Mariusz Głąbowski

A simple approximation of the link model with reservation by a one-dimensional Markov chain

Abstract This paper presents a new approximate calculation algorithm of the blocking probability in the full-availability group with reservation carrying a mixture of different multi-rate traffic streams. The algorithm is based on transforming multi-dimensional service processes in the system into a one-dimensional discrete Markov chain, which is characterised by a product form solution. Special attention is paid to the method for determining reverse transition rates and state probabilities in this Markov chain. The results of analytical calculations of the blocking probability are compared with the results of digital simulation of systems with bandwidth reservation. This research has shown a better accuracy of the proposed method as compared to the accuracy of other known solutions. The derived formulae can be useful for the analysis of ISDN and B-ISDN switching systems.

Modelling of state-dependent multirate systems carrying BPP traffic

This paper presents a simple approximate calculation methodology of the occupancy distribution and the blocking probability in state-dependent systems with multirate Binomial–Poisson–Pascal traffic. The particular traffic streams are generated by an infinite, as well as by a finite, population of traffic sources. The proposed methodology is based on the generalized Kaufman–Roberts recursion. The model enables calculations to be carried out for the systems in which accepting a new call depends on an admission control algorithm (e.g., a model of a full-availability group with bandwidth reservation) as well as for those systems in which accepting a new call depends on the structure of a system (e.g., a model of a limited-availability group). The results of the analytical calculations have been compared with the simulation results of exemplary state-dependent systems.

Multi-rate Model of the Group of Separated Transmission Links of Various Capacities

In this paper it is proposed an approximate recurrent method of calculations of the occupancy distribution and the blocking probability in the generalised model of the limited-availability group, i.e. the group which consists of separated transmission links of various capacities. The group is offered a mixture of different multi-rate traffic streams. The results of the analytical calculations of blocking probability are compared with the results of the simulation of the limited-availability groups.

Modelling of Cellular Networks with Traffic Overflow

The paper proposes a new method for modelling multiservice cellular networks with traffic overflow. The proposed method employs a model of Erlang’s Ideal Grading (EIG) with multiservice traffic and differentiated availability. The fundamental advantage of the proposed method, as compared to other relevant methods, is a major simplification in modelling systems with traffic overflow that results from the elimination of the necessity of a determination of the parameters of overflow traffic, that is, the average value and the variance. According to the proposed method, calculations in the overflow system can be reduced to calculations in a system composed of one grading only. The paper presents the method for determining availability in such a grading that models a system with traffic overflow. The results of analytical calculations were compared with the results of simulation experiments. The results of the research study confirm high accuracy of the proposed method.

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.

Properties of Recurrent Equations for the Full-Availability Group with BPP Traffic

The paper proposes a formal derivation of recurrent equations describing the occupancy distribution in the full-availability group with multirate Binomial-Poisson-Pascal (BPP) traffic. The paper presents an effective algorithm for determining the occupancy distribution on the basis of derived recurrent equations and for the determination of the blocking probability as well as the loss probability of calls of particular classes of traffic offered to the system. A proof of the convergence of the iterative process of estimating the average number of busy traffic sources of particular classes is also given in the paper.

ND++ – an extended IPv6 Neighbor Discovery protocol for enhanced stateless address autoconfiguration in MANETs

SUMMARY Recent trends in information and communications technologies are oriented toward the design of the Future Internet and the Internet of Things. While IPv6-based mobile ad hoc networks (MANETs) are emerging as an important building block of these new technologies, it is necessary to come up with adequate self-configuration capabilities allowing for seamless and automated configuration of addresses in mobile environment. The mechanisms of stateless address autoconfiguration proposed for IPv6 networks are supposed to automate some configuration steps; however, they would need to be aligned with the requirements imposed by MANET networks. Therefore, in this article, we present Neighbor Discovery ++ – an extended IPv6 Neighbor Discovery protocol for enhanced duplicate address detection in MANETs, which provides increased coverage of network nodes, while minimizing protocol overhead. It exploits efficient flooding mechanism on the basis of the multipoint relay concept, which makes it an interesting approach also for large-scale networks. Trials performed on the designated real-world testbed platform indicate that ND++ is a promising solution to support efficient address autoconfiguration in MANETs. Copyright

Modelling of virtual‐circuit switching nodes with multicast connections

This paper presents an approximate calculation methodology of the occupancy distribution and the blocking probability in a virtual circuit switching node with multi-rate unicast and multicast traffic streams. Particular traffic streams are generated by an infinite as well as by a finite population of traffic sources. The model enables calculations of any structure of the groups forming the outgoing directions of the node. Additionally, bandwidth reservation algorithms are also proposed in order to improve traffic characteristics of different traffic classes. The results of the analytical calculations have been compared with the simulation results of a switching node carrying multicast and unicast traffic streams. Copyright

An Algorithm for Finding Shortest Path Tree Using Ant Colony Optimization Metaheuristic

This paper introduces the ShortestPathTreeACO algorithm designed for finding near-optimal and optimal solutions for the shortest path tree problem. The algorithm is based on Ant Colony Optimization metaheuristic, and therefore it is of significant importance to choose proper operation parameters that guarantee the results of required quality. The operation of the algorithm is explained in relation to the pseudocode introduced in the paper. An exemplary execution of the algorithm is depicted and discussed on a step-by-step basis. The experiments carried out within the custom-made framework of the experiment are the source of suggestions concerning the parameter values. The influence of the choice of the number of ants and the pheromone evaporation speed is investigated. The quality of generated solutions is addressed, as well as the issues of execution time.

Modelling of multiservice switching networks with overflow links for any traffic class

This study proposes a new analytical model of a multi-service switching network with overflow links with finite capacity in the first stage of the network. The proposed model assumes that overflow links can service a number of selected call classes from among all classes offered to the network. A particular attention is given to the method for a determination of the effective availability parameter for networks with overflow links. The proposed model can be also used to determine the dependence between the internal blocking probability and the capacity of overflow links. A relevant simulation study has confirmed high accuracy of the proposed method as well as the applicability of the model in engineering practice, in modelling of multi-stage switching networks both optical and electronic.