2010/07/10 by David Gamarnik, Gamarnik, David, Dmitriy Katz +1
Business, Management and Accounting · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Data Processing Techniques #Advanced Queuing Theory Analysis #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR) #Quantum chaos and dynamical systems #cs.CC #math.PR
paper · pdf · doi:10.48550/arxiv.1007.1694
arxiv created 2010/07/10 · openalex publication_date 2010/07/10 · arxiv updated 2010/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Skorokhod problem arises in studying Reflected Brownian Motion (RBM) on an non-negative orthant, specifically in the context of queueing networks in the heavy traffic regime. One of the key problems is identifying conditions for stability of a Skorokhod problem, defined as the property that trajectories are attracted to the origin. The stability conditions are known in dimension up to three, but not for general dimensions. In this paper we explain the fundamental difficulties encountered in trying to establish stability conditions for general dimensions. We prove that stability of Skorokhod problem is an undecidable property when the starting state is a part of the input. Namely, there does not exist an algorithm (a constructive procedure) for identifying stable Skorokhod problem in general dimensions.