Stability of periodic polling system with BMAP arrivals

Saffer, Zsolt; Telek, Miklós

doi:10.1016/j.ejor.2008.05.016

Cited by 9 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we note some papers dealing with stability conditions in polling systems. Saffer and Telek [51] establish stability conditions for a system with periodic polling, BMAP input of customers and a mixed service discipline, and generalize the results obtained in their earlier works. They note that there are three possible types of stability of a polling system:…”

Section: Stability Conditions For Polling Systemssupporting

confidence: 75%

Polling Systems and Their Application to Telecommunication Networks

Vishnevsky

2021

Mathematics

View full text Add to dashboard Cite

The paper presents a review of papers on stochastic polling systems published in 2007–2020. Due to the applicability of stochastic polling models, the researchers face new and more complicated polling models. Stochastic polling models are effectively used for performance evaluation, design and optimization of telecommunication systems and networks, transport systems and road management systems, traffic, production systems and inventory management systems. In the review, we separately discuss the results for two-queue systems as a special case of polling systems. Then we discuss new and already known methods for polling system analysis including the mean value analysis and its application to systems with heavy load to approximate the performance characteristics. We also present the results concerning the specifics in polling models: a polling order, service disciplines, methods to queue or to group arriving customers, and a feedback in polling systems. The new direction in the polling system models is an investigation of how the customer service order within a queue affects the performance characteristics. The results on polling systems with correlated arrivals (MAP, BMAP, and the group Poisson arrivals simultaneously to all queues) are also considered. We briefly discuss the results on multi-server, non-discrete polling systems and application of polling models in various fields.

show abstract

Section: Stability Conditions For Polling Systemssupporting

confidence: 75%

Polling Systems and Their Application to Telecommunication Networks

Vishnevsky

2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…We take the expectations of all four terms in (13), divide them by the expectation of the total number of i-customer departures in the first k polling cycle (E[ k =1 G i ( )]) and take the limit for k → ∞. Thus we get a relation among the four stationary probabilities for each j phase of the ith BMAP.…”

Section: Fundamental Relationshipmentioning

confidence: 98%

“…The server utilization at station i and the overall utilization are ρ i = λ i b i and ρ = N i=1 ρ i , respectively. We assume that all stations of the polling system are stable (for stability condition see [13]). WhenŶ(z), |z| ≤ 1 is a matrix GF, Y (k) denotes its kth (k ≥ 1) factorial moment, i.e., Y (k) = d k dz kŶ (z)| z=1 and Y denotes its value at z = 1, i.e., Y =Ŷ(1).…”

Section: The Bmap/g/1 Cyclic Polling Modelmentioning

confidence: 99%

Unified analysis of BMAP/G/1 cyclic polling models

Saffer

Telek

2009

Queueing Syst

Self Cite

View full text Add to dashboard Cite

In this paper we present a unified analysis of the BMAP/G/1 cyclic polling model and its application to the gated and exhaustive service disciplines as examples. The applied methodology is based on the separation of the analysis into service discipline independent and dependent parts. New expressions are derived for the vectorgenerating function of the stationary number of customers and for its mean in terms of vector quantities depending on the service discipline. They are valid for a broad class of service disciplines and both for zero-and nonzero-switchover-times polling models.We present the service discipline specific solution for the nonzero-switchovertimes model with gated and exhaustive service disciplines. We set up the governing equations of the system by using Kronecker product notation. They can be numerically solved by means of a system of linear equations. The resulting vectors are used to compute the service discipline specific vector quantities.

show abstract

“…The switch over time between service cycles is shown in ACTIVITY number 2. TNOW or current time is stored in XX in order to collect the statistic of CYCLE PERIOD time, 6 and finally entities leave the system through TERMINATE node (T2). In the second queue, entities are created in the CREATE node according to Poisson process with rate of 0.2, and they wait to be serviced in AWAIT node (AW2), while the server is servicing at queue 1, they have to wait until the server finishes its tasks on the first queue.…”

Section: Experiment: the Case Studymentioning

confidence: 99%

“…1,2 Polling systems have been applied to various cases, including production, communication, transportation, and maintenance systems. 3–8 When conventional methods are used to analyze polling systems, it is impossible to use different distributions for arrival and service times because most such methods are based on Markovian assumptions. In addition, exact methods are unable to handle more than three queues, and as the number of queues increases, the complexity of the problem will also increase.…”

Section: Introductionmentioning

confidence: 99%

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

2014

View full text Add to dashboard Cite

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.

show abstract

Stability of periodic polling system with BMAP arrivals

Cited by 9 publications

References 14 publications

Polling Systems and Their Application to Telecommunication Networks

Polling Systems and Their Application to Telecommunication Networks

Unified analysis of BMAP/G/1 cyclic polling models

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

Contact Info

Product

Resources

About