Maciej Stasiak

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.

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.

Blocking probability in a limited-availability group carrying mixture of different multichannel traffic streams

In this paper we propose an approximate, recurrent method of calculations of the blocking probability and of the distribution of being busy in limited- availability groups to which the mixture of different multichannel traffic streams is offered. The method is based on introducing the relevant combinatorically- determined conditional probabilities of passages between adjacent states of the group into the equations determining the distribution of busy channels in a full- availability group. The result of analytical calculations of the blocking probability are compared with the results of digital simulation of limited- availability groups. The proposed method can be used in analysis of isdn and b-isdn networks and systems.RésuméĽarticle présente une méthode récurrente approchée de calcul de distribution ďoccupation et de probabilité de blocage dans lesfaisceaux ° accessibilité limitée avec trafic intégré. Cette méthode résulte de ľintroduction, dans les équations donnant la distribution ďoccupation dufaisceau ° accessibilité totale, des probabilités conditionnelles de passages entre les états voisins du faisceau, déterminées combinatoirement. Les résultats du calcul analytique de la probabilité de blocage sont compares aux résultats de simulation numérique des faisceaux ° accessibilité limitée. La méthode proposée peut être appliquée dans Ľanalyse des systèmes isdn et b-isdn.

Uplink Blocking Probability Calculation for Cellular Systems with WCDMA Radio Interface, Finite Source Population and Differently Loaded Neighbouring Cells

This paper presents the uplink blocking probability calculation method in cellular systems with WCDMA radio interface, finite source population and differently loaded neighbouring cells. The method is based on the model of the full availability group with multi-rate traffic streams. A fixed point methodology has been used in the proposed method. The proposed scheme could be utilized for cost-effective radio resource management in 3G mobile networks and can be easily applied to network capacity calculations

Point-to-point blocking probability in switching networks with reservation

In this paper reservation algorithms for multi-service switching networks are proposed. Two new approximate methods of the point-to-point blocking probability calculation in the multi-service switching networks are also presented in the paper. These methods can be used for blocking calculation in the switching networks with and without reservation. Special attention is paid to the method for determining the effective availability, which directly affects the accuracy of the final results. The results of analytical calculations are compared with the data of digital simulation of switching networks without and with reservation.In this paper reservation algorithms for multi-service switching networks are proposed. Two new approximate methods of the point-to-point blocking probability calculation in the multi-service switching networks are also presented in the paper. These methods can be used for blocking calculation in the switching networks with and without reservation. Special attention is paid to the method for determining the effective availability, which directly affects the accuracy of the final results. The results of analytical calculations are compared with the data of digital simulation of switching networks without and with reservation.RésuméCet article présente les algorithmes de réservation dans les réseaux de connexion à trafic intégré. On propose deux méthodes approchées du calcul de la probabilité du blocage point à point dans les réseaux de connexion multiservices. Ces méthodes proposées peuvent être appliquées au calcul du blocage dans les reseaux avec (et sans) mécanisme de réservation. En particulier, on fait attention à la manière de déterminer l’accessibilité effective de laquelle dépend l’exactitude du résultat final. Les résultats du calcul analytique de la probabilité du blocage sont comparés aux résultats de la simulation numérique des réseaux de connexion avec et sans réservation.

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.

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.

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.

Modelling of the WCDMA Interface in the UMTS Network with Soft Handoff Mechanism

The paper proposes an analytical approach to blocking probability calculation in the UMTS network carrying a mixture of multi-rate traffic, under the assumption that the part of resources of the interface is dedicated for servicing handoff traffic. In the proposed method, handoff connections are modeled on the basis of the fixed point methodology and dynamic reservation. The results of analytical calculation of the blocking probability in the group of cells carrying a mixture of different multi-rate traffic streams are compared with the results of the simulation experiments, which confirms a rather high accuracy of the method. The described calculation scheme is applicable for cost-effective resource management in 3G mobile networks and can be easily applied to network capacity calculations.

An Approximate Model of the WCDMA Interface Servicing a Mixture of Multi-rate Traffic Streams with Priorities

The paper presents an approximate method for blocking probability determination in the WCDMA interface of the UMTS network with priorities. In our considerations we use a new model of the full-availability group servicing multi-rate traffic with priorities. In the proposed model we assume that a new call with a higher priority can terminate connections already in service if they are characterized by a lower priority than a new call. The proposed scheme is applicable for cost-effective WCDMA resource management in 3G mobile networks and can be easily applied to network capacity calculations.