Springer

We investigate clusters of extremes defined as subsequent exceedances of high thresholds in a Lindley process. The latter is usually used to model the waiting time or the length of a queue in queuing systems. Distributions of the cluster and inter-cluster sizes of the Lindley process are obtained for a given value of the threshold assuming that the process begins from the zero value. An example of a M/M/1 queue and the impact of service and arrival rates on the cluster and inter-cluster distributions are shown.

Taking account for the graph randomness, our purpose is a node classification by their extremal indexes (EI) as the local dependence measure of node influence characteristics. The EI was calculated by node PageRanks of the local tree related to the node, which is a kind of Thorny Branching Tree (TBT). The blocks estimator was used for the EI estimation by sliding and disjoint block definitions. The classification by the node EI value and the average block size for the local node TBT was introduced for simulated graphs by the Forest Fire and Erdős-Rényi Models and the Berkeley-Stanford dataset as a real example. The new classification methodology is proposed irrespective on the graph structure.

We consider the multipath communication between a client and a server that is established at the transport and session layers of an SDN/NFV protocol stack in a fog computing scenario. We analyze the reliability function of an associated redundant transport system comprising two logical channels that are susceptible to failures. The failure processes of both channels are described by Markov-modulated failure times that are driven by the transitions of a common Markovian environment. We model the error-prone system with repair and independent phase-type distributed repair times by a continuous-time Markov chain. We identify its generator matrix in terms of Kronecker products of the underlying parameter matrices that are determined by the interarrival times driven by Markov-modulated failure processes and the independent phase-type distributed repair times. We show that the steady-state distribution of the restoration model can be eectively calculated by an iterative aggregation-disaggregation method for block matrices and compute the associated reliability function of the transport system by a uniformization method.

A new class of semiparametric estimators of the tail index is proposed. These estimators are based on a rather general class of semiparametric statistics. Their asymptotic normality is proved. The new estimators are compared with several other recently introduced estimators of the tail index in terms of the asymptotic mean-square error. An algorithm to calculate the new estimators is developed and then applied to several real data sets.

As a result of the climate change the situation in Arctic area leads to several important consequences. On the one hand, fossil fuels can be exploited much easier than before. On the other hand, their excavation leads to serious potential threats to fishing by changing natural habitats which in turn creates serious damage to the countries’ economies. Another set of problems arises due to the extension of navigable season for shipping routes. Thus, there are already discussions on how should resources be allocated among countries. In Aleskerov and Victorova (An analysis of potential conflict zones in the Arctic Region, HSE Publishing House, Moscow, 2015) a model was presented analyzing preferences of the countries interested in natural resources and revealing potential conflicts among them. We present several areas allocation models based on different preferences over resources among interested countries. As a result, we constructed several allocations where areas are assigned to countries with respect to the distance or the total interest, or according to the procedure which is counterpart of the Adjusted Winner procedure. We consider this work as an attempt to help decision-making authorities in their complex work on adjusting preferences and conducting negotiations in the Arctic zone. We would like to emphasize that these models can be easily extended to larger number of parameters, to the case when some areas for some reasons should be excluded from consideration, to the case with ‘weighted’ preferences with respect to some parameters. And we strongly believe that such models and evaluations based on them can be helpful for the process of corresponding decision making.

Рассматриваются проблемы управления в области обеспечения безопасности дорожного движения, развивается системный подход к решению этих проблем на основе программно-целевого управления. Дается описание математических моделей и механизмов обеспечения безопасности дорожного движения. Это, в первую очередь, механизмы комплексного оценивания применительно к оценке деятельности органов Государственной инспекции безопасности дорожного движения, методы разработки программ повышения уровня безопасности дорожного движения с учетом фактора надежности (вероятности реализации программы).

For modern energy markets it is typical to use dynamic real-time pricing schemes even for residential customers. Such schemes are expected to stimulate rational energy consumption by the end customers, provide peak shaving and overall energy efficiency. But under dynamic pricing planning a household’s energy consumption becomes complicated. So automated planning of household appliances is a promising feature for developing smart home environments. Such a planning should adapt to individual user’s habits and preferences over comfort to cost balance. We propose a novel approach based on learning customer preferences expressed by a utility function. In the paper an algorithm based on inverse reinforcement learning (IRL) framework is used to infer the user’s hidden utility. We compare IRL-based approach to multiple state-of-the art machine learning techniques and the proposed earlier parametric Bayesian learning algorithm. The training and test datasets are generated by the simulated user’s behavior with different price volatility settings. The goal of the algorithms is to predict a user’s behavior based on the existing history. The IRL and Bayesian approaches showed similar performance and both of them outperforms modern machine learning algorithms such as XGBoost, random forest etc. In particular, the preference learning algorithms significantly better generalize to data generated with parameters different from the training sample. The experiments showed that preference learning approach can be especially useful for smart home automation problems where future situations can be different from those available for training.

We model the end-to-end delay of advanced services in the Internet by means of a heavy-tailed Weibull-Pareto distribution (WPD). First we summarize the structural properties of the three-parameter WPD class and indicate its relation to the general Weibull-TX class. Then we present an eective estimation scheme to compute the parameters of a WPD distribution by a nite sample. Finally we show how a WPD distribution can be applied to determine the relevant QoE performance metric MOS of end-to-end delay dependent services in the Internet.

We propose the new EI-clustering method for random networks. Regarding the underlying graph of a random network, EI-clustering is an advanced statistical tool for community detection and based on the estimation of the extremal index (EI) associated with each node. The EI metric is estimated by samples of indices of the node in uences. The latter quantities are determined by the PageRank and a Max-Linear Model. The EI values of both models are estimated by a blocks estimator for each node which is considered as the root of a Thorny Branching Tree. Generations of descendant nodes related to the root node of the tree are used as blocks. The reciprocal of the EI value indicates the average number of in uential nodes per generation containing at least one in uential node. In the context of random graphs the EI metric indicates the ability of a randomly selected node to attract highly ranked nodes in its orbit. Looking at the changing shape of a plot of the EI metric versus the node number, the node communities are detected. The EI-clustering method is compared with the conductance measure regarding the data set of a real Web graph.

Modern tools to measure Internet traffic such as Wireshark or Atheris offer complex opportunities to collect packet data from high speed networks. Advanced statistical methods are required to support an adequate teletraffic analysis of these traces and the evaluation of relevant performance indices, for instance, of captured packet flows stemming from new multimedia services in Internet. They allow us to cope with immanent dependencies and underlying heavy-tailed distributions of interesting features of the traffic such as the bitrates, volumes or lengths of sessions, the inter-arrival times, loss rates and delay distributions of the packet streams or their equivalent bandwidth.  In the tutorial we shall discuss useful statistical techniques to handle the arising strongly correlated or long-range dependent time series and heavy-tailed marginal distributions. The latter features characterize the underlying random variables of the observed data. Advanced procedures to compute the demanded bandwidth of observed streams or the delay-loss profiles of packet flows during a session will be stated. The analysis concepts will be illustrated by real traces arising from some popular Internet applications.  The tutorial shall stimulate the participants to incorporate adaptations of the sketched statistical procedures into open source tools or their own codes according to their personal needs.