterogeneous agents. One class of agents demand immediate service, would leave the system if not provided. The second class of customers have longer job requirements and can wait for their turn. We discuss the achievable region of such a two class system, which is the region of all possible pairs of performance metrics. Blocking probability is the relevant performance for eager/impatient class while the expected sojourn time is appropriate for the second tolerant class. We obtain the achievable region, considering static policies that do not depend upon the state of the second class. We conjecture a pseudo conservation law, in a fluid limit for eager customers, which relates the blocking probability of eager customers with the expected sojourn time of the tolerant customers. Using this conjecture we obtain the static achievable region. We validate the pseudo conservation law using two example families of static schedulers, both of which achieve all the points on the achievable region. Along the way we obtain smooth control (sharing) of resources between voice and data calls. We also consider an example dynamic policy to establish that the dynamic achievable region is strictly bigger than the static region, for this heterogeneous queueing system.Index terms-Heterogeneous users, achievable region, processor sharing, capacity division, dynamic and static scheduling.

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Section: Conjecture Of a Pseudo Conservation Lawmentioning

confidence: 87%

Section: Conjecture Of a Pseudo Conservation Lawmentioning

confidence: 96%

Section: Expected Sojourn Time and Achievable Regionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Queuing with Heterogeneous Users: Block Probability and Sojourn times

Kavitha,

Sinha

2017

Preprint

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“…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%

Dynamic scheduling in a partially fluid, partially lossy queueing system

Chaudhary¹,

Kavitha²,

Nair³

2019

Preprint

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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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Pseudo conservation for partially fluid, partially lossy queueing systems

Cited by 2 publications

References 20 publications

Queuing with Heterogeneous Users: Block Probability and Sojourn times

Queuing with Heterogeneous Users: Block Probability and Sojourn times

Dynamic scheduling in a partially fluid, partially lossy queueing system

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