We investigate local-density dependent Markov processes on a class of large graphs sampled from graphon, where the transition rates vertices are influenced by states their neighbors. show that as average degree converges to infinity (faster than given threshold), evolution process in transient regime solution set non-local integro-partial differential equations depending limit graphon. also provide rigorous derivation for epidemic threshold case Susceptible–Infected–Susceptible (SIS) such graphons.

This paper presents matrix-exponential (ME) distributions, whose squared coefficient of variation (SCV) is very low. Currently, there no symbolic construction available to obtain the most concentrated ME and numerical optimization-based approaches construct them have many pitfalls. We present a procedure which avoids issues.

We propose a numerical inverse Laplace transformation method without overshoot which is derived from matrix exponential (ME) distributions with minimal coefficient of variation. discuss the properties through an integral based interpretation methods belonging to Abate–Whitt framework. Compared previously applied non-overshooting alternative, "Erlang" method, error proposed improves O(1/n) O(1/n2) while it maintains same computational complexity.

In this paper, we investigate dimension reduction possibilities of multidimensional time series data and introduce a graph based clustering approach using the cross-correlation between series. The proposed solution consists two main steps: introducing novel similarity measure for measuring cross-correlations graph-based technique. These parts are both compared to existing techniques, including noise tolerance our performs better in noisy environment. is applied performance metrics specific...

Load balancing plays a crucial role in many large scale computer systems. Much prior work has focused on systems with First-Come-First-Served (FCFS) servers. However, servers practical are more complicated. They serve multiple jobs at once, and their service rate can depend the number of service. Motivated by this, we study load for using Limited-Processor-Sharing (LPS). Our model heterogeneous servers, meaning curve multiprogramming level (limit sharing processor) differs between We focus...

Numerical inverse Z-transformation (NIZT) methods have been efficiently used in engineering practice for a long time. In this paper, we compare the abilities of most widely NIZT methods, and propose new variant classic method based on contour integral approximation, which is efficient when point interest (at value function needed) smaller than order method. We also introduce vastly different concentrated matrix geometric (CMG) distributions that tackles limitations many larger

The paper presents a new proof of O'Cinneide's characterization theorem.[7 O'Cinneide, C.A. Characterization phase-type distributions. Comm. Stat. Stochastic Models 1990, 6, 1–57.[Taylor & Francis Online] , [Google Scholar]] It is much simpler than the original one and constructive in sense that we not only show existence phase type representation, but present procedure which creates representation. We prove succeeds when conditions theorem hold.

In spite of the fact that discrete phase type (DPH) distributions are used almost as often continuous (CPH) canonical representation is not available for general (cyclic) order 3 DPH yet. this paper we investigate 3. During course investigation find problem far more complex than one CPH distribution. As a result needed to distinguish 8 different subclasses distributions, while it was enough their representation. Additionally, were able prove all with relatively simple methodology which...

Load balancing plays a crucial role in many large scale systems. Several different load principles have been proposed the literature, such as Join-Shortest-Queue (JSQ) and its variations, or Join-Below-Threshold. We provide high level mathematical framework to examine heterogeneous server clusters mean-field limit system number of servers proportionally. aim identify both transient stationary for various choices principles, compute relevant performance measures distribution mean time jobs,...

Abstract The steepest increase property of phase-type (PH) distributions was first proposed in O’Cinneide (1999) and proved Yao (2002), but since then has received little attention the research community. In this work we demonstrate that can be applied for proving previously unknown moment bounds PH with infinite or finite support. Of special interest are free specific representations except size representation. For support, it is shown such a distribution stochastically smaller than equal...

Load balancing plays a crucial role in many large scale computer systems. Much prior work has focused on systems with First-Come-First-Served (FCFS) servers. However, servers practical are more complicated. They serve multiple jobs at once, and their service rate can depend the number of service. Motivated by this, we study load for using Limited-Processor-Sharing (LPS). Our model heterogeneous servers, meaning curve multiprogramming level (limit sharing processor) differs between We focus...

We provide error bounds for the N-intertwined mean-field approximation (NIMFA) local density-dependent Markov population processes with a well-distributed underlying network structure showing NIMFA being accurate when typical vertex has many neighbors. The result justifies some of most common approximations used in epidemiology, statistical physics and opinion dynamics literature under certain conditions. allow interactions between more than 2 individuals, an hypergraph accordingly.

The self-repelling Brownian polymer model (SRBP) initiated by Durrett and Rogers in [Durrett-Rogers (1992)] is the continuous space-time counterpart of myopic (or 'true') self-avoiding walk (MSAW) introduced physics literature Amit, Parisi Peliti [Amit-Parisi-Peliti (1983)]. In both cases, a random motion space pushed towards domains less visited past kind negative gradient occupation time measure. We investigate asymptotic behaviour SRBP non-recurrent dimensions. First, extending...

Highly concentrated functions play an important role in many research fields including control system analysis and physics, they turned out to be the key idea behind inverse Laplace transform methods as well. This paper uses matrix-exponential family of create highly functions, whose squared coefficient variation (SCV) is very low. In field stochastic modeling, have been used for decades. They advantages: are easy manipulate, always non-negative, integrals involving often closed-form...