Physics Event Generators computational Complexity

The computational core of physics event generator is the code that numerically calculates,from first principles, the fully differential cross section $e$.

In general terms, a cross section $e$ represents events $N$_exp=$e$$L$,(collision event with a given ‘final state’) that are expected per unit "integrated luminosity "$L$ of the colliding beams (parameter that depends on their intensities and geometries,
and overall duration of data-taking time [1]).

Question 1. According to this description (… duration of data-taking time ), could we say that,the physics event generator is equivalent to a concurrent temporal planning problem [2]?.

A. If so,what is its Computational complexity?. I mean the current working Physics Event Generators; in large hadron collider LHC or in the future international linear collider.

B. If not so,what is the computational problem out there that could be equivalent to the Physics Event generator?.

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[1]. Challenges in Monte Carlo event generator software for High-Luminosity LHC. Report by The HSF Physics Event Generator WG · Andrea Valassi (editor)1 …

[2]. Complexity of Concurrent Temporal Planning.
Jussi Rintanen NICTA Ltd and the Australian National University Canberra, Australia