One of the most important quantities of the exact Markovian SIS epidemic process is the time-dependent prevalence, which is the average fraction of infected nodes. Unfortunately, the Markovian SIS epidemic model features an exponentially increasing computational complexity with growing network size N . In this paper, we evaluate a recently proposed analytic approximate prevalence function intro...

Abstract: This paper examines the problem of designing a robust H∞ state-feedback controller for a class of uncertain nonlinear descriptor Markovian jump systems described by a Takagi-Sugeno (TS) fuzzy model with Markovian jumps. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor Markovian jump systems to have an H∞ perform...

Sensitivity analysis of Markovian models amounts to computing the constants in polynomial functions of a parameter under study. To handle the computational complexity involved, we propose a method for approximate sensitivity analysis of such models. We show that theoretical properties allow us to reason for the present time using just few observations from the past with small loss in accuracy. ...

We develop an optimization model based on Markovian approach to determine the optimum value of thresholds in a proposed acceptance sampling design. Consider an acceptance sampling plan where items are inspected and when the number of conforming items between successive defective items falls below a lower control threshold value, then the batch is rejected, and if it falls above a control thresh...

We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the los...

In this paper, the non-Markovian dissipative dynamics of the phase damped Jaynes-Cummings model in the presence of a classical homogeneous gravitational field will be analyzed. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a non-Markovian phase damping mechanism. First, the non-Marko...

Markovian modeling of systems is a promising technique used to gauge the performance, dependability, and performability of systems. It can be used to aid design decisions by evaluating a range of design options for a range of environments, and it can be used to increase understanding of operational systems. Unfortunately, Markovian modeling is limited by the “state-space explosion,” or the expo...

Abstract The interrelationship between the non-Markovian stochastic Schrödinger equations and the corresponding non-Markovian master equations is investigated in the finite temperature regimes. We show that the general finite temperature non-Markovian trajectories can be used to derive the corresponding non-Markovian master equations. A simple, yet important solvable example is the well-known d...

This paper studies a single-stage production system, two-stage production system where specification limits are designed for inspection. When quality characteristics fall below a lower threshold or above an upper threshold, a decision is made to rework or scrap the item. The target is to determine the optimum target for a process based on rework or scrap costs. In contrast to previous studies, ...

We study a variant of Hanski's incidence function model that allows habitat patch characteristics to vary over time following a Markov process. The widely studied case where patches are classified as either suitable or unsuitable is included as a special case. For large metapopulations, we determine a recursion for the probability that a given habitat patch is occupied. This recursion enables u...