Further Results on Delay-distribution-dependent Robust Stability Criteria for Delayed Systems

This paper concerns the robust stability analysis of uncertain systems with time delays as random variables drawn from some probability distribution. The delay-distribution-dependent criteria for the exponential stability of the original system in mean square sense are achieved by Lyapunov functional method and the linear matrix inequality （LMI） technique. The proposed approach involves neither free weighting matrices nor any model transformation, and it shows that the new criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Modification of Wirsching’s Model for Fatigue Reliability Analysis

First, Wirsching's model, which is widely employed in fatigue reliability anlysis of marine and offshore structures, is analysed systematically. It is found that the very important random variable A in Wirsching's model can not be directly determined from fatigue experiment because of the irreversibility of fatigue test, and in fact, what Wirsching studied from testing results is not A but a of the statistical Miner's rule. Second, by use of the statistical Miner's rule, a modified Wirsching's model is proposed. Thirdly and more importantly, based on the two-dimensional probabilistic Miner's rule, a new model is established for fatigue reliability analysis of structural components subjected to specified cyclic loading of variable amplitude or stochastic time history. In the end, an example is presented, from which it will be seen that this new model is very convenient to use and feasible to engineering practice.

A Double Shot Noise Process and Its Application in Insurance

The authors consider a compound Cox model of insurance risk with the additional economic assumption of a positive interest rate. As the authors note a duality result relating a compound Cox model of insurance risk with a positive interest rate and a double shot noise process, the authors analyze a double shot noise process systematically for its theoretical distributional properties, based on the piecewise deterministic Markov process theory, and the martingale methodology. The authors also obtain the moments of aggregate accumulated/discounted claims where the claim arrival process follows a Cox process with shot noise intensity. Removing the parameters in a double shot noise process gradually, the authors show that it becomes a compound Cox process with shot noise intensity, a single shot noise process and a compound Poisson process. Numerical comparisons are shown between the moments （i.e. means and variances） of a compound Poisson model and their counterparts of a compound Cox model with/without considering a positive interest rate. For that purpose, the authors assume that claim sizes and primary event sizes follow an exponential distribution, respectively.

A supply chain model for imperfect production system with stochastic lead time demand

This study deals an integrated manufacturer-buyer supply chain system for imperfect production under stochastic lead time demand.Here,defective rate has been followed as a function of production rate.Also,the produced units have been inspected in order to screen the defective units but screening rate is less than the production rate and greater than the demand rate.Buyer purchases the products from the manufacturer.Also,we assume that shortage during the lead time is permitted and demand during the shortage period is fully backordered.The objective is to derive the optimal production rate,ordering quantity and to maximize joint total profit.Basically,two different models for different probability distribution functions of stochastic lead time demand have been developed.Some numerical examples are provided to show the applicability of the proposed models comparing the optimum average profits.Finally,sensitive analysis,conclusion and future researches are presented.

Stochastic Bi-level Programming Model for Home Healthcare Scheduling Problems Considering the Degree of Satisfaction with Visit Time

Home health care(HHC)includes a wide range of healthcare services that are performed in customers'homes to help them recover.With the constantly increasing demand for health care,HHC policymakers are eager to address routing and scheduling problems from the perspective of optimization.In this paper,a bi-level programming model for HHC routing and scheduling problems with stochastic travel times is proposed,in which the degree of satisfaction with the visit time is simultaneously considered.The upper-level model is formulated for customer assignment with the aim of minimizing the total operating cost,and the lower-level model is formulated as a routing problem to maximize the degree of satisfaction with the visit time.Consistent with Stackelberg game decision-making,the trade-off relationship between these two objectives can be achieved spontaneously so as to reach an equilibrium state.A three-stage hybrid algorithm combining an iterated local search framework,which uses a large neighborhood search procedure as a sub-heuristic,a set-partitioning model,and a post-optimization method is developed to solve the proposed model.Numerical experiments on a set of instances including 10 to 100 customers verify the effectiveness of the proposed model and algorithm.

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional.For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.

Modelling and analysis of hybrid stochastic timed Petri net

In this paper,an interesting Hybrid Stochastic Timed Petri Net(HSTPN)is proposed for a class of hybrid systems.The proposed HSTPN can be adopted to represent hybrid systems with discrete,continuous,conflicting,time-delay and stochastic characteristics simultaneously.The proposed HSTPN outperforms conventional hybrid Petri net models in terms of describing the scalability and immediacy of hybrid systems.Advantages of the HSTPN on describing hybrid system are verified by establishing some equivalent models of HPN and its derived models.

A New Method of State Estimation for Singular Discrete-time Stochastic Linear System

Using theory of Bayesian Dynamic Models and Forecasting , this paper mainly deals with the problem on state estimation for singular discrete time stochastic linear system. And a new method of state estimation linear Bayes estimation (LBE for short) has been proposed.

Feedback control for stochastic finite-time/fixed-time synchronization of stochastic coupled nonlinear systems

A novel feedback control is proposed to investigate the stochastic finite-time/fixed-time synchronization between two stochas-tic coupled nonlinear systems(SCNSs).Based on graph theory and Lyapunov function methods,some effective stochastic finite-time/fixed-time synchronization criteria for SCNSs are established.Finally,the examples are included to demonstrate our analytical results.

Optimal charging plan for electric bus considering time-of-day electricity tariff

Purpose–The purpose of this study is to develop an optimization method for charging plans with the implementation of time-of-day(TOD)electricity tariff,to reduce electricity bill.Design/methodology/approach–Two optimization models for charging plans respectively with fixed and stochastic trip travel times are developed,to minimize the electricity costs of daily operation of an electric bus.The charging time is taken as the optimization variable.The TOD electricity tariff is considered,and the energy consumption model is developed based on real operation data.An optimal charging plan provides charging times at bus idle times in operation hours during the whole day(charging time is 0 if the bus is not get charged at idle time)which ensure the regular operation of every trip served by this bus.Findings–The electricity costs of the bus route can be reduced by applying the optimal charging plans.Originality/value–This paper produces a viable option for transit agencies to reduce their operation costs.

The valuation of barrier options under a threshold rough Heston model

In this paper,we propose a novel model for pricing double barrier options,where the asset price is modeled as a threshold geometric Brownian motion time changed by an integrated activity rate process,which is driven by the convolution of a fractional kernel with the CIR process.The new model both captures the leverage effect and produces rough paths for the volatility process.The model also nests the threshold diffusion,Heston and rough Heston models.We can derive analytical formulas for the double barrier option prices based on the eigenfunction expansion method.We also implement the model and numerically investigate the sensitivities of option prices with respect to the parameters of the model.

A mathematical model for preventing HIV virus from proliferating inside CD4 T brownian cell using Gaussian jump nanorobot

We present a statistical distribution of a nanorobot motion inside the blood.This distribution is like the distribution of A and B particles in continuous time random walk scheme inside the fAuid reactive anomalous transport with stochastic waiting time depending on the Gaussian distribution and a Gaussian jump length which is detailed in Zhang and Li[J.Stat.Phys,Published Online with doi:10.1007/s10955-018-2185-8,2018].Rather than estimating the length parameter of the jumping distance of the nanorobot,we normalize the Probability Density Function(PDF)and present some reliability properties for this distribution.In addition,we discuss the truncated version of this distribution and its statistical properties,and estimate its length parameter.We use the estimated distance to study the conditions that give a finite expected value of the first meeting time between this nanorobot in the case of nonlinear flow with independent d-dimensional Gaussian jumps and an independent d-dimensional CD4 T Brownian cell in the blood(d-space)to prevent the HIV virus from proliferating within this cell.