Operational Calculi for the Euler Operator

2000 Mathematics Subject Classification: 44A40, 44A35

The B-Terminal Busy Probability Prediction

In the teletraffic engineering of all the telecommunication networks, parameters characterizing the terminal traffic are used. One of the most important of them is the probability of finding the called (B-terminal) busy. This parameter is studied in some of the first and last papers in Teletraffic Theory. We propose a solution in this topic in the case of (virtual) channel systems, such as PSTN and GSM. We propose a detailed conceptual traffic model and, based on it, an analytical macro-state model of the system in stationary state, with: Bernoulli– Poisson–Pascal input flow; repeated calls; limited number of homogeneous terminals; losses due to abandoned and interrupted dialling, blocked and interrupted switching, not available intent terminal, blocked and abandoned ringing and abandoned conversation. Proposed in this paper approach may help in determination of many network traffic characteristics at session level, in performance evaluation of the next generation mobile networks.

Primary and Secondary Empirical Values in Network Redimensioning

A model of an overall telecommunication network with virtual circuits switching, in stationary state, with Bernoulli-Poisson-Pascal (BPP) input flow, repeated calls, limited number of homogeneous terminals and 8 types of losses is considered. One of the main problems of network redimensioning is estimation of the traffic offered in the network because it reflects on finding of necessary number of equivalent switching lines on the basis of the consideration of detailed users behavior and target Quality of Service (QoS). The aim of this paper is to find a new solution of Network Redimensioning Task (NRDT) [4], taking into account the inconvenience of necessary measurements, not considered in the previous research [5]. The results are applicable for redimensioning of every (virtual) circuit switching telecommunication system, both for wireline and wireless systems (GSM, PSTN, ISDN and BISDN). For packet - switching networks proposed approach may be used as a comparison basis and when they work in circuit switching mode (e.g. VoIP).

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05

Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function

AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37

Hamilton’s Principle with Variable Order Fractional Derivatives

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Five Turning Points in the Historical Progress of Statistics - My Personal Vision

Statistics has penetrated almost all branches of science and all areas of human endeavor. At the same time, statistics is not only misunderstood, misused and abused to a frightening extent, but it is also often much disliked by students in colleges and universities. This lecture discusses/covers/addresses the historical development of statistics, aiming at identifying the most important turning points that led to the present state of statistics and at answering the questions “What went wrong with statistics?” and “What to do next?”. ACM Computing Classification System (1998): A.0, A.m, G.3, K.3.2.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

Class Number Two for Real Quadratic Fields of Richaud-Degert Type

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.