HEAVY-TRAFFIC ANALYSIS OF <i>K</i>-LIMITED POLLING SYSTEMS

Boon, Marko; Winands, Emm Erik

doi:10.1017/s0269964814000096

Cited by 9 publications

(13 citation statements)

References 23 publications

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“…The three results are obtained by equating the O(1), O(δ), and O(δ 2 ) terms in the set of equations from the previous subsection. These steps follow the line of reasoning introduced in [4] and, therefore, the details are omitted in interest of space.…”

Section: Resultsmentioning

confidence: 99%

“…The approach in the present note has its origin in [4], where systems with zero switch-over times are studied. At face value the extension to nonzero switch-over times may seem a small one, however this extension impels us to, considerably, modify and extend the analysis in [4]. This reveals itself clearly in the determination of the parameter of the exponential distribution for the scaled queue length of the critically loaded queue.…”

Section: Introductionmentioning

confidence: 99%

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Critically loaded k-limited polling systems

Boon¹,

Winands

2016

Proceedings of the 9th EAI International Conference on Performance Evaluation Methodologies and Tools

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We consider a two-queue polling model with switch-over times and k-limited service (serve at most k i customers during one visit period to queue i) in each queue. The major benefit of the k-limited service discipline is that it -besides bounding the cycle time -effectuates prioritization by assigning different service limits to different queues. System performance is studied in the heavy-traffic regime, in which one of the queues becomes critically loaded with the other queue remaining stable. By using a singular-perturbation technique, we rigorously prove heavy-traffic limits for the joint queue-length distribution. Moreover, it is observed that an interchange exists among the first two moments in service and switch-over times such that the HT limits remain unchanged. Not only do the rigorously proven results readily carry over to N (≥ 2) queue polling systems, but one can also easily relax the distributional assumptions. The results and insights of this note prove their worth in the performance analysis of Wireless Personal Area Networks (WPAN) and mobile networks, where different users compete for access to the shared scarce resources.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Critically loaded k-limited polling systems

Boon¹,

Winands

2016

Proceedings of the 9th EAI International Conference on Performance Evaluation Methodologies and Tools

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“…5. The singular-perturbation technique applied in the heavy traffic In the heavy traffic, Morrison and Boon both provide rigorous proofs of the heavy-traffic asysmptotics with the singular-perturbation technique in [5,18]. Since the singular-perturbation technique only depends on the balance equations, it is easy to extend it to polling systems with multiple queues.…”

Section: The Light Traffic and Heavy Traffic Asymptotics For Multiplementioning

confidence: 99%

On the three-queue priority polling system with threshold service policy

Liu

Chu

2016

J. Appl. Math. Comput.

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In this paper, a priority polling system consisting of three M/M/1 queues, served by a single server is investigated. Queue 1 has the Head-of-Line (HoL) priority and Queue 2 has a higher priority over Queue 3 with threshold N . All the switches are instantaneous and preempting. Using the Kernel method we derive the probability of generating functions of the stationary joint queue-length distributions, which yields the mean queue lengths and the mean sojourn times. Furthermore, we consider the limit behaviors in the light-traffic and heavy-traffic scenarios. And an interpolation approximation for the sojourn times utilizing the light and heavy traffic limits are illustrated. To test the validity, we also undertake some simulation works.

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“…The singular-perturbation technique was first applied to investigate the heavytraffic behavior of interacting queues in [9]. Later, Boon and Winands [10] used this technique to a model with k-limited policies and presented the heavy-traffic behavior. It is noted that the singular-perturbation technique can be easily extended to a multi-queue system since it only needs the balance equations.…”

Section: Introductionmentioning

confidence: 99%

Heavy-traffic asymptotics of a priority polling system with threshold service policy

Liu

Chu

2016

Computers & Operations Research

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In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system consisting of three M/M/1 queues with threshold policy. It turns out that the scaled queue-length of the critically loaded queue is exponentially distributed, independent of that of the stable queues. In addition, the queue lengths of stable queues possess the same distributions as a priority polling system with N -policy vacation. Based on this fact, we provide the exact tail asymptotics of the vacation polling system to approximate the tail distribution of the queue lengths of the stable queues, which shows that it has the same prefactors and decay rates as the classical M/M/1 preemptive priority queues. Finally, a stochastic simulation is taken to test the results aforementioned.

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HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Cited by 9 publications

References 23 publications

Critically loaded k-limited polling systems

Critically loaded k-limited polling systems

On the three-queue priority polling system with threshold service policy

Heavy-traffic asymptotics of a priority polling system with threshold service policy

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