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In this article we consider an aggregate loss model with dependent losses. The losses occurrence process is governed by a two-state Markovian arrival process (MAP2), a Markov renewal process process that allows for (1) correlated…
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the…
Recently it has been shown that tensor networks (TNs) have the ability to represent the expected return of a single-agent finite Markov decision process (FMDP). The TN represents a distribution model, where all possible trajectories are…
Regression classes modeling more than the mean of the response have found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this family of models. Expectiles offer a quantile-like…
We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a…
Randomized load-balancing algorithms play an important role in improving performance in large-scale networks at relatively low computational cost. A common model of such a system is a network of $N$ parallel queues in which incoming jobs…
The past year saw the introduction of new architectures such as Highway networks and Residual networks which, for the first time, enabled the training of feedforward networks with dozens to hundreds of layers using simple gradient descent.…
Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much…
As a representation of relational data over time series, longitudinal networks provide opportunities to study link formation processes. However, networks at scale often exhibits community structure (i.e. clustering), which may confound…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
In general, obtaining the exact steady-state distribution of queue lengths is not feasible. Therefore, we establish bounds for the tail probabilities of queue lengths. Specifically, we examine queueing systems under Heavy-Traffic (HT)…
Distributed storage systems provide large-scale reliable data storage services by spreading redundancy across a large group of storage nodes. In such a large system, node failures take place on a regular basis. When a storage node breaks…
In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we…
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…
We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential…
In this paper, we study a multidimensional risk model with a common renewal process and in the presence of a constant interest force. The claim sizes are independent and identically distributed random vectors, with the distribution of…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
This paper considers a particular renewal-reward process with multivariate discounted rewards (inputs) where the arrival epochs are adjusted by adding some random delays. Then this accumulated reward can be regarded as multivariate…
We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…
The efficient management of large-scale queueing networks is critical for a variety of sectors, including healthcare, logistics, and customer service, where system performance has profound implications for operational effectiveness and cost…