Affiliation:
1. Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia
Abstract
In this paper, we consider a two-dimensional Moran model of random walks consisting of two queues evolving in parallel which can (at each unit of time) either increase by one or reset to 0. We analyze the joint law of their final altitude and prove that the asymptotic distribution of each component is a shifted geometric distribution and we analyze the maximum of these two components, also giving closed forms for the mean and variance.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference16 articles.
1. Basic analytic combinatorics of directed lattice paths;Banderier;Theor. Sci.,2002
2. Flajolet, P., and Sedgewick, R. (2009). Analytic Combinatorics, Cambridge University Press.
3. The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions;Flajolet;Adv. Appl. Probab.,2000
4. Drmota, M. (2009). An Interplay between Combinatorics and Probability, Springer.
5. Banderier, C., and Nicodème, P. (2010). Bounded discrete walks. Discret. Math. Theor. Comput. Sci., 35–48.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献