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

Erlang analysis of cellular networks using stochastic Petri nets and user-in-the-loop extension for demand control

Abstract—Cellular networks face severe challenges due to the expected growth of application data rate demand with an increase rate of 100 % per year. Over-provisioning capacity has been the standard approach to reduce the risk of overload situations. Traditionally in telephony networks, call blocking and overload probability have been analyzed using the Erlang-B and Erlang-C formulas, which model limited capacity communication systems without or with session request buffers, respectively. While a closed-form expression exists for the blocking probability for constant load and service, a steady-state Markov chain (MC) analysis can always provide more detailed data, as long as the Markov property of the arrival and service processes hold. However, there is a significant modeling advantage by using the stochastic Petri net (SPN) paradigm to model the details of such a system. In addition, software tool support allows getting numeric analysis results quickly by solving the state probabilities in the background and without the need to run any simulation. Because of this efficiency, the equivalent SPN model of the Engset, Erlang-B and Erlang-C situation is introduced as novelty in this paper. Going beyond the original Erlang scenario, the user-in-the-loop (UIL) approach of demand shaping by closed-loop control is studied as an extension. In UIL, demand control is implemented by a dynamic usage-based tariff which motivates users to reduce or postpone the use of applications on their smart phone in times of light to severe congestion. In this paper, the effect of load on the price and demand reduction is modeled with an SPN based on the classical Erlang Markov chain structure. Numeric results are easily obtained and presented in this paper, including probability density functions (PDF) of the load situation, and a parameter analysis showing the effectiveness of UIL to reduce the overload probability. Keywords—User-in-the-loop (UIL); demand shaping; demand control; congestion; Erlang; stochastic Petri-net (SPN). I

A study of teletraffic problems in multicast networks

This dissertation studies teletraffic engineering of dynamic multicast connections. The traditional models in teletraffic engineering do not handle multicast connections properly, since in a dynamic multicast tree, users may join and leave the connection freely, and thus the multicast tree evolves in time. A model called multicast loss system is used to calculate blocking probabilities in a single link and in tree-type networks. In a single link case, the problem is a generalised Engset problem, and a method for calculating call blocking probabilities for users is presented. Application of the reduced load approximation for multicast connections is studied. Blocking probabilities in a cellular system are studied by means of simulation. The analysis is mainly concentrated on tree type networks, where convolution-truncation algorithms and simulation methods for solving the blocking probabilities exactly are derived. Both single layer and hierarchically coded streams are treated. The presented algorithms reduce significantly the computational complexity of the problem, compared to direct calculation from the system state space. An approximative method is given for background traffic. The simulation method presented is an application of the Inverse Convolution Monte-Carlo method, and it gives a considerable variance reduction, and thus allows simulation with smaller sample sizes than with traditional simulation methods. Signalling load for dynamic multicast connections in a node depends on the shape of the tree as well as the location of the node in the tree. This dissertation presents a method for calculating the portion of signalling load that is caused by call establishments and tear-downs.reviewe

Study of Queuing Systems with a Generalized Departure Process

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based on birth and death processes and state-dependent service rates. We consider the system M/M(g)/n/0 and M/M(g)/1/k (in Kendal notation) with a generalized departure process Mg. The output intensity depends nonlinearly on the system state with a defined parameter: “peaked factor p”. We obtain the state probabilities of the system using the general solution of the birth and death processes. The influence of the peaked factor on the state probability distribution, the congestion probability and the mean system time are studied. It is shown that the state-dependent service rates changes significantly the characteristics of the queueing systems. The advantages of simplicity and uniformity in representing both peaked and smooth behaviour make this queue attractive in network analysis and synthesis

Burst switched optical networks supporting legacy and future service types

Focusing on the principles and the paradigm of OBS an overview addressing expectable performance and application issues is presented. Proposals on OBS were published over a decade and the presented techniques spread into many directions. The paper comprises discussions of several challenges that OBS meets, in order to compile the big picture. The OBS principle is presented unrestricted to individual proposals and trends. Merits are openly discussed, considering basic teletraffic theory and common traffic characterisation. A more generic OBS paradigm than usual is impartially discussed and found capable to overcome shortcomings of recent proposals. In conclusion, an OBS that offers different connection types may support most client demands within a sole optical network layer

Introduction to Queueing Theory and Stochastic Teletraffic Models

The aim of this textbook is to provide students with basic knowledge of stochastic models that may apply to telecommunications research areas, such as traffic modelling, resource provisioning and traffic management. These study areas are often collectively called teletraffic. This book assumes prior knowledge of a programming language, mathematics, probability and stochastic processes normally taught in an electrical engineering course. For students who have some but not sufficiently strong background in probability and stochastic processes, we provide, in the first few chapters, background on the relevant concepts in these areas.Comment: 298 page

Performance analysis of cellular networks.

Thesis (Ph.D.)-University of Natal, Durban, 2000.Performance analysis in cellular networks is the determination of customer orientated grade-of-service parameters, such as call blocking and dropping probabilities, using the methods of stochastic theory. This stochastic theory analysis is built on certain assumptions regarding the arrival and service processes of user-offered calls in a network. In the past, cellular networks were analysed using the classical assumptions, Poisson call arrivals and negative exponential channel holding times, borrowed from earlier fixed network analysis. However, cellular networks are markedly different from fixed networks, in that, they afford the user a unique opportunity: the ability to communicate while on the move. User mobility and various other cellular network characteristics, such as customer-billing, cell· layout and hand·off mechanisms, generally invalidate the use of Poisson arrivals and negative exponential holding times. Recent measurements on live networks substantiate this view. Consequently, over the past few years, there has been a noticeable shift towards using more generalised arrival and service distributions in the performance analysis of cellular networks. However, two shortcomings with the resulting models are that they suffer from state space explosion and / or they represent hand off traffic as a state dependent mean arrival rate (thus ignoring the higher moments of the hand-off arrival process). This thesis's contribution to cellular network analysis is a moment-based approach that avoids full state space description but ensures that the hand-off arrival process is modelled beyond the first moment. The thesis considers a performance analysis model that is based on Poisson new call arrivals, generalised hand-off call arrivals and a variety of channel holding times. The thesis shows that the performance analysis of a cellular network may be loosely decomposed into three parts, a generic cell traffic characterising model, a generic cell traffic blocking model and a quality of service evaluation model. The cell traffic characterising model is employed to determine the mean and variance of hand-off traffic offered by a cell to its neighbour. The cell traffic-blocking model is used to detennine the blocking experienced by the various traffic streams offered to each cell. The quality of service evaluation part is essentially afued-point iteration of the cell traffic characterising and cell traffic blocking parts to determine customer orientated grade-of-service parameters such as blocking and dropping probabilities. The thesis also presents detailed mathematical models for user mobility modelling. Finally, the thesis provides extensive results to validate the proposed analysis and to illustrate the accuracy of the proposed analysis when compared to existing methods