Timed Branching Processes

We study Timed Branching Processes (TBPs), a natural extension of (multitype) Branching Processes (BPs) where each entity is equipped with a finite set of private continuous variables, called clocks. Clocks grow uniformly with the same rate and using them various timing constraints can be imposed on the branching rules of the system, e.g. the way an entity reproduces (branches) can depend on its age. In comparison with discretetime BPs, where all the entities live for a constant amount of time before they branch (and die), and more general continuoustime BPs, where for each entity the amount of time before the branching takes place is governed by an exponential distribution, l can be seen as an abstraction of continuous-time BPs where we do not know the exact distribution on the time before an entity branches, but rather some time interval when it happens. Allowing an external controller to decide at what point in time the branching takes place permits us to study the best/worst behavi...

• Type: Journal
• Year: 2010
• Where: QEST
• Authors: Ashutosh Trivedi, Dominik Wojtczak
• Keywords: Branching Processes, Keywords-Multitype Branching Processes, Modeling And Simulation, QEST 2010, Supremum Probability