Integer and combinatorial optimization
Integer and combinatorial optimization
A heavy traffic limit theorem for networks of queues with multiple customer types
Mathematics of Operations Research
IEEE/ACM Transactions on Networking (TON)
Large deviations and the generalized processor sharing scheduling for a two-queue system
Queueing Systems: Theory and Applications
A Skorokhod Problem formulation and large deviation analysis of a processor sharing model
Queueing Systems: Theory and Applications
Heavy traffic approximations of large deviations of feedforward queueing networks
Queueing Systems: Theory and Applications
Large deviations and the generalized processor sharing scheduling for a multiple-queue system
Queueing Systems: Theory and Applications
Statistical analysis of the generalized processor sharing scheduling discipline
IEEE Journal on Selected Areas in Communications
Explicit Solutions for Variational Problems in the Quadrant
Queueing Systems: Theory and Applications
Large Deviation Bounds for Single Class Queueing Networks and Their Calculation
Queueing Systems: Theory and Applications
Reflected Brownian motion in the quadrant: tail behavior of the stationary distribution
Queueing Systems: Theory and Applications
Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks
Mathematics of Operations Research
Conjectures on tail asymptotics of the marginal stationary distribution for a multidimensional SRBM
Queueing Systems: Theory and Applications
Variational problem in the non-negative orthant of R3: reflective faces and boundary influence cones
Queueing Systems: Theory and Applications
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We consider a Skorohod map \mathbf{R} which takes paths in \mathbb{R}^n to paths which stay in the positive orthant \mathbb{R}_+^n. We let \mathcal{S} be the domain of definition of \mathbf{R}. A convex and lower semi-continuous function \lambda \dvtx \mathbb{R}^n \rightarrow [0,\infty] and a set A \subset \mathbb{R}_+^n are given. We are concerned[-2pt] with the calculation of the infimum of the value \int_0^t \lambda(\dot{\omega}(s))\,{\rm d}s for t \geq 0 and absolutely continuous \omega \in \mathcal{S} subject to the conditions \omega(0) = 0 and \mathbf{R}(\omega)(t) \in A. We show that such minimization problems characterize large deviation asymptotics of tail probabilities of the steady-state distribution of certain reflected processes. We approximate the infimum by a sequence of finite-dimensional minimization problems. This approximation allows to formulate an algorithm for the calculation of the infimum and to derive analytical bounds for its value. Several applications are discussed including large deviations of generalized processor sharing and large deviations of heavily loaded queueing networks.