2011/06/21 by Yang Zhang, Zhang, Yang, Edwin K. P. Chong +5
Business, Management and Accounting · Computer Science · Mathematics · #Advanced Queuing Theory Analysis #Analysis of PDEs (math.AP) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mobile Ad Hoc Networks #Network Traffic and Congestion Control #Networking and Internet Architecture (cs.NI) #cs.IT #cs.NI #math.AP #math.IT
paper · pdf · doi:10.48550/arxiv.1106.4288
15 pages, 10 figures
arxiv created 2011/06/21 · openalex publication_date 2011/06/21 · arxiv updated 2011/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains converges in some sense to the solution of a partial differential equation. Based on such convergence we approximate Markov chains modeling networks with a large number of components by partial differential equations. While traditional Monte Carlo simulation for very large networks is practically infeasible, partial differential equations can be solved with reasonable computational overhead using well-established mathematical tools.