Polling Systems and Their Application to Telecommunication Networks

Abstract

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.

Optimal Scheduling in General Multi-Queue System by Combining Simulation and Neural Network Techniques

“…of the average cost function for a given initial parameter vector θ (0) and the corresponding first empirical moment ḡ(θ (0) ). These values are set as the current solution g * and θ * to the optimization problem (13). At the perturbation step, a randomly chosen element of the previous parameter vector θ (n−1) must be randomly perturbed on the specified set…”

“…For analytic and numerical results in various types of polling systems with applications to broadband wireless Wi-Fi and Wi-MAX networks, we refer interested readers to the textbook by Vishnevsky and Semenova [ 12 ] and the references therein. The same authors in [ 13 ] developed their research on polling systems to systems with correlated arrival flows such as , , and the group Poisson arrivals. In Vishnevskiy et al [ 14 ], it was shown that the results obtained by a neural network are close enough to the results of analytical or simulation calculations for the and -type polling systems with cyclic polling.…”

Applications of Generating Functions to Stochastic Processes and to the Complexity of the Knapsack Problem

“…Probability generating functions are also used to model Queuing System [3], redundant renewable system [4], waiting Time Problems [5]. A good review of application of Probability generating functions to Stochastic Polling systems is done by Vishnevsky [6].…”

Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption

“…A popular discipline for service provision, in particular information transmission, in many systems with multiple access, is polling, see, for example, [1][2][3]. Under this discipline, different flows of information, which should be transmitted in the system, sequentially obtain time slots for access to the transmission thread.…”