pedestrain cellular automata and industrial process simulation alan jolly (a), rex oleson ii (b),...
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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.
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