Correlation Decay in Random Decision Networks
We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the corresponding nodes. The ...
A Numerical Scheme for Invariant Distributions of Constrained Diffusions
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady-state performance of the corresponding ...
Derivation of a Cardinal Utility Through a Weak Trade-off Consistency Requirement
An axiomatic model is presented in which a utility function over consequences, unique up to location and unit, is derived. The assumptions apply to a binary relation over purely subjective acts, namely, no exogenous probabilities are assumed. The main ...
Nonsmooth Cone-Constrained Optimization with Applications to Semi-Infinite Programming
This paper is devoted to the study of general nonsmooth problems of cone-constrained optimization (or conic programming) important for various aspects of optimization theory and applications. Based on advanced constructions and techniques of variational ...
Excursion-Based Universal Approximations for the Erlang-A Queue in Steady-State
We revisit many-server approximations for the well-studied Erlang-A queue. This is a system with a single pool of i.i.d. servers that serve one class of impatient i.i.d. customers. Arrivals follow a Poisson process and service times are exponentially ...
A Unifying Approximate Dynamic Programming Model for the Economic Lot Scheduling Problem
We formulate the well-known economic lot scheduling problem (ELSP) with sequence-dependent setup times and costs as a semi-Markov decision process. Using an affine approximation of the bias function, we obtain a semi-infinite linear program determining a ...
Large Deviations for the Stationary Measure of Networks Under Proportional Fair Allocations
We address a conjecture introduced by Massoulié [Massoulié L (2007) Structural properties of proportional fairness: Stability and insensitivity. Ann. Appl. Probab. 17(3):809–839], concerning the large deviations of the stationary measure of bandwidth-...
An Approximate Dynamic-Programming Approach to the Joint Replenishment Problem
The main contribution of this paper is to propose a new dynamic-programming approach that ε-approximates the joint replenishment problem, with stationary demands and holding costs, in its discrete-time finite-horizon setting. Our first and foremost ...
Lattices and Lotteries
We consider the consumer problem under uncertainty when the consumer can choose the quantity of a risk-free good and the lottery, or distribution, of a risky good from a set of distributions. These goods are imperfect substitutes in the consumer ...
Singular Control and Optimal Stopping of SPDEs, and Backward SPDEs with Reflection
We consider general singular control problems for random fields given by a stochastic partial differential equation (SPDE). We show that under some conditions the optimal singular control can be identified with the solution of a coupled system of SPDE and ...
Closed-Form Expansion, Conditional Expectation, and Option Valuation
Enlightened by the theory of Watanabe [Watanabe S (1987) Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels. Ann. Probab. 15:1–39] for analyzing generalized random variables and its further development in Yoshida [...
On Optimal Policies for Production-Inventory Systems with Compound Poisson Demand and Setup Costs
In this paper, we consider a single-item, one-machine production-inventory system with compound Poisson demand. The production facility may be on or off. While on, the production rate is constant, and, while off, the production rate is zero. System costs ...
Fluid Limits for Bandwidth-Sharing Networks in Overload
Bandwidth-sharing networks as considered by Roberts and Massoulié [28] (Roberts JW, Massoulié L (1998) Bandwidth sharing and admission control for elastic traffic. Proc. ITC Specialist Seminar, Yokohama, Japan) provide a natural modeling framework for ...
Approximability of Robust Network Design
We consider robust (undirected) network design (RND) problems where the set of feasible demands may be given by an arbitrary convex body. This model, introduced by Ben-Ameur and Kerivin [Ben-Ameur W, Kerivin H (2003) New economical virtual private ...
Concave Generalized Flows with Applications to Market Equilibria
We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper [Truemper K (1978) Optimal flows in nonlinear gain networks. ...
