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

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 cm 2 –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 Cellular automaton approach to pedestrian dynamics – theory. In: M. Schreckenberg and S.D. Sharma, eds. Pedestrian and Evacuation Dynamics, Berlin, Germany: Springer-Verlag

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 p ij = N exp{βJ s ∆s(i, j)}exp{βJ d ∆d(i, j)}(1 − n ij )d ij p ij is the probability a pedestrian will move to a neighboring cell N is a normalization factor insuring that ∑p ij = 1 β is an inverse temperature J s and J d 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 n ij = 1 if the cell is occupied (obstacle or entity), otherwise 0 d ij 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 – UCF Crowd Simulation Framework built using MASON Library –

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 Yes No Yes

Job Model Set Up Number of work stations: 5 Number of tasks for each job type: Distribution function of job types: mean interarrival of jobs: 0.25 hrs (Exponential) Job type Work stations on route Number of machines in each station: Job Mean service time (in hours) Type for successive tasks (Erlang)

Two Comparison Simulations Queue Exit Arrive Workstation Queue Exit Arrive Workstation Queue Set Up 1 Set Up 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 Type Average Total Delay in Queue KeltonSet Up 1Set Up Overall Delay in Queue

Results - Workstation Average # in QueueAverage Delay in Queue (hours) StationKeltonSet up 1 Set Up 2 KeltonSetUp1Set Up

Individual Statistics Set Up 1

Individual Statistics Set Up 2