Optimal surplus capacity utilization in polling systems via fluid models

Rawal, Ayush; Kavitha, Veeraruna; Gupta, Manu K.

doi:10.1109/wiopt.2014.6850323

Cited by 10 publications

(11 citation statements)

References 23 publications

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“…Researchers in this field have come up with geometrical structure of achievable region in case of multiple servers and even for networks of queues ( [18], [19]). Unbounded achievable region for mean waiting time in two class deterministic polling system (non work conserving) is recently identified in [20]. Note that achievable region described in literature so for is with respect to mean waiting time.…”

Section: A Related Literaturementioning

confidence: 98%

“…Optimal pricing and admission control problem for two classes is solved by exploiting the completeness structure of delay dependent priority queue (see [25] and [26]). Optimal control policy in two class polling system for certain optimization problems using achievable region approach is recently developed in [20]. This paper introduces the notion of achievable region for second moment of waiting time in single class queue for non pre-emptive, non anticipative and work conserving scheduling policies.…”

Section: A Related Literaturementioning

confidence: 99%

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On 2-moment completeness of non pre-emptive, non anticipative work conserving scheduling policies in some single class queues

Gupta

Hemachandra

2015

2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)

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Completeness of some scheduling policies with mean waiting time performance measure is used quiet extensively in literature for dynamic control of multi-class queues due to its wide range of applications in computers, communication networks and manufacturing systems. For a single class queue, we introduce the idea of 2-moment completeness of a parametrized class of policies that also have to be non pre-emptive, non anticipative and work conserving. Significance of this idea lies in the importance of variance (or second moment) of waiting time in any queuing system. Some parametrized classes of policies are identified and shown to be 2-moment complete for M/M/1 queues. Some well known queue disciplines viz random order of service (ROS), Random Assigned Priority (RAP), etc., turn out to be 2-moment incomplete. We introduce a parametrized priority scheme that also turns out to be 2-moment incomplete. Further, few preemptive and anticipative scheduling disciplines are shown to have second moment beyond the achievable region of non pre-emptive, non anticipative and work conserving scheduling policies. Some optimal control problems are discussed to illustrate the possible applications of 2-moment complete parametrized set of policies.

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Section: A Related Literaturementioning

confidence: 98%

Section: A Related Literaturementioning

confidence: 99%

On 2-moment completeness of non pre-emptive, non anticipative work conserving scheduling policies in some single class queues

Gupta

Hemachandra

2015

2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)

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“…Some further results on sensitivity of optimal operating parameters for the model described in [24] can be seen in [11]. Optimal control policy in two class polling system (non work conserving) for certain optimization problems using achievable region approach is recently developed in [22]. Note that in each of these, a suitable class of parametrized dynamic priority schemes are used; to ensure optimality, such classes have to be complete as discussed below.…”

Section: Introductionmentioning

confidence: 99%

“…Researchers in this field have come up with geometrical structure of achievable region in case of multiple servers and even for some networks (See [9], [6]). Unbounded achievable region of mean waiting time is recently identified in [22] for two class deterministic polling system. Consider a service system for which demand consists of different types of jobs, for example computer systems, production facility, etc.…”

Section: Introductionmentioning

confidence: 99%

On mean waiting time completeness and equivalence of EDD and HOL-PJ dynamic priority in 2-class M/G/1 queue

Gupta¹,

Hemachandra²,

Venkateswaran³

2015

Proceedings of the 8th International Conference on Performance Evaluation Methodologies and Tools

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This paper identifies two different parametrized dynamic priority queue disciplines, earliest due date (EDD) based and head of line priority jump (HOL-PJ), which are found to be mean waiting time complete in two class M/G/1 queue. An explicit one-to-one non linear transformation is obtained between earliest due date and delay dependent priority policy. Mean waiting time equivalence between these queue disciplines is established. Motivation behind the mean completeness and equivalence results is discussed from optimal control perspective. Notion of minmax fairness is introduced and it is argued that a simple global FCFS policy is the only solution for minmax fairness problem in two class by exploiting completeness in the structure of EDD based dynamic priority. Further, these completeness results are used to propose a simpler way for developing optimal control policy in celebrated c/ρ rule for two class M/G/1 queues.

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“…One of the main tools for such control problems is to characterize the achievable region for performance measure of interest, then use optimization methods to find optimal control policy (see [17], [18], [19]). Optimal control policy for certain non linear optimization problems for two class work conserving queueing systems is derived in [20].…”

mentioning

confidence: 99%

Performance analysis and decomposition results for some dynamic priority schemes in 2-class queues

Mayekar

Venkateswaran

Gupta

et al. 2015

2015 13th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt)

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Many device to device communication networks can be modelled by multi-class tandem queues. In many applications, it is desired to have different quality of service for various classes. This can be achieved by implementing dynamic priority across classes. Performance analysis is an important aspect in such multi-class tandem queueing models for resource allocation. In this paper, we analyse two important, relatively complex and analytically intractable performance measures, tail probability and switching frequency, for two class queueing system with two different (relative and earliest due date based) dynamic priority schemes across classes. Such a two class queueing system can be used to model voice and data calls in communication networks. A simulator is built to analyse such queueing systems and various observations are made. Based on computational evidence, it is conjectured that two stage exponential queueing network with two classes of customers is decomposable as far as mean waiting times are concerned when relative priority is used across classes to schedule the customers. Based on further experiments, it is conjectured that departure processes with relative dynamic priority are indeed Poisson in two class exponential queue. We also conduct relevant statistical analysis in support of the conjectures.

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Optimal surplus capacity utilization in polling systems via fluid models

Cited by 10 publications

References 23 publications

On 2-moment completeness of non pre-emptive, non anticipative work conserving scheduling policies in some single class queues

On 2-moment completeness of non pre-emptive, non anticipative work conserving scheduling policies in some single class queues

On mean waiting time completeness and equivalence of EDD and HOL-PJ dynamic priority in 2-class M/G/1 queue

Performance analysis and decomposition results for some dynamic priority schemes in 2-class queues

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