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

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

Methods for performance evaluation of networks : fast simulation of loss systems and analysis of Internet congestion control

Performance evaluation of modern telecommunication networks by means of mathematical modeling frequently results in a situation, whereby an exact analytical solution poses a difficult problem in terms of computational evaluation. In this thesis, two such problems are studied and a different approach for easing the computational burden is developed in each case. The first part of the thesis considers the problem of evaluating blocking probabilities in loss systems, which are often used as models for the call scale behavior of modern networks. In this case, the solution to the problem can be given a well known analytical expression, but in practice it can not be used for computing the blocking probabilities due to the prohibitive size of the state space of the system. Then one can use simulation to obtain estimates of the blocking probabilities. For increasing the efficiency of the simulation, i.e., for reducing the variance of the estimates, several novel and increasingly more efficient methods are presented. Noticeable variance reductions are obtained by applying the method of conditional expectations. However, even greater variance reductions are gained by using importance sampling. In the thesis several importance sampling based methods are presented, of which the inverse convolution approach provides variance reductions surpassing all previously reported results in the literature. In the second part of the thesis, the problem of congestion control in the Internet is studied. Specifically, the focus is on modeling the interaction between the TCP rate control algorithm and the RED buffer management mechanism. By using various analytical approximations, a novel dynamic model is derived for describing the interaction between an idealized TCP source population and a RED controlled buffer. Ultimately, the model consists of a set of coupled retarded functional differential equations (RFDEs) governing the time dependent expectations of the stochastic system state variables. This model is used to explore the dependency of the equilibrium of the system on the parameters of the physical system. Additionally, methods are derived allowing the stability of the system to be analyzed. In particular, sufficient and necessary conditions are obtained for the RFDE system, such that the system is asymptotically stable.reviewe

Journal of Telecommunications and Information Technology, 2018, nr 1

We consider a two-link system that accommodates Poisson arriving calls from different service-classes and propose a multirate teletraffic loss model for its analysis. Each link has two thresholds, which refer to the number of in-service calls in the link. The lowest threshold, named support threshold, defines up to which point the link can support calls offloaded from the other link. The highest threshold, named offloading threshold, defines the point where the link starts offloading calls to the other link. The adopted bandwidth sharing policy is the complete sharing policy, in which a call can be accepted in a link if there exist enough available bandwidth units. The model does not have a product form solution for the steady state probabilities. However, we propose approximate formulas, based on a convolution algorithm, for the calculation of call blocking probabilities. The accuracy of the formulas is verified through simulation and found to be quite satisfactory

State-Dependent Bandwidth Sharing Policies for Wireless Multirate Loss Networks

We consider a reference cell of fixed capacity in a wireless cellular network while concentrating on next-generation network architectures. The cell accommodates new and handover calls from different service-classes. Arriving calls follow a random or quasi-random process and compete for service in the cell under two bandwidth sharing policies: 1) a probabilistic threshold (PrTH) policy or 2) the multiple fractional channel reservation (MFCR) policy. In the PrTH policy, if the number of in-service calls (new or handover) of a service-class exceeds a threshold (difference between new and handover calls), then an arriving call of the same service-class is accepted in the cell with a predefined state-dependent probability. In the MFCR policy, a real number of channels is reserved to benefit calls of certain service-classes; thus, a service priority is introduced. The cell is modeled as a multirate loss system. Under the PrTH policy, call-level performance measures are determined via accurate convolution algorithms, while under the MFCR policy, via approximate but efficient models. Furthermore, we discuss the applicability of the proposed models in 4G/5G networks. The accuracy of the proposed models is verified through simulation. Comparison against other models reveals the necessity of the new models and policies

Performance evaluation of multicast networks and service differentiation mechanisms in IP networks

The performance of a communication network depends on how well the network is designed in terms of delivering the level of service required by a given type of traffic. The field of teletraffic theory is concerned with quantifying the three-way relationship between the network, its level of service and the traffic arriving at the network. In this thesis, we study three different problems concerning this three-way relationship and present models to assist in designing and dimensioning networks to satisfy the different quality of service demands. In the first part of the thesis, we consider service differentiation mechanisms in packet-switched IP networks implementing a Differentiated Services (DiffServ) architecture. We study how bandwidth can be divided in a weighted fair manner between persistent elastic TCP flows, and between these TCP flows and streaming real-time UDP flows. To this end, we model the traffic conditioning and scheduling mechanisms on the packet and the flow level. We also model the interaction of these DiffServ mechanisms with the TCP congestion control mechanism and present closed-loop models for the sending rate of a TCP flow that reacts to congestion signals from the network. In the second part, we concentrate on non-persistent elastic TCP traffic in IP networks and study how flows can be differentiated in terms of mean delay by giving priority to flows based on their age. We study Multi Level Processor Sharing (MLPS) disciplines, where jobs are classified into levels based on their age or attained service. Between levels, a strict priority discipline is applied; the level containing the youngest jobs has the highest priority. Inside a particular level, any scheduling discipline could be used. We present an implementation proposal of a two-level discipline, PS+PS, with the Processor Sharing discipline used inside both levels. We prove that, as long as the hazard rate of the job-size distribution is decreasing, which is the case for Internet traffic, PS+PS, and any MLPS discipline that favors young jobs, is better than PS with respect to overall mean delay. In the final part, we study distribution-type streaming traffic in a multicast network, where there is, at most, one copy of each channel transmission in each network link, and quantify the blocking probability. We derive an exact blocking probability algorithm for multicast traffic in a tree network based on the convolution and truncation algorithm for unicast traffic. We present a new convolution operation, the OR-convolution, to suit the transmission principle of multicast traffic, and a new truncation operator to take into account the case of having both unicast and multicast traffic in the network. We also consider different user models derived from the single-user model.reviewe

Performance Evaluation in Single or Multi-Cluster C-RAN Supporting Quasi-Random Traffic

In this paper, a cloud radio access network (C-RAN) is considered where the remote radio heads (RRHs) are separated from the baseband units (BBUs). The RRHs in the C-RAN are grouped in different clusters according to their capacity while the BBUs form a centralized pool of computational resource units. Each RRH services a finite number of mobile users, i.e., the call arrival process is the quasi-random process. A new call of a single service-class requires a radio and a computational resource unit in order to be accepted in the C-RAN for a generally distributed service time. If these resource units are unavailable, then the call is blocked and lost. To analyze the multi-cluster C-RAN, we model it as a single-rate loss system, show that a product form solution exists for the steady state probabilities and propose a convolution algorithm for the accurate determination of congestion probabilities. The accuracy of this algorithm is verified via simulation. The proposed model generalizes our recent model where the RRHs in the C-RAN are grouped in a single cluster and each RRH accommodates quasi-random traffic