# MoN10: Tenth Mathematics of Networks meeting, 16th September, Loughborough University

## Niels Hoffmann (Paxassign Consulting) - A dynamic stochastic multipath network decision process: A framework which adheres to the central limit theorem throughout a network

The DV3 framework for routing pedestrians in complex networks has been used
since the beginning of the nineties in modelling passenger flows and densities
in railway stations, airports and at major events such as
Olympic/Commonwealth games and a million plus population at the projected
Mecca expansion . The method is shown to be a probit model dealing
appropriately with multiple paths and their correlation, reflecting the
behaviour of infinitely many travellers. This is achieved by combining $E(X)$
and $V(X)$ in an assignment process over the network as an integral part of
the tree/vine building process towards each destination subject to no
circular path being generated. In the process splitting rate/progression
probabilities are calculated at each stage from $E$, $V$ and $C$, where
$C$=capacity or quality factor. A deterministic function for calculating Path
Progression Probabilities $PPP= G(E,V,C)$ is presented and shown to give
results corresponding well with the equivalent Monte Carlo simulation
probabilities. $C$ deals with the problem of the well-known IIA problem.
Finally, each destination process enables travellers from everywhere to
reach its destination by evaluating multiple paths at every stage of the
progression either by flow or individual agents.
Since the process is linear in $E$ and $V$ we assume that changes to journey
times in the simulation/model is scalable and the process hence able to cope
with the dynamics of a seamless update of simulated or observed journey
times.

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Richard G. Clegg (richard@richardclegg.org)