Bounding the Inefficiency of the Multiclass, Multicriteria C-Logit Stochastic User Equilibrium in a Transportation Network

We derive the exact inefficiency upper bounds of the multiclass C-Logit stochastic user equilibrium (CL-SUE) in a transportation network. All travelers are classified on the basis of different values of time (VOT) into M classes. The multiclass CL-SUE model gives a more realistic path choice probability in comparison with the logit-based stochastic user equilibrium model by considering the overlapping effects between paths. To find efficiency loss upper bounds of the multiclass CL-SUE, two equivalent variational inequalities for the multiclass CL-SUE model, i.e., time-based variational inequality (VI) and monetary-based VI, are formulated. We give four different methods to define the inefficiency of the multiclass CL-SUE, i.e., to compare multiclass CL-SUE with multiclass system optimum, or to compare multiclass CL-SUE with multiclass C-Logit stochastic system optimum (CL-SSO), under the time-based criterion and the monetary-based criterion, respectively. We further investigate the effects of various parameters which include the degree of path overlapping (the commonality factor), the network complexity, degree of traffic congestion, the VOT of user classes, the network familiarity, and the total demand on the inefficiency bounds.

Analysis of stochastic system status of electrificated railways based on machine learning

Stochastic systems are the systems in which changes are random, the predicted values depend on the probability distribution. An example of a stochastic system is a power system, the operation of which is influenced by many random factors, their analysis and control will give an opportunity to control the safe cycle as well as operation reliability. Improving the efficiency and reliability of the energy system is impossible without the development of special monitoring tools and predicting their state.

Stochastic system dynamics modelling for climate change water scarcity assessment of a reservoir in the Italian Alps

Water management in mountain regions is facing multiple pressures due to climate change and anthropogenic activities. This is particularly relevant for mountain areas where water abundance in the past allowed for many anthropogenic activities, exposing them to future water scarcity. Here stochastic system dynamics modelling (SDM) was implemented to explore water scarcity conditions affecting the stored water and turbined outflows in the Santa Giustina (S. Giustina) reservoir (Autonomous Province of Trento, Italy). The analysis relies on a model chain integrating outputs from climate change simulations into a hydrological model, the output of which was used to test and select statistical models in an SDM for replicating turbined water and stored volume within the S. Giustina dam reservoir. The study aims at simulating future conditions of the S. Giustina reservoir in terms of outflow and volume as well as implementing a set of metrics to analyse volume extreme conditions. Average results on 30-year slices of simulations show that even under the short-term RCP4.5 scenario (2021–2050) future reductions for stored volume and turbined outflow are expected to be severe compared to the 14-year baseline (1999–2004 and 2009–2016; −24.9 % of turbined outflow and −19.9 % of stored volume). Similar reductions are expected also for the long-term RCP8.5 scenario (2041–2070; −26.2 % of turbined outflow and −20.8 % of stored volume), mainly driven by the projected precipitations having a similar but lower trend especially in the last part of the 2041–2070 period. At a monthly level, stored volume and turbined outflow are expected to increase for December to March (outflow only), January to April (volume only) depending on scenarios and up to +32.5 % of stored volume in March for RCP8.5 for 2021–2050. Reductions are persistently occurring for the rest of the year from April to November for turbined outflows (down to −56.3 % in August) and from May to December for stored volume (down to −44.1 % in June). Metrics of frequency, duration and severity of future stored volume values suggest a general increase in terms of low volume below the 10th and 20th percentiles and a decrease of high-volume conditions above the 80th and 90th percentiles. These results point at higher percentage increases in frequency and severity for values below the 10th percentile, while volume values below the 20th percentile are expected to last longer. Above the 90th percentile, values are expected to be less frequent than baseline conditions, while showing smaller severity reductions compared to values above the 80th percentile. These results call for the adoption of adaptation strategies focusing on water demand reductions. Months of expected increases in water availability should be considered periods for water accumulation while preparing for potential persistent reductions of stored water and turbined outflows. This study provides results and methodological insights that can be used for future SDM upscaling to integrate different strategic mountain socio-economic sectors (e.g. hydropower, agriculture and tourism) and prepare for potential multi-risk conditions.

Relative controllability of a stochastic system using fractional delayed sine and cosine matrices

In this paper, we study the relative controllability of a fractional stochastic system with pure delay in finite dimensional stochastic spaces. A set of sufficient conditions is obtained for relative exact controllability using fixed point theory, fractional calculus (including fractional delayed linear operators and Grammian matrices) and local assumptions on nonlinear terms. Finally, an example is given to illustrate our theory.

IMPACT OF THE SAME DEGENERATE ADDITIVE NOISE ON A COUPLED SYSTEM OF FRACTIONAL SPACE DIFFUSION EQUATIONS

In this paper, we present a class of stochastic system of fractional space diffusion equations forced by additive noise. Our goal here is to approximate the solutions of this system via a system of ordinary differential equations. Moreover, we study the influence of the same degenerate additive noise on the stability of the solutions of the stochastic system of fractional diffusion equations. We are interested in the systems that have nonlinear polynomial and give applications as Lotka–Volterra system from biology and the Brusselator model for the Belousov–Zhabotinsky chemical reaction from chemistry to illustrate our results.

Threshold dynamics for a class of stochastic SIRS epidemic models with nonlinear incidence and Markovian switching

In this paper, we consider a stochastic SIRS epidemic model with nonlinear incidence and Markovian switching. By using the stochastic calculus background, we establish that the stochastic threshold R_{ swt} can be used to determine the compartment dynamics of the stochastic system. Some examples and numerical simulations are presented to confirm the theoretical results established in this paper.