This short note discusses open problems and partial solutions related to Sheldon M Ross's second conjecture about the classical single server queue subject a randomly time-varying rate arrival rate.

Control scheduling refers to the problem of assigning agents or actuators act upon a dynamical system at specific times so as minimize quadratic control cost, such objectives linear-quadratic-Gaussian (LQG) linear regulator problems. When budget operational constraints are imposed on schedule, this is in general NP-hard and its solution can therefore only be approximated even for moderately siz...

Abstract In this note we consider the class of weighted multi-glove games. We will show that these games are totally balanced and characterize supermodular pmas-admissible. Moreover, provide an explicit expression for Shapley value a large part pmas-admissible

We derive comparison results for Markov processes with respect to stochastic orderings induced by function classes. Our main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes. Unlike in previous work no boundedness assumptions on the function classes are needed anymore. We also present an integral versio...

I identify assumptions under which policies that maximize expected surplus are Pareto Optimal–even when expected consumer surplus does not even locally represent preferences over price-income lotteries. Besides the oft-made partial equilibrium assumptions that only one price varies, and that income changes do not affect demand, the two other assumptions are that every consumer’s indirect utilit...

This paper is dedicated to the risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of the convex ordering of their corresponding m...