Simulative Comparison of the Waiting Time Distributions in Cyclic Polling Systems with Different Service Strategies

Charzinski, Joachim; Renger, Thomas; Tangemann, M.

doi:10.1016/b978-0-444-82031-0.50077-9

Cited by 6 publications

(5 citation statements)

References 2 publications

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“…The interest for this model is fueled by a number of different application areas. That is, the k-limited strategy did not only prove its merit in communication systems (see, e.g., [5,8]), but also in the field of logistics (see, e.g. [28]), and vehicle actuated traffic signals [4].…”

Section: Introductionmentioning

confidence: 99%

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Boon¹,

Winands²

2014

Prob. Eng. Inf. Sci.

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In this paper, we study a two-queue polling model with zero switchover times and klimited service (serve at most k i customers during one visit period to queue i, i = 1, 2) in each queue. The arrival processes at the two queues are Poisson, and the service times are exponentially distributed. By increasing the arrival intensities until one of the queues becomes critically loaded, we derive exact heavy-traffic limits for the joint queue-length distribution using a singular-perturbation technique. It turns out that the number of customers in the stable queue has the same distribution as the number of customers in a vacation system with Erlang-k 2 distributed vacations. The queue-length distribution of the critically loaded queue, after applying an appropriate scaling, is exponentially distributed. Finally, we show that the two queue-length processes are independent in heavy traffic.

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Section: Introductionmentioning

confidence: 99%

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Boon¹,

Winands²

2014

Prob. Eng. Inf. Sci.

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“…Significant gains in system performance have been observed in many application areas, e.g. communication [5,6]) and production systems (see, e.g. [13]), by implementing the k-limited strategy instead of the traditional exhaustive and gated strategies (see, also, [2] for a survey of applications of polling systems).…”

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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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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“…34–36 Charzinski et al described simulated polling systems. 37 They introduced the principle of measurement of distributions and quantiles in a simulation and concluded with results comparing the waiting time distributions and quantiles in systems with different service strategies and asymmetric load. Simulation is also used to compare different models, and to show the behavior of the models in various situations.…”

Section: Introductionmentioning

confidence: 99%

An efficient computer simulation–based approach for optimization of complex polling systems with general arrival distributions

2014

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This study proposes an efficient computer simulation approach for estimation and optimization of performance measures in a polling system. A single server polling system operating under exhaustive, gated, and mixed service disciplines is developed. In this system, the arrival process is a Poisson process and service and setup times are exponentially distributed. The polling model is solved through two different methods: an exact method that requires the complete characterization of the system, and a computer simulation-based solution that reduces the solving time and the complexity of the model. A set of numerical experiments are presented in which it is shown that the computer simulation model outperforms the exact method in terms of estimating a system’s performance measures. Moreover, it is shown that the optimizer simulation model is capable of handling general distributions and several queuing systems, whereas the exact method requires the complete characterization of the system through a Markov chain, which is a time-consuming and inefficient approach. In addition, the efficient computer simulation-based solution could be easily applied to polling systems with different numbers of queues and service disciplines.

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Simulative Comparison of the Waiting Time Distributions in Cyclic Polling Systems with Different Service Strategies

Cited by 6 publications

References 2 publications

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

HEAVY-TRAFFIC ANALYSIS OF K-LIMITED POLLING SYSTEMS

Critically loaded k-limited polling systems

An efficient computer simulation–based approach for optimization of complex polling systems with general arrival distributions

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