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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Contact: Keith Briggs (mailto:keith.briggs_at_bt_dot_com) or Richard G. Clegg (