2017/07/18 by Toshihisa Ozawa, Ozawa, Toshihisa, Masahiro Kobayashi +1 · 1 citation
Business, Management and Accounting · Decision Sciences · Mathematics · #60J10 #60K25 #Advanced Queuing Theory Analysis #Algorithm #Combinatorics #Computer science #Discrete time and continuous time #Distribution (mathematics) #FOS: Mathematics #Homogeneous #Markov chain #Markov process #Mathematical analysis #Mathematics #Physics #Probability (math.PR) #Probability and Risk Models #Process (computing) #State (computer science) #Stationary distribution #Statistics #Stochastic processes and statistical mechanics #math.PR #msc:60J10 #msc:60K25
paper · pdf · doi:10.48550/arxiv.1707.05475
54 pages
arxiv created 2017/07/18 · openalex publication_date 2017/07/18 · arxiv updated 2017/07/19 · openalex created_date 2017/07/31 · openalex updated_date 2026/08/05
We consider a discrete-time two-dimensional process \(L1,n,L2,n)\ on ℤ+2 with a supplemental process \Jn\ on a finite set, where individual processes \L1,n\ and \L2,n\ are both skip free. We assume that the joint process \Yn\=\(L1,n,L2,n,Jn)\ is Markovian and that the transition probabilities of the two-dimensional process \(L1,n,L2,n)\ are modulated depending on the state of the background process \Jn\. This modulation is space homogeneous except for the boundaries of ℤ+2. We call this process a discrete-time two-dimensional quasi-birth-and-death (2D-QBD) process and, under several conditions, obtain the exact asymptotic formulae of the stationary distribution in the coordinate directions.