Techniques for the Fast Simulation of Models of Highly dependable Systems

With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable system

Evaluation of Pareto/D/1/k Queue by Simulation

The finding that Pareto distributions are adequate to model Internet packet interarrival times has motivated the proposal of methods to evaluate steady-state performance measures of Pareto/D/1/k queues. Some limited analytical derivation for queue models has been proposed in the literature, but their solutions are often of a great mathematical challenge. To overcome such limitations, simulation tools that can deal with general queueing system must be developed. Despite certain limitations, simulation algorithms provide a mechanism to obtain insight and good numerical approximation to parameters of queues. In this work, we give an overview of some of these methods and compare them with our simulation approach, which are suited to solve queues with Generalized-Pareto interarrival time distributions. The paper discusses the properties and use of the Pareto distribution. We propose a real time trace simulation model for estimating the steady-state probability showing the tail-raising effect, loss probability, delay of the Pareto/D/1/k queue and make a comparison with M/D/1/k. The background on Internet traffic will help to do the evaluation correctly. This model can be used to study the long- tailed queueing systems. We close the paper with some general comments and offer thoughts about future work

An acceleration simulation method for power law priority traffic

A method for accelerated simulation for simulated self-similar processes is proposed. This technique simplifies the simulation model and improves the efficiency by using excess packets instead of packet-by-packet source traffic for a FIFO and non-FIFO buffer scheduler. In this research is focusing on developing an equivalent model of the conventional packet buffer that can produce an output analysis (which in this case will be the steady state probability) much faster. This acceleration simulation method is a further development of the Traffic Aggregation technique, which had previously been applied to FIFO buffers only and applies the Generalized Ballot Theorem to calculate the waiting time for the low priority traffic (combined with prior work on traffic aggregation). This hybrid method is shown to provide a significant reduction in the process time, while maintaining queuing behavior in the buffer that is highly accurate when compared to results from a conventional simulatio

Modelling of self-similar teletraffic for simulation

Recent studies of real teletraffic data in modern computer networks have shown that teletraffic exhibits self-similar (or fractal) properties over a wide range of time scales. The properties of self-similar teletraffic are very different from the traditional models of teletraffic based on Poisson, Markov-modulated Poisson, and related processes. The use of traditional models in networks characterised by self-similar processes can lead to incorrect conclusions about the performance of analysed networks. These include serious over-estimations of the performance of computer networks, insufficient allocation of communication and data processing resources, and difficulties ensuring the quality of service expected by network users. Thus, full understanding of the self-similar nature in teletraffic is an important issue. Due to the growing complexity of modern telecommunication networks, simulation has become the only feasible paradigm for their performance evaluation. In this thesis, we make some contributions to discrete-event simulation of networks with strongly-dependent, self-similar teletraffic. First, we have evaluated the most commonly used methods for estimating the self-similarity parameter H using appropriately long sequences of data. After assessing properties of available H estimators, we identified the most efficient estimators for practical studies of self-similarity. Next, the generation of arbitrarily long sequences of pseudo-random numbers possessing specific stochastic properties was considered. Various generators of pseudo-random self-similar sequences have been proposed. They differ in computational complexity and accuracy of the self-similar sequences they generate. In this thesis, we propose two new generators of self-similar teletraffic: (i) a generator based on Fractional Gaussian Noise and Daubechies Wavelets (FGN-DW), that is one of the fastest and the most accurate generators so far proposed; and (ii) a generator based on the Successive Random Addition (SRA) algorithm. Our comparative study of sequential and fixed-length self-similar pseudo-random teletraffic generators showed that the FFT, FGN-DW and SRP-FGN generators are the most efficient, both in the sense of accuracy and speed. To conduct simulation studies of telecommunication networks, self-similar processes often need to be transformed into suitable self-similar processes with arbitrary marginal distributions. Thus, the next problem addressed was how well the self-similarity and autocorrelation function of an original self-similar process are preserved when the self-similar sequences are converted into suitable self-similar processes with arbitrary marginal distributions. We also show how pseudo-random self-similar sequences can be applied to produce a model of teletraffic associated with the transmission of VBR JPEG /MPEG video. A combined gamma/Pareto model based on the application of the FGN-DW generator was used to synthesise VBR JPEG /MPEG video traffic. Finally, effects of self-similarity on the behaviour of queueing systems have been investigated. Using M/M/1/∞ as a reference queueing system with no long-range dependence, we have investigated how self-similarity and long-range dependence in arrival processes affect the length of sequential simulations being executed for obtaining steady-state results with the required level of statistical error. Our results show that the finite buffer overflow probability of a queueing system with self-similar input is much greater than the equivalent queueing system with Poisson or a short-range dependent input process, and that the overflow probability increases as the self-similarity parameter approaches one

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

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

Quality of Service Differentiation in Heterogeneous CDMA Networks : A Mathematical Modelling Approach

Next-generation cellular networks are expected to enable the coexistence of macro and small cells, and to support differentiated quality-of-service (QoS) of mobile applications. Under such conditions in the cell, due to a wide range of supported services and high dependencies on efficient vertical and horizontal handovers, appropriate management of handover traffic is very crucial. Furthermore, new emerging technologies, such as cloud radio access networks (C-RAN) and self-organizing networks (SON), provide good implementation and deployment opportunities for novel functions and services. We design a multi-threshold teletraffic model for heterogeneous code division multiple access (CDMA) networks that enable QoS differentiation of handover traffic when elastic and adaptive services are present. Facilitated by this model, it is possible to calculate important performance metrics for handover and new calls, such as call blocking probabilities, throughput, and radio resource utilization. This can be achieved by modelling the cellular CDMA system as a continuous-time Markov chain. After that, the determination of state probabilities in the cellular system can be performed via a recursive and efficient formula. We present the applicability framework for our proposed approach, that takes into account advances in C-RAN and SON technologies. We also evaluate the accuracy of our model using simulations and find it very satisfactory. Furthermore, experiments on commodity hardware show algorithm running times in the order of few hundreds of milliseconds, which makes it highly applicable for accurate cellular network dimensioning and radio resource management

Investigation of delay jitter of heterogeneous traffic in broadband networks

Scope and Methodology of Study: A critical challenge for both wired and wireless networking vendors and carrier companies is to be able to accurately estimate the quality of service (QoS) that will be provided based on the network architecture, router/switch topology, and protocol applied. As a result, this thesis focuses on the theoretical analysis of QoS parameters in term of inter-arrival jitter in differentiated services networks by deploying analytic/mathematical modeling technique and queueing theory, where the analytic model is expressed in terms of a set of equations that can be solved to yield the desired delay jitter parameter. In wireless networks with homogeneous traffic, the effects on the delay jitter in reference to the priority control scheme of the ARQ traffic for the two cases of: 1) the ARQ traffic has a priority over the original transmission traffic; and 2) the ARQ traffic has no priority over the original transmission traffic are evaluated. In wired broadband networks with heterogeneous traffic, the jitter analysis is conducted and the algorithm to control its effect is also developed.Findings and Conclusions: First, the results show that high priority packets always maintain the minimum inter-arrival jitter, which will not be affected even in heavy load situation. Second, the Gaussian traffic modeling is applied using the MVA approach to conduct the queue length analysis, and then the jitter analysis in heterogeneous broadband networks is investigated. While for wireless networks with homogeneous traffic, binomial distribution is used to conduct the queue length analysis, which is sufficient and relatively easy compared to heterogeneous traffic. Third, develop a service discipline called the tagged stream adaptive distortion-reducing peak output-rate enforcing to control and avoid the delay jitter increases without bound in heterogeneous broadband networks. Finally, through the analysis provided, the differential services, was proved not only viable, but also effective to control delay jitter. The analytic models that serve as guidelines to assist network system designers in controlling the QoS requested by customer in term of delay jitter

On the Queue Length Distribution in BMAP Systems

Batch Markovian Arrival Process – BMAP – is a teletraffic model which combines high ability to imitate complex statistical behaviour of network traces with relative simplicity in analysis and simulation. It is also a generalization of a wide class of Markovian processes, a class which in particular include the Poisson process, the compound Poisson process, the Markovmodulated Poisson process, the phase-type renewal process and others. In this paper we study the main queueing performance characteristic of a finite-buffer queue fed by the BMAP, namely the queue length distribution. In particular, we show a formula for the Laplace transform of the queue length distribution. The main benefit of this formula is that it may be used to obtain both transient and stationary characteristics. To demonstrate this, several numerical results are presented

On Channel Sharing Policies in LEO Mobile Satellite Systems

We consider a low earth orbit (LEO) mobile satellite system with "satellite-fixed" cells that accommodates new and handover calls of different service-classes. We provide an analytical framework for the efficient calculation of call blocking and handover failure probabilities under two channel sharing policies, namely the fixed channel reservation and the threshold call admission policies. Simulation results verify the accuracy of the proposed formulas. Furthermore, we discuss the applicability of the policies in software-defined LEO satellites