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math.PR2021
A fluid approach to total-progeny-dependent birth-and-death processes
Sophie Hautphenne, Minyuan Li
We introduce a class of branching processes in which the reproduction or lifetime distribution at a given time depends on the total cumulative number of individuals who have been b…
math.PR2021
Markovian Transition Counting Processes: An Alternative to Markov Modulated Poisson Processes
Azam Asanjarani, Sophie Hautphenne, Yoni Nazarathy
Stochastic models for performance analysis, optimization and control of queues hinge on a multitude of alternatives for input point processes. In case of bursty traffic, one very p…