PEDESTRAIN CELLULAR AUTOMATA AND

INDUSTRIAL PROCESS SIMULATION

Alan Jolly(a), Rex Oleson II(b), Dr. D. J. Kaup(c)

(a,b,c) Institute for Simulation and Training, 3100 Technology Parkway, Orlando, FL 32826

(c) Mathematics Department, University of Central Florida, Orlando, FL 32816-1364

Outline

• Introduction• Motivation for Research Effort• Background

– Cellular Automata for Pedestrian Simulation– Modifications to base CA model

• Description of Job Shop/Pedestrian Simulation• Simulation Results and Analysis• Conclusions • Future Efforts

Introduction

• ‘Proof-of-concept’ that explicit models of pedestrian motion can be integrated into manufacturing job shop production simulations – and provide useful information.

• Research simulates an idealized fixed workstation walking-worker job-shop with explicit modeling of worker movement.

Motivation

• Expand the usefulness of pedestrian behavior models by applying them in non-traditional areas.– A considerable amount of research has been

done on simulating collective behavior of pedestrians.

• Not meant to replace current methods just provide additional information.

Why Industrial Simulation?

• Simulations for job shop performance and layout have traditionally been solved mathematically as ‘static’ problems.– Allows application of optimization techniques.

• In reality job shops are dynamic systems with complex interactions between workers and machines.

• Pedestrian models operate as complex systems:

• self-organization. • no central control.

• non-linear behaviors.• overall state of the system

affects individual behavior.

Value of Pedestrian Simulation

• Job Shop simulations rarely explore:– Patterns of worker movement.– The impact of shop-floor layout (local and global

configurations) on workers.– The impact of the presence of other workers.

• Simulations using explicit models for worker movement may:– address questions related to worker movement.– allows for emergent behaviors resulting from worker /

environment interactions.

Job Shop Definitions

• Fixed Workstation – workstations fixed and operators move between workstations.

• Walking Worker – operators generally build a product from beginning to end.

• Walking workers production designs provide flexibility in production capacity.– workers may be added or removed in response to

demand without redesign of workstations and/or assemble line.

Cellular Automata Model

• Lattice of cells 40x40 cm2

– corresponds to the average amount of space an individual occupies in a dense crowd

• The cells have one of two states: empty or occupied by a single person.

• Pedestrians are only allowed to move one cell per time step

• Time step = 0.3 sec 1.33m/s

Floor Field Approach• Pedestrian ‘intelligence’, i.e. choice of movement

direction, is modeled through the use of floor fields.

• Dynamic Floor Field changes with each time step as a function of the density and diffusion of an individual’s virtual trace.

• Static floor field remains constant and contains attraction to exits and the location of obstacles.

• Ref: Schadschneider, A. 2002. Cellular automaton approach to pedestrian dynamics – theory. In: M. Schreckenberg and S.D. Sharma, eds. Pedestrian and Evacuation Dynamics, Berlin, Germany: Springer-Verlag. 76-85.

Examples of Floor Fields

• Dynamic Floor Field with red→black representing strong→weak virtual trace.

• Static Floor Field with shading proportional to distance from exit.

Equation of Motion

pij = N exp{βJs∆s(i, j)}exp{βJd∆d(i, j)}(1 − nij)dij

• pij is the probability a pedestrian will move to a neighboring cell• N is a normalization factor insuring that ∑pij = 1• β is an inverse temperature• Js and Jd are floor field coupling factors• ∆s and ∆d are the change value for dynamic and static floor fields• (i,j) – (0,0) where (0,0) is current position on the lattice• nij = 1 if the cell is occupied (obstacle or entity), otherwise 0• dij is a correction factor taking into account the heading of the

pedestrian

Integrating Job Shop and CA model

• Implemented in UCF Crowd Simulation Framework which is available at– http://www.simmbios.ist.ucf.edu

• UCF Crowd Simulation Framework built using MASON Library– http://cs.gmu.edu/~eclab/projects/mason/

Modifications to CA model

• Deviate from Schadschneider’s homogeneous approach by allowing each individual to store their own representation of a modified static field.– one field for obstacles and static

environmental forces .– second field representing individual’s

attraction towards a goal or point of interest for the individual.

• Not using any virtual trace.

Process Flow Chart Individual

Assign Job

Determine Workstation

Calculate Movement Parameters

Move

Set Machine to Busy

Set Machine to Idle

Place Worker in

Queue

Task Complete?

Job Complete?

At Workstation?

Machine Available? Exit

No

Yes

No

No

Yes

Yes

No

Yes

Job Model Set Up

Number of work stations: 5

Number of tasks for each job type: 4 3 5

Distribution function of job types: 0.3 0.5 0.2

mean interarrival of jobs: 0.25 hrs (Exponential)

Job type Work stations on route

1 3 1 2 5

2 4 1 3

3 3 1 5 2 4

Number of machines in each station:2 3 3 4 1

Job Mean service time (in hours)Type for successive tasks (Erlang)

1 1.17 0.25 0.90 0.69

2 1.00 0.25 1.17 3 1.17 0.25 0.69 0.90 1.00

Two Comparison Simulations

1 2

3

4 5QueueExit

Arrive

Workstation

Queue

5 4

3

2 1QueueExit

Arrive

Workstation

Queue

Set Up 1 Set Up 2

3 5

1

2 4

Circle’s are Individuals and Lines represent job routes

Job’s 1,2,3 = Red, Green, Blue

Mean Floor Tracking Information

Colors represent the mean number of times a cell has been occupied (number of runs ≈ 30 per case).

Results – Job Shop

Job TypeAverage Total Delay in Queue

Kelton Set Up 1 Set Up 2

1 11.54 6.99 6.72

2 6.65 6.35 5.99

3 11.59 6.04 5.89

Overall Delay in Queue

9.90 6.46 6.20

Results - Workstation

Average # in Queue Average Delay in Queue (hours)

Station Kelton Set up 1

Set Up 2

Kelton SetUp1 Set Up 2

1 0.09 0.13 0.12 0.03 0.14 0.14

2 0.03 0.25 0.23 0.03 0.25 0.24

3 33.97 61.52 62.30 8.66 12.69 12.38

4 0.23 3.16 2.69 0.09 0.94 0.82

5 3.31 2.49 2.57 2.43 2.30 2.39

Descriptive Statisticsa

805 65.40 226.80 116.1447 32.05285

805 .00 172109.10 51000.27 34720.58602

805 4093.50 33898.20 14619.63 5019.30819

805 7347.00 190005.30 65736.05 34954.22294

805

TimeWalking

TimeQueue

TimeWorking

TotTime

Valid N (listwise)

N Minimum Maximum Mean Std. Deviation

PathID = 2a.

Descriptive Statisticsa

2170 40.50 168.30 64.4459 17.14353

2170 .00 180225.00 47584.09 34282.31567

2170 1269.00 31720.20 8779.5928 3952.14956

2170 1849.50 193623.90 56428.13 34357.99801

2170

TimeWalking

TimeQueue

TimeWorking

TotTime

Valid N (listwise)

N Minimum Maximum Mean Std. Deviation

PathID = 1a.

Descriptive Statisticsa

1292 46.50 129.90 80.5261 21.12873

1292 .00 157762.50 49279.87 35497.05982

1292 2311.50 33585.90 10743.59 4156.63969

1292 3668.10 167302.50 60103.98 35469.02792

1292

TimeWalking

TimeQueue

TimeWorking

TotTime

Valid N (listwise)

N Minimum Maximum Mean Std. Deviation

PathID = 0a.

Individual Statistics Set Up 1

Individual Statistics Set Up 2

Descriptive Statisticsa

699 53.40 255.00 92.1717 25.47941

699 .00 169895.70 49678.75 35222.62060

699 5248.20 33885.90 14264.98 4873.87386

699 5941.50 177286.80 64035.90 35256.81768

699

TimeWalking

TimeQueue

TimeWorking

TotTime

Valid N (listwise)

N Minimum Maximum Mean Std. Deviation

PathID = 2a.

Descriptive Statisticsa

2030 46.20 164.10 72.3625 16.11432

2030 .00 178950.90 47828.63 36165.92772

2030 1034.10 31824.30 8678.2779 4006.96376

2030 1601.10 190178.10 56579.27 36397.63062

2030

TimeWalking

TimeQueue

TimeWorking

TotTime

Valid N (listwise)

N Minimum Maximum Mean Std. Deviation

PathID = 1a.

Descriptive Statisticsa

1245 51.90 255.30 87.8159 23.60262

1245 .00 159864.60 50613.36 36743.54992

1245 2289.90 34827.00 10943.97 4269.45244

1245 2776.80 169083.90 61645.14 36841.93039

1245

TimeWalking

TimeQueue

TimeWorking

TotTime

Valid N (listwise)

N Minimum Maximum Mean Std. Deviation

PathID = 0a.