Multitype branching processes with immigration in random environment and\n polling systems

2010/04/28 by Vladimir Vatutin, Vatutin, Vladimir
Biochemistry, Genetics and Molecular Biology · Business, Management and Accounting · Computer Science · Decision Sciences · Mathematics · #60J80 (Primary) 60J85 #60K25 (Secondary) #Advanced Queuing Theory Analysis #Bayesian Methods and Mixture Models #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1004.4973

openalex publication_date 2010/04/28 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

For multitype branching processes with immigration evolving in a random\nenvironment and producing a final product we find the tail distribution of the\nsize of the final product accumulated in the system for a life period. Using\nthis result we investigate the tail distribution of the busy periods of the\nbranching type polling systems with random service disciplines and random\npositive switch-over times\n

Citations

• On Branching Processes with Random Environments: I: Extinction Probabilities
• On Branching Processes in Random Environments

Related

• Polling systems and multitype branching processes in random environment counted by random characteristics
• Subcritical branching processes in random environment with immigration stopped at zero
• Branching processes in random environment with immigration stopped at zero
• Multitype branching process with nonhomogeneous Poisson and generalized\n Polya immigration
• Multitype branching processes with immigration generated by point processes