In this paper, we study a double-sided queueing model with marked Markovian arrival processes and finite discrete abandonment times. We apply the theory of multi-layer Markov modulated fluid flow (MMFF) processes to analyze the queueing model. First, we define three age processes for the queueing system and convert them into a multi-layer MMFF process. Then we analyze the multi-layer MMFF process to

In the original Bitcoin paper and other research papers since, it is assumed that Bitcoin blocks are mined at the instants of a homogeneous Poisson process. Based on blockchain block arrival data and stochastic analysis of the block arrival process, we demonstrate that this is not the case. We present a framework for studying the block arrival process, including two refined mathematical models for

This paper investigates a financial market where stock returns depend on a hidden Gaussian mean reverting drift process. Information on the drift is obtained from returns and expert opinions in the form of noisy signals about the current state of the drift arriving at the jump times of a homogeneous Poisson process. Drift estimates are based on Kalman filter techniques and described by the conditional

Consider (Xk,Yk)(k=1,…,n+1) a random sample from a bivariate random variable. If the sample is ordered according to the Y-variates, then the X-variate paired with the r-th order statistic is called the concomitant of the r-th order statistic (or the r-th concomitant). Given a sample of independent, identically distributed and bivariate phase-type random variables with continuous density function, we

This article studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is induced by a random bipartite network. In analogy with the non-network scenario, a network ruin parameter is introduced. This random parameter, which depends on the

We consider two bivariate models with two-way interactions in context of risk and queueing theory. The two entities interact with each other by providing assistance but otherwise evolve independently. We focus on certain random quantities underlying the joint survival probability and the joint stationary workload, and show that these admit stochastic decomposition. Each one can be seen as an independent

We consider two different continuous-time Markov chain models recently studied in Göbel et al.[8 Göbel, J.; Keeler, H. P.; Krzesinski, A. E.; Taylor, P. G. Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay. Perform. Eval. 2016, 104, 23–41. DOI: 10.1016/j.peva.2016.07.001.[Crossref], [Web of Science ®] , [Google Scholar]], which were created to model the interactions

Abstract Current evolutionary biology models usually assume that a phenotype undergoes gradual change. This is in stark contrast to biological intuition, which indicates that change can also be punctuated—the phenotype can jump. Such a jump could especially occur at speciation, i.e., dramatic change occurs that drives the species apart. Here we derive a Central Limit Theorem for punctuated equilibrium

(2020). Preface. Stochastic Models: Vol. 36, 10th International Conference on Matrix-Analytic Methods for Stochastic Models, pp. 173-175.

A man has a house with n doors. Initially he places k pairs of walking shoes at each door. For each walk, he chooses one door at random, and puts on a pair of shoes, returns after the walk to a randomly chosen door and takes off the shoes at the door. Let Tn be the first time a door is chosen to walk out but with no shoes available. We show that as n→∞, Tn has the same asymptotic distribution and moments

In this paper, we are concerned with strong convergence rate of Euler scheme for time-inhomogeneous one-dimensional stochastic differential equations involving the local time (SDELT) of the unknown process at point zero. We use a space transform in order to remove the local time from this class of stochastic differential equations. We provide the approximation of Euler for the stochastic differential

We apply physical interpretations to construct algorithms for the key matrix G of discrete-time quasi-birth-and-death (dtQBD) processes which records the probability of the process reaching level  (n−1) for the first time given the process starts in level n. The construction of G and its z-transform G(z) was motivated by the work on stochastic fluid models (SFMs). In this methodology, we first write

The focus of this work is the numerical application of a stochastic decision support model for the patient admission scheduling problem with random arrivals and departures. Here, we discuss the methodology for applying our model to real-world problems. We outline a solution approach for efficient computation, provide a numerical analysis of the model, and illustrate the methodology with examples. A

We study a future Internet networking paradigm where instead of congestion control an open loop traffic control is applied. We aim to give theoretical foundations for data transfer controlled only by the access points of the network. The key characteristics of networks without congestion control are stability and efficiency addressed in this paper. We consider the queue length processes of data-flows

We prove a counterintuitive result concerning the expected hitting/absorption time for a class of Markov chains. The “paradox” already shows itself in the following elementary example that is suitable for undergraduate teaching: Batman and the Joker perform independent discrete-time random walks on the vertices of a square until they meet, starting from opposite vertices. Batman always moves (and clockwise

In this paper, we consider the number of departures seen by a tagged customer while in service in a classical M/M/1 processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system revealed in an earlier study, we compute the probability mass function of the random variable under consideration. We moreover derive the asymptotic behavior of this probability mass function

We consider in this paper a risk reserve process where the claims and gains arrive according to two independent Poisson processes. While the gain sizes are phase-type distributed, we assume instead that the claim sizes are phase-type perturbed by a heavy-tailed component; that is, the claim size distribution is formally chosen to be phase-type with large probability 1−ϵ and heavy-tailed with small

In the stochastic network model of Britton and Lindholm, the number of individuals evolves according to a supercritical linear birth and death process, and a random social index is assigned to each individual at birth, which controls the rate at which connections to other individuals are created. We derive a rate for the convergence of the degree distribution in this model towards the mixed Poisson

A Markov modulated Brownian motion (MMBM) is a substantial generalization of the classical Brownian motion and is obtained by allowing the Brownian parameters to be modulated by an underlying Markov chain of environments. As in Brownian motion, the stationary analysis of the MMBM becomes easy once the distributions of the first passage time between levels are determined. Asmussen (Stochastic Models

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

We investigate a new class of separable systems which exhibit a product-form stationary distribution. These systems consist of parallel production systems (servers) at several locations, each with a local inventory under base stock policy, connected with a common supplier network. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory

This article provides a computational formula for the the stability of the probability of ruin of the compound Poisson risk process. This stability is the infinitesimal standardized variation of the probability of ruin resulting from pointwise perturbation of the distribution of the individual claim amounts. The proposed formula is obtained from the saddlepoint approximation to the distribution of

In this article, we study the asymptotic behavior of the realized quadratic variation of a process ∫0tusdYs(1), where u is a β-Hölder continuous process with β>1−H and Yt(1)=∫0te−sdBasH, where at=HetH and BH is a fractional Brownian motion with Hurst index H∈(0,1). By exploiting the concentration phenomena, we prove almost sure convergence of the quadratic variation, that holds uniformly in time and

In this article, we develop a new methodology for integrating epistemic uncertainties into the computation of performance measures of Markov chain models. We developed a power series algorithm that allows for combining perturbation analysis and uncertainty analysis in a joint framework. We characterize statistically several performance measures, given that distribution of the model parameter expressing

We consider an individual or household endowed with an initial capital and an income, modeled as a linear function of time. Assuming that the discount rate evolves as an Ornstein-Uhlenbeck process, we target to find an unrestricted consumption strategy such that the value of the expected discounted consumption is maximized. Differently than in the case with restricted consumption rates, we can determine

A gene family is a set of evolutionarily related genes formed by duplication. Genes within a gene family can perform a range of different but possibly overlapping functions. The process of duplication produces a gene that has identical functions to the gene it was duplicated from with subsequent divergence over time. In this paper, we explore different models for the ongoing evolution of a gene family

This article studies Ornstein-Uhlenbeck (OU) diffusions with sticky reflection at zero. Sticky reflecting OU diffusions are defined as weak solutions of a system of SDEs involving the local time at the boundary at zero. The transition semigroup and the distribution of the first hitting time up are characterized analytically via their spectral representations. The results are applied to the Vasicek