Adam Kaliszan

Modeling product-form state-dependent systems with BPP traffic

This article proposes models of product-form state-dependent class of systems. Two methods for determining the occupancy distribution and the blocking and loss probability in communication systems with state-dependent arrival processes and state-dependent admission processes are presented. The first proposed method, the recursive BPP-KR method, is based on a modification of the generalized Kaufman-Roberts formula. In the second method, the hybrid BPP-Hyb method, a convolution algorithm is used in the computational process. Particular attention is given to the multiservice traffic streams offered to the systems, which can be generated both by infinite number of traffic sources and by a finite number of sources.

Asymmetric convolution algorithm for blocking probability calculation in full-availability group with bandwidth reservation

The paper proposes a new approximate calculation method of occupancy distribution and blocking probability in the full-availability group (FAG) with multi-rate traffic streams and bandwidth reservation. The algorithm involves calculation of system state probabilities by a convolution operation. In the paper, an effective method of calculating state probabilities in a reservation space of the system is derived. The analytical results of blocking probabilities in the FAG with bandwidth reservation, obtained on the basis of the proposed analytical method, are compared with the data obtained on the basis of other known analytical methods and with the simulation results. The accuracy of the proposed method is evaluated for different multi-rate Bernoulli (Erlang), Poisson (Engset), Pascal traffic streams. The method proposed is characterised by lower complexity than the convolution algorithm for the FAG with bandwidth reservation devised earlier.

Two-Dimensional Convolution Algorithm for Modelling Multiservice Networks with Overflow Traffic

The present paper proposes a new method for analytical modelling multiservice networks with implemented traffic overflow mechanisms. The basis for the proposed method is a special two-dimensional convolution algorithm that enables determination of the occupancy distribution and the blocking probability in network systems in which traffic streams of individual classes can be serviced by both primary and alternative resources. The algorithm worked out by the authors makes it possible to model systems with any type of traffic offered to primary resources. In order to estimate the accuracy of the proposed method, the analytical results of blocking probabilities in selected networks with traffic overflow have been compared with simulation data.

Simulator of Full-Availability Group with Bandwidth Reservation and Multi-Rate Bernoulli-Poisson-Pascal Traffic Streams

This paper presents an approach to simulation investigations of a full-availability group with multi-rate Poisson, Bernoulli and Pascal traffic streams. In the paper the models of a full-availability group with and without bandwidth reservation are described. The particular distributions of various traffic streams are also presented. The proposed simulator is based on events-scheduling approach. The paper deals also with implementation issues related to simulation research of the systems with Bernoulli, Poisson and Pascal traffic streams.

Modelling overflow systems with distributed secondary resources

This article presents, in short, the state of the art of modelling overflow systems and proposes a new method for a determination of characteristics of multi-service overflow systems with elastic traffic and with distributed secondary resources. A particular attention is given to the method for a determination of the parameters of multi-service traffic that overflows to secondary resources and the method for modelling of these resources that takes into consideration both the structure of the distributed resources, elastic traffic management-handling mechanisms and the level of peakedness degeneration of overflow traffic. The results of the analytical calculations are compared with the results of the simulation experiments of a number of selected structures of overflow systems with distributed secondary resources. The results of the study have confirmed and verified the correctness of all the theoretical assumptions adopted throughout the article.

On the application of the asymmetric convolution algorithm in modeling of full-availability group with bandwidth reservation

The paper proposes a new method to calculate the occupancy distribution and the blocking probability in the full-availability group with multi-rate traffic and bandwidth reservation. In the presented method, the occupancy distribution in a group is calculated with the application of the proposed asymmetric convolution operation that takes into consideration the influence of the reservation mechanism upon the probability of passing between the states. The results of the analytical calculations of the blocking probability in the system with bandwidth reservation obtained on the basis of the proposed analytical method are compared to the data obtained on the basis of other known analytical methods and to the results of the simulation.

Generalised convolution algorithm for modelling state-dependent systems

This study proposes a new method for calculations of the blocking probability in multiservice state-dependent systems. In the method proposed in this study the occupancy distribution is determined on the basis of an appropriately modified convolution operation. This operation is of a universal applicability and provides an opportunity to model approximately any state-dependent systems. The results of the calculations were compared with the results of the simulation experiments of some selected multiservice systems and with the results provided by other analytical methods that are available in the literature of the subject. The study has confirmed high accuracy of the proposed method. The effectiveness of the computational process carried out according to the proposed method can be significantly increased as a result of parallelisation of computation.

Routing and control plane in the Parallel Internet IPv6 QoS

The article is devoted to an implementation of the Control Plane module (responsible for the routing) for the nodes of Parallel Internet IPv6 QoS network. The mentioned network is one out of three IIP System networks, built within the Future Internet Engineering project. A characteristic feature of the PI IPv6 QoS network is to provide an appropriate quality of services. This functionality is dependent on the routing as well. Therefore, the CP module must meet the numerous criteria. A way of applying the Control Plane module for the nodes of PI IPv6 QoS network, proposed by the authors of this article, has been implemented, tested and integrated with this network. The conducted tests have proved a correctness of the named assumptions.

Asymmetric Convolution Algorithm for Full-Availability Group with Bandwidth Reservation

In the paper a new asymmetric convolution algorithm for the calculation of the occupancy distribution and the blocking probability in the full-availability group (FAG) with bandwidth reservation and multirate traffic streams is proposed. In the paper, an effective method of calculating state probabilities in a reservation space of the system is derived. The analytical results of the blocking probabilities in the FAG with bandwidth reservation obtained on the basis of the proposed method, are compared with the simulation results. This comparison has proved a high accuracy of the proposed algorithm. The proposed asymmetric convolution algorithm can be applied for systems with bandwidth reservation and with arbitrary multirate traffic streams

Convolution Model of a Queueing System with the cFIFO Service Discipline

This article presents an approximate convolution model of a multiservice queueing system with the continuous FIFO (cFIFO) service discipline. The model makes it possible to service calls sequentially with variable bit rate, determined by unoccupied (free) resources of the multiservice server. As compared to the FIFO discipline, the cFIFO queue utilizes the resources of a multiservice server more effectively. The assumption in the model is that the queueing system is offered a mixture of independent multiservice Bernoulli-Poisson-Pascal (BPP) call streams. The article also discusses the results of modelling a number of queueing systems to which different, non-Poissonian, call streams are offered. To verify the accuracy of the model, the results of the analytical calculations are compared with the results of simulation experiments for a number of selected queueing systems. The study has confirmed the accuracy of all adopted theoretical assumptions for the proposed analytical model.