Leonid A. Ponomarenko

Performance Analysis and Optimization of Multi-Traffic on Communication Networks

Promptly growing demand for telecommunication services and information interchange has led to the fact that communication became one of the most dynamical branches of an infrastructure of a modern society. The book introduces to the bases of classical MDP theory; problems of a finding optimal in models are investigated and various problems of improvement of characteristics of traditional and multimedia wireless communication networks are considered together with both classical and new methods of theory MDP which allow defining optimal strategy of access in teletraffic systems. The book will be useful to specialists in the field of telecommunication systems and also to students and post-graduate students of corresponding specialties.

Investigation of Cellular Network Characteristics with Limited Queue of Impatient h -Calls

we suggested a model of competitiveness of brand product, which takes into account 10 factors. The model is based on 52 fuzzy rules of type. Potential of application of the model for control of competitiveness of brand product is shown. We state a problem of learning of fuzzy model of competitiveness on the basis of experimental data.

Methods for Analysis of Queueing Models with Instantaneous and Delayed Feedbacks

The new Markov models of multi-channel queueing systems with instantaneous and delayed feedback are proposed. In these models part of already serviced calls instantaneously feeds back to channel while the rest part either leaves the system or feeds back to channel after some delay in orbit. Behavior of already serviced calls is handled by randomized parameters. Both exact and asymptotic methods to calculate the quality of service (QoS) metrics of the proposed models are developed. Exact method is based on the system of balance equations (SBE) for steady-state probabilities of appropriate three dimensional Markov chain (3-D MC) while asymptotic method uses the new hierarchical space merging algorithm for 3-D MC. Results of numerical experiments are demonstrated.

Multidimensional Queueing Models in Telecommunication Networks

The increasing complexity of telecommunication networks requires us to develop adequate mathematical models. We must find their characteristics, optimize them subject to chosen criteria, and develop the corresponding control algorithms. Multidimensional queueing models are used to design and optimize modern and next-generation networks (NGN). The central problem of the related mathematical theory is to apply multidimensional and large-size queueing models to improve efficiency. In this book new methods are successively developed and applied to solve related problems. The book is recommended for researchers engaged with the mathematical theory of telecommunications traffic.

A Numerical Method to Study Mobile Cellular Networks Models with Finite Queue of h -Calls

we suggested a model of competitiveness of brand product, which takes into account 10 factors. The model is based on 52 fuzzy rules of type. Potential of application of the model for control of competitiveness of brand product is shown. We state a problem of learning of fuzzy model of competitiveness on the basis of experimental data.

Hierarchical Space Merging Algorithm for Analysis of Two Stage Queueing Network with Feedback

A Markov model of two stage queuing network with feedback is proposed. Poisson flows arriving to both stages from outside and part of already serviced calls in the first node instantaneously enter to the second node (if there is free space here) while the remaining part leaves the network. At the completion of call processing in the second node there are three possibilities: (1) it leaves the network; (2) it instantaneously feeds back to the first node (if there is free space here); (3) it feeds back to the first node after some delay in orbit. All feedbacks are determined by known probabilities. Both nodes have finite capacities. The mathematical model of the investigated network is a three dimensional Markov chain (3-D MC) and hierarchical space merging algorithm to calculate its steady-state probabilities is developed. This algorithm allows asymptotic analysis of the quality of service (QoS) metrics of the investigated network as well.

Multidimensional Loss Models of Queueing Systems and Their Applications in Telecommunication Networks

This chapter presents the foundations of multidimensional Erlang’s models, and the discussion has been concentrated on Markov models with pure losses. Both single-rate and multi-rate Erlang’s loss models with uncontrolled access schemes are considered. Effective computational procedures to calculate the main quality of service (QoS) metrics are shown.

Analytical Methods for Analysis of Integral Cellular Networks

The classical theory of multidimensional queueing systems is based on many assumptions, one of them is basic: one call—one channel. However, in modern integral (multiservice) communication networks, this assumption is not carried out. Thus, in them, for example, a video information requires the wider band in a digital transmission line than data or voice information. In the teletraffic theory the calls, requiring a large number of channels in a transmission line, are called wideband, and the calls that require a smaller number of channels—narrowband. As it was noted in the previous chapter, the multi-flow system, in which heterogeneous calls require for simultaneous maintenance a random number of channels, is called multi-rate queue (MRQ).

Priority Schemes in Packet Switching Networks

In this chapter, new queueing models of switching equipment in packet networks and corresponding algorithms necessary for their analyzing are developed. Traditional approaches to solving the indicated problems focused mainly on simple queueing models with single traffic and do not take into account various QoS requirements of heterogeneous cells (packets). However, nowadays we have to consider the models of switch that supported both delay-sensitive applications (such as real-time voice calls) and delay-insensitive applications (such as non-real-time data calls). Note that usually delay-insensitive applications are loss sensitive, while delay-sensitive applications have some tolerance to loss. In other words, in unique model, it is necessary to take into consideration various QoS requirements for heterogeneous cells which contradict each other.

Algorithmic Methods for Analysis of Mono-service Cellular Networks

In this chapter, methods for exact and approximate evaluation of the characteristics of mono-service cellular networks with single traffic are developed. In other words, models with only one type of traffic in which new and handover calls have the same bandwidth requirements and identically distributed channel holding time with common average value are investigated. Two kinds of models have been considered. In models with queues (finite or infinite) of both new and handover calls, it is assumed that unlike calls may leave the queue if their waiting time is greater than some threshold value. Another type of models takes into account repetitions of new calls, while to provide high priority to handover calls, guard channel scheme is used. For both types of models results of numerical experiments are presented.