it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the innitesimal covariance give...

In this paper, we present a stochastic model with optimization and risk analyses in Communication Networks (CNs). The model is proposed for offline traffic engineering optimization with bandwidth allocation and performance analysis. First, we present an analysis of the bandwidth allocation problem to derive the optimal bandwidth capacity with a loss rate constraint. And, we also use a mean–vari...

In this paper we consider a region which is divided into serveral subregions. Each region is served by a station with a finite capacity. This means that the station can only serve customers within the limits of its capacity (maximum number of connections simultaneously). In connection with this the following question arises: What is the first occurrence time for this event? More exactly, what i...

This paper studies stochastic programs with first-stage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly NP-hard in general. We provide pseudo-polynomial algorithms for three special cases o...

The problem of maximizing the input-output mutual information rate for a Markov channel is cast as a problem of controlling a partially observed controlled Markov chain on a suitable state space with time-averaged reward. This establishes the equivalence of its channel capacity with the value of a certain dynamic program. 1. Introduction. The problem of characterizing and computing the capacity...

Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics. We present an efficient method for...

The reliability and accuracy of spike trains have been shown to depend on the nature of the stimulus that the neuron encodes. Adding ion channel stochasticity to neuronal models results with a macroscopic behavior that replicates the input-dependent reliability and precision of real neurons. We calculate the amount of information that an ion channel based stochastic Hodgkin-Huxley (HH) neuron m...

n this paper the problem of capacity planning under risk from demand and price/cost uncertainty of the finished products is addressed. The deterministic model is extended into a two-stage stochastic model with fixed recourse by means of various expected levels of demand as random. A recourse penalty is also included in the objective for both shortage and surplus in the finished products. The mo...

Among different stochastic user equilibrium (SUE) traffic assignment models, the Logit-based stochastic user equilibrium (SUE) is extensively investigated by researchers. It is constantly formulated as the low-level problem to describe the drivers' route choice behavior in bi-level problems such as network design, toll optimization et al. The Probit-based SUE model receives far less attention c...