We consider the problem of service rate control of a single server queueing system when the arrival process is governed by a finite-state Markov-modulated Poisson process. There are two main technical contributions. First, in keeping with intuition, we show that the optimal service rate is non-decreasing in the number of customers in the system. That is, higher congestion rates warrant higher s...

We consider a Poisson cluster model, motivated by insurance applications. At each claim arrival time, modeled by the point of a homogeneous Poisson process, we start a cluster process which represents the number or amount of payments triggered by the arrival of a claim in a portfolio. The cluster process is a Lévy or truncated compound Poisson process. Given the observations of the process over...

In this work, a class of multidimensional stochastic hybrid dynamic models is studied. The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the syste...

Coal mining in India has a history of over 225 years. The industry currently occupies a covetable third ranking in the world league table of hard coal production after China and the USA. Mechanization has made possible major breakthroughs in coal mining technology. The record of production and productivity of Indian underground coal mines over the years is dismal, to say the least. At the time ...

The space-fractional Poisson process is a time-changed homogeneous Poisson process where the time change is an independent stable subordinator. In this paper, a further generalization is discussed that preserves the Lévy property. We introduce a generalized process by suitably time-changing a superposition of weighted space-fractional Poisson processes. This generalized process can be related t...

This paper investigates a SRGM (software reliability growth model) based on the NHPP (nonhomogeneous Poisson process) which incorporates a logistic testing-effort function. SRGM proposed in the literature consider the amount of testing-effort spent on software testing which can be depicted as an exponential curve, a Rayleigh curve, or a Weibull curve. However, it might not be appropriate to rep...

A mathematical model based on stochastic and statistics theories is useful to describe the software fault-removal phenomena or the software failure-occurrence phenomena and estimate the software reliability quantitatively. A mathematical tool which describes software reliability aspect is a software reliability growth model (SRGM). Discrete time models in software reliability are important and ...

This paper presents a reliability analysis of Local Exchange Carrier telecommunication switches in the United States, based upon empirical data. Telecommunication switch outage statistics are analyzed for a multiyear period, allowing examination into switch failure frequency, causes, and trends. Failure categories are created by reported outage cause codes, including human error, design error, ...

We analyze the statistical properties of the coverage of a one-dimensional path induced by a two dimensional non homogeneous random sensor network. The sensor locations form a non homogeneous Poisson process and the coverage area of each sensor are circles of random i.i.d. radii. We first describe the onedimensional coverage (sensing) process on the line and describe an equivalent time-inhomoge...

In this project, I will introduce a method to estimate the function by cubic splines. As an example, I will focus on the non-homogeneous Poisson process. Since this method uses an optimization model based on the maximum likelihood principle, it may applied to other stochastic processes. The most critical point of this presentation is a nonnegativity constriant on the splines. In addition, choos...