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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...
We begin by observing that (discrete-time) Quasi-Birth-Death Processes (QBDs) are equivalent, in a precise sense, to (discrete-time) probabilistic 1-Counter Automata (p1CAs), and both Tree-Like QBDs (TL-QBDs) and Tree-Structured QBDs (TS-QBDs) are equivalent to both probabilistic Pushdown Systems (pPDSs) and Recursive Markov Chains (RMCs). We then proceed to exploit these connections to obtain a number...
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