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

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Mariusz Głąbowski ◽  
Adam Kaliszan ◽  
Maciej Stasiak
Keyword(s):  
Blocking Probability ◽  
Model Systems ◽  
Two Dimensional ◽  
Network Systems ◽  
Multiservice Networks ◽  
Occupancy Distribution ◽  
Blocking Probabilities ◽  
Convolution Algorithm ◽  
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.

scholarly journals Modelling of Multiservice Networks with Separated Resources and Overflow of Adaptive Traffic

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Mariusz Głąbowski ◽  
Damian Kmiecik ◽  
Maciej Stasiak
Keyword(s):  
Blocking Probability ◽  
Mobile Systems ◽  
Model Systems ◽  
Analytical Determination ◽  
Multiservice Networks ◽  
Traffic Characteristics ◽  
Grade Of Service ◽  
Network Load ◽  
Proposed Model

The article proposes a new method of determining traffic characteristics of multiservice overflow systems that carry adaptive traffic. When the total offered load in primary resources exceeds a certain value, this type of traffic is admitted for service with lower bitrate. A particular attention is given in the article to a method for a determination of the parameters of traffic that overflows to secondary resources as well as to the way adaptive traffic is serviced. The method takes into consideration three possible types of traffic: Erlang, Engset, and Pascal traffic. It is based on a generalization of Hayward’s concept and its application to model systems with adaptive traffic with threshold compression. The method can be used for optimal dimensioning of logical networks (slices) in modern mobile systems due to possibility of analytical determination of grade of service parameters (blocking probability, carried traffic, and network load). To verify the accuracy of the proposed model the results of analytical calculations, obtained on the basis of the proposed model, are then compared with the results of simulation experiments for a number of selected structures of overflow systems that service adaptive traffic. The results of the study demonstrate high accuracy of the proposed theoretical model.

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

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Mariusz Głąbowski ◽  
Maciej Stasiak ◽  
Joanna Weissenberg
Keyword(s):  
Iterative Process ◽  
Blocking Probability ◽  
Loss Probability ◽  
Effective Algorithm ◽  
Formal Derivation ◽  
System A ◽  
Occupancy Distribution

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.

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

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