Modelling pedestrian movement and choices, from micro to urban scale;

Modelling pedestrian movement and choices, from micro to urban scale;

Vassilis ZachariadisPh.D Candidate

Dip.Eng M.Sc M.PhilCasa.UCL.London

[email protected]

The 3 levels of pedestrian movement modelling:

• Strategic level i) departure time choiceii) activity pattern choice (shopping and leisure, travel to work etc.)

2. Tactical leveli) activity scheduling (order of activities)ii) activity area choice (area each activity will take place in)iii) route-choice (to reach selected activity areas)

3. Operational level Walking behavior

Modelling strategy

The main behavioural assumption here, is that all actions of the pedestrian, let it be performing an activity or walking along a certain route, will provide utility (or equivalently, induce cost) to him.

The pedestrian will predict and optimize this expected utility, taking into account the uncertainty in the expected traffic conditions, spatial configuration of the walking facility and the environmental aspects of space (stimulation, walkability etc)

Utility maximisation may not fully cover real-life human choice behaviour but it does provide a very convenient framework for modelling human decision making (Van Berkum and Van Der Mede, 1993)

Empirical studies have shown the applicability of utility-based approaches to pedestrian route choice (Hill, 1982; Bovy and Stern, 1990)

Modelling strategy

• Trip generation Frequency of origins of trips in each zone by trip purpose, as a function of land uses

and household demographics, and other socio-economic factors (outside model’s scope)

• Trip distribution Matching origins with destinations, often using a gravity model function, equivalent

to an entropy maximizing model.

• Mode choice Proportion of trips between each origin and destination that use a particular

transportation mode. This model is often of the logit form. (non applicable)

• Route assignment Allocates trips between an origin and destination by a particular mode to a route.

Often each traveler chooses the shortest (travel time) path, subject to every other driver doing the same. The difficulty is that travel times are a function of demand, while demand is a function of travel time, the so-called bi-level problem.

four steps of the classical urban transportation planning system model

• Trip generation – Strategic levelNumber of pedestrians entering the modelled area from each entrance by trip

purpose (activity pattern choice) - outside pedestrian model’s scope

• Trip distribution – Tactical levelActivity scheduling and activity area choice using utility maximisation

• Mode choice – not applicable, all actors are pedestriansProportion of trips between each origin and destination that use a particular

transportation mode. This model is often of the logit form.

• Route assignment – Tactical levelAllocates trips between an origin and destination by a particular mode to a route.

Often each traveller chooses the path offering the minimum subjective cost (the maximum utility), subject to every other pedestrian doing the same. The difficulty is that subjective costs are a function of demand (number of interactions with other pedestrians), while demand is a function of subjective cost, the so-called bi-level problem.

four steps – equivalence for pedestrian movement

Restating the bi-level problem

The tactical level behaviour is influenced by both external factors (spatial configuration, activity map), and internal (personal) factors (time–pressure, preferences etc.).

Together with the expected traffic conditions (congestion, average speeds etc.), the decisions at the tactical level serve as input for pedestrians walking behaviour.

In turn, the traffic conditions resulting from the pedestrian traffic demands and the collective walking behaviour will affect the expected traffic conditions and thus the behaviour at the tactical level.

*** Complex system ***

Addressing the bi-level problem in continuous space and time

The simultaneous activity area – path selection approach

By adopting a two-stage approach, modelling in separate instances destinations choices (activity areas) and path choices we fail to allow for stochastic (uncertainty) elements during the route choice process.

Why?Destination choice implies, most commonly, a discrete choice model (logit model) –

e.g. a random utility model.

Utilities Vi in such models are partly based on objective –zero uncertainty- running costs for reaching each of the finite number of activity areas (destinations).

Therefore, by using subjective expected costs during the route assignment process (2nd stage) the probability values of the logit model are put under question


In order to address both the bi-level and the destination choice – route assignment problem Hoogendoorn and Bovy (2004) proposed a single stage process:

A simultaneous optimisation process of the route choice - activity area choice problem using dynamic programming for different traffic conditions and uncertainty levels

Alternatively, a random utility model using subjective expected route costs to calculate utilities of the discrete activity areas choices could be used.

However in this case we should be aware that the developed model would retain two levels of randomness. A random element implying lack of design certainty from the point of the developer and the random element of the pedestrians’ uncertainty on forthcoming traffic situation


Proposed approach to the tactical level

The adopted single stage variation:

At the tactical level, a pedestrian makes a simultaneous decision at time t0 minimizing the expected disutility or cost C. This decision covers all decision variables: activity patterns S, terminal times Ti , utilities of activity areas, and the velocity path υ(.)

The total disutility can be written as follows:

Where:

denotes the running costs, and

denotes the terminal costs (utility)


Each pedestrian use0s the following model to predict his future position:

where is distributed (std. Wiener process)

Pedestrians aim to minimise the subjective expected route cost by applying the optimal velocity υ*[t, T)

According to Bellman’s optimization principle (Bellman, 1957):

And it can be proved that:


It can be shown that

with terminal conditions

can be solved numerically by discretising the area A into small cells, and considering approximate solutions on this lattice at fixed time instants.

The resulting problem is a Markov diffusion process in two dimensions with nearest-neighbour transitions that are determined by the stochastic differential equation:

This is done backwards in time: starting from the terminal conditions we can apply the resulting equations to solve the problem for times t = T-h, T-2h,…,t0.

Defining running costs

Running costs L of a route will depend among other things on (Gipps, 1986):

1. Distance or travel time between origin and destination.2. Proximity of obstacles or other physical obstructions (closeness to walls).3. Number of turns and directional changes (route complexity).4. Expected number of interactions with other pedestrians (level-of-service).5. Stimulation of environment, and attractiveness (e.g. shopping windows).

For the sake of simplicity, we assume that the running cost is linear in parameters

where Lk denote the contribution of the different route attributes k, and ck denote the relative weights (importance of the attributes)


Modelling strategy

B. Stimulation… vision – Operational level

Awareness of network, activities and traffic

However: Implementation of direct vision algorithms to agents extremely power consuming.

INDIRECT VISION: calculation of isovists for every network node (or grid point) and every activity.

Modelling strategy B. Stimulation… vision – Operational level

Pedestrians receive traffic information through visual stimulation regarding existing conditions and choose their planned schedule and route accordingly.

Therefore the route costs at the operational level are simply computed using the given prevailing conditions. This way pedestrians are able to subtract part of the uncertainty of the path’s cost (the traffic and configuration elements) by precisely calculating the cost of reaching any of the point within their isovists.

It is likely that pedestrians will reconsider the choices made at the tactical level several times t during their stay in the walking facility, thereby considering the observed in the current traffic conditions.

CRITICAL DENSITIES – Operational level

With respect to the operational level, it has been hypothesized that pedestrians adhere to their planned route (determined at the tactical level) as much as possible. In addition, walking is affected by interactions with other pedestrians or obstacles

In critical densities such interactions are expected to play a considerable part in the flow distribution outcome. Under such conditions pedestrian behaviour is likely to need to be modelled by a crowd dynamics model

Microscopic movement simulation. The adopted optional module is based on Teknomo's (2002) microscopic movement model and provides fully customisable menus for all parameters of the agents' behaviour.

Notably, it demonstrates self-organisation pattern development (lane formation etc.) and is based on three behavioural laws (forward drive, collision avoidance and crowd repulsion).

Modelling strategy

D. The architecture

The platform has been developed around the software package OpenJump (java-based open-source GIS suite)

It offers a full series of tools designed to facilitate pedestrian movement modelling across a wide range of scales and applications.

It brings under the same suite a fully developed agent-based pedestrian behaviour simulation tool-kit and an expandable GIS package.

This is only possible because the OpenJump structure and modular architecture fits perfectly the agent-based, pedestrian behaviour modelling, providing an extensible and light workbench for development.

LAND USE INTERFACE

Compatibility for future land-use flows interaction…

Activity agents are constantly updating information related to visitors and by-passers numbers and profiles.

It is possible to keep track of the number of pedestrians that have, at any time, visual contact and/or walk on the pavement in front of any activity unit and of the number of visitors to each destination.

This information will be used in the future to estimate rent rates and to base retail agents behaviour on.

The 3D window

The 3D facilities are based on Java3D and specifically, are powered by “Agency 9”‘s AgentFX suite.

The 3D version is maintaining the GIS integration:

It is seamlessly deployed, set up and controlled from within the GIS application and it is also updating the related GIS layers

The 3D window: Features

1. Dynamic view: the user can freely move in real time into the modelled area

1. The 3D extension can either read the blocking layer (layer including

the blocking lines - barriers) or load a 3D model saved in popular 3D formats.In the first case the model replicates a 3D environment by extruding the layer lines by a user-defines height. In this way it is possible to rapidly introduce large amounts of spatial information with no extra effort.

3. By loading 3D models prepared in any 3D software, we can simulate detailed behaviour and populate existing 3D environments with autonomous walking agents.

3. The 3D pedestrian avatars are highly customisable and compatible to any 3D skeletons loaded from well-known 3D software (3dmax, XSI, Maya).

5. The degree of realism to the 3D Window viewer (and capturing classes) is not restricted by the model and is subject only to the hardware’s performance.

Thank [email protected]

a. communication – interaction between actors

b. “predictable” individual behaviour (rule based vs. erratic)

c. lack of hierarchy

d. Inclination to collectivistic behaviour

Complex systems Complexity theory

Emerging outcome cannot be predicted by examination of individual cases.

Reductionistic approaches are insufficient

Complex systems

Documents

Modelling pedestrian movement and choices, from micro to urban scale;