A note on the invariant distribution of a quasi-birth-and-death process

The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach. We will show that the invariant distribution can be computed using the squared norms of the corresponding matrix-valued orthogonal polynomials, no matter if they are or not diagonal matrices. We will give an example where the squared norms are not diagonal matrices, but nevertheless we can compute its invariant distribution

Decision support system for the environmental impact of e-business

With less than half a century's development, e-business and the Information and Communication Technologies it relies on, have been growing rapidly. With an even shorter history than the technology itself, the study of its impact on the environment and sustainable development in general, is still in its infancy. A review of past literature has revealed that the problem is complex. Both negative and positive impacts have been identified. Traditional systematic approaches have been found to be insufficient for this research topic. To explore the relationship further, a new methodology is proposed in this thesis. In particular the main objective of this PhD study is to demonstrate and develop an Expert Decision Support System at the meso level, to simulate the relationship between e-business and the environment. In pursuit of this aim, results are presented of two surveys that were conducted to collect data and build a knowledge base. Analysis of the data using various techniques was considered, based on data mining technologies and Fuzzy Logic. The development of the Expert Decision Support System is then discussed, adopting a two-way simulation approach. The forward chain of the system is developed based on Decision Support System technology, with the heart of the system built on Neural Networks. Calculation, estimation and prediction of environmental indicator values based e-business indicators are conducted in this part. The backward chain is based on Expert System technology, where conditions and rules are presented to reach certain pre-defined environmental targets. An individual company should then be able to use this system within a certain industry, for example, to simulate its environmental performance by adopting or limiting Information and Communication technologies. A demonstration of how the system can be used and operated on various occasions for different purposes is presented, based on four application scenarios: predictions, simulations, comparisons and solutions. It is claimed that the results from the Expert Decision Support System, which ideally should be integrated into a company's financial system and other information management systems, will provide important information that could be incorporated into a company's strategic plans, action plans and technological reformation. The research presents a pilot study which tries to not only build a quantitative model but also to construct a decision support system to simulate this relationship in the real world. It is claimed that the work both extends research methodologies in this field and endows traditional Neural Network applications with new meanings and challenges.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Temporally correlated zero-range process with open boundaries: Steady state and fluctuations

19 pages, 14 figures, v2: minor revisions, close to final published version at http://dx.doi.org/10.1103/PhysRevE.92.02213

Methods for performance evaluation of VBR video traffic models

Abstract-Models for predicting the performance of multiplexed variable bit rate video sources are important for engineering a network. However, models of a single source are also important for parameter negotiations and call admittance algorithms. In this paper we propose to model a single video source as a Markov renewal process whose states represent different bit rates. We also propose two novel goodness-of-fit metrics which are directly related to the specific performance aspects that we want to predict from the model. The first is a leaky bucket contour plot which can be used to quantify the burstiness of any traffic type. The second measure applies only to video traffic and measures how well the model can predict the compressed video quality. I. INTTtODUCTtON I T is well recognized that the viability of B-ISDN/ATM depends on the development of effective and implementable congestion control schemes. While many frameworks and techniques are under discussion (see, e.g., [l]), at least two capabilities have been agreed to as necessary in any framework that might arise.) The first is a comection admission control (CAC) by which the network will decide to accept or reject a new connection based on a set of agreed to traffic descriptors and on available resources. Once a connection is accepted, a second necessary control issome form of usage parameter control (UPC) which will insure that connections stay within their negotiated resource parameters. A popular UPC would involve a leaky bucket monitor of traffic entering the system, where traffic deemed as excessive by the monitor could either be dropped or tagged as low priority and allowed to proceed through the network to take advantage of potentially unused resources. Performance modeling is necessary to determine which techniques or set of techniques will be appropriate for eventual implementation in a B-ISDN network. Such models need to take into account traffic characteristics from realistic services that would be carried in a B-ISDN network. In particular, we need traffic models which will accurately represent the statistical nature of very high-speed, bursty services. Two classes of traffic models need to be developed: multiplexed source models and single source models. Although the same traffic model might be used in both cases, some models might be more suitable for one than the other. Multiplexed models will capture the effects of statistically multiplexing bursty sources and will predict to what extent the superposition of bursty streams is "smoothed". These models will be useful in traffic engineering the network (e.g., deciding how many links or virtual paths to put between different locations) and in traffic management (e.g., designing connection admission control algorithms, etc.) Several models have already been proposed in this direction (see, e.g., There are several areas where single source models are useful. They could be used to study what types of traffic descriptors make sense for parameter negotiation with the network at call setup. For example, if leaky bucket monitoring is used as a traffic descriptor, the negotiation might consist of the source specifying what parameters could be used in the leaky bucket for a given connection. Single source models can help in the selection of these parameters. Also, some applications may do some end-to-end rate control to ensure that minimal traffic is lost during periods of network congestion. Source models could be used in testing various rate control algorithms, Finally, these models are also useful in predicting the qualityof-service (QOS) that a particular application might experience during different levels of congestion. In deriving traffic models, we need metrics which can determine how "close" the model is to the actual traffic. Standard statistical measures such as means, variances, and other goodness-of-fit tests may not be appropriate here since they may not be measuring the characteristics of the process that are most important for either predicting the effect of the source on the resources in the network or the performance the source will experience. Instead, the goodness-of-fit metrics need to be directly related to the specific aspects of performance that we want to predict from the model; see e.g., [6]. In this paper, we propose two criteria for judging the appropriateness of a traffic model for bursty services. The first one applies to any high speed bursty data service and the second is specific to a variable-bit-rate (VBR) video application. To illustrate these measures we compare a previous model of VBR video with a new model proposed here. II. MODELING VARIABLE-BIT-RATE VIDEO The data we are modeling was recorded at an actual teleconference meeting. Each scene depicts the head and shoulders of one person, and is 5 rein, or 9000 frames, long. Since each 5 min of video required approximately one week to encode using software, the motivation for developing accurate models with a low computational burden is clear. A typical 10634692i94$04.0

Petri Nets Validation of Markovian Models of Emergency Department Arrivals

International audienceModeling of hospital’s Emergency Departments (ED) is vital for optimisation of health services offered to patients that shows up at an ED requiring treatments with different level of emergency. In this paper we present a modeling study whose contribution is twofold: first, based on a dataset relative to the ED of an Italian hospital, we derive different kinds of Markovian models capable to reproduce, at different extents, the statistical character of dataset arrivals; second, we validate the derived arrivals model by interfacing it with a Petri net model of the services an ED patient undergoes. The empirical assessment of a few key performance indicators allowed us to validate some of the derived arrival process model, thus confirming that they can be used for predicting the performance of an ED

A general piecewise multi-state survival model: Application to breast cancer

Multi-state models are considered in the field of survival analysis for modelling illnesses that evolve through several stages over time. Multi-state models can be developed by applying several techniques, such as non-parametric, semi-parametric and stochastic processes, particularly Markov processes. When the development of an illness is being analysed, its progression is tracked periodically. Medical reviews take place at discrete times, and a panel data analysis can be formed. In this paper, a discrete-time piecewise non-homogeneous Markov process is constructed for modelling and analysing a multi-state illness with a general number of states. The model is built, and relevant measures, such as survival function, transition probabilities, mean total times spent in a group of states and the conditional probability of state change, are determined. A likelihood function is built to estimate the parameters and the general number of cut-points included in the model. Time-dependent covariates are introduced, the results are obtained in a matrix algebraic form and the algorithms are shown. The model is applied to analyse the behaviour of breast cancer. A study of the relapse and survival times of 300 breast cancer patients who have undergone mastectomy is developed. The results of this paper are implemented computationally with MATLAB and R.Ministerio de Economía y Competitividad FQM-307European Regional Development Fund (ERDF) MTM2017-88708-PUniversity of Milano-Bicocca 2014-ATE-022