Dynamic Pedestrian and Dynamic Pedestrian and Vehicular ModellingVehicular Modelling

J. MacGregor Smith & M. Blakey J. MacGregor Smith & M. Blakey SmithSmith• Department of Mechanical and Department of Mechanical and

Industrial Engineering & Facilities Industrial Engineering & Facilities PlanningPlanning

• University of Massachusetts University of Massachusetts • Amherst MA 01003 Amherst MA 01003

http://www.ecs.umass.edu/mie/faculty/smith/http://www.ecs.umass.edu/mie/faculty/smith/

OverviewOverview

MethodologyMethodology• RepresentationRepresentation• AnalysisAnalysis • SynthesisSynthesis

Case Studies– Newton-Wellesley Hospital Campus Newton-Wellesley Hospital Campus – Engineered Polymers Warehouse FacilitEngineered Polymers Warehouse Facility– Automated Teller and Walkup FacilityAutomated Teller and Walkup Facility

Basic MethodologyBasic Methodology

RepresentationRepresentation• Step Step 1.01.0: Define Customer Classes: Define Customer Classes• Step Step 2.02.0: Define Routing vectors: Define Routing vectors• Step Step 3.03.0: Define Distance and Flow Matrices : Define Distance and Flow Matrices

AnalysisAnalysis• Step Step 4.04.0: Topological Diagrams: Topological Diagrams• Step Step 5.05.0: Layout Alternatives: Layout Alternatives• Step Step 6.06.0: Flow Analysis: Flow Analysis

SynthesisSynthesis• Step Step 7.07.0: Evaluation of Alternatives: Evaluation of Alternatives• Step Step 8.08.0: Synthesis: Synthesis• Step Step 9.09.0: Implementation: Implementation

Representation

Step 1.0:Step 1.0: What customers (patients, staff, What customers (patients, staff, visitors) are moving through the facility?visitors) are moving through the facility?

Step 2.0: Step 2.0: Define the route sheets for the Define the route sheets for the customer classescustomer classes

Step 3.0:Step 3.0: From-To Charts, Distance and From-To Charts, Distance and Flow Matrices: P(i,j); D(i,j)Flow Matrices: P(i,j); D(i,j)

),...,2,1;,...2,1( KkJjjk

),...,2,1( jkjkl Llr

Analysis

Step 4.0:Step 4.0: Generate the topological Generate the topological diagram relating the route sheets and the diagram relating the route sheets and the physical facility.physical facility.

Step 5.0:Step 5.0: Generate the alternative layouts Generate the alternative layouts• STEP/MAFLADSTEP/MAFLAD

Step 6.0:Step 6.0: Generate the analytical and Generate the analytical and simulation models for analysissimulation models for analysis• QNET/ARENAQNET/ARENA

Synthesis

Step 7.0:Step 7.0: Evaluation of Alternatives Evaluation of Alternatives

Step 8.0:Step 8.0: Synthesis of Results Synthesis of Results (sensitivity analysis)(sensitivity analysis)

Step 9.0:Step 9.0: Implementation of Plans Implementation of Plans

p

j

j

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ijj

i wxwU11

/

Design IssuesDesign Issues

What are the fundamental What are the fundamental designdesign and and performanceperformance variables variablesinvolved in designing a circulation involved in designing a circulation system? system?

How are these fundamental design (d), How are these fundamental design (d), performance (p), and contextual (c) performance (p), and contextual (c) variables related? variables related? P=f(c,d)P=f(c,d)

What is What is Congestion?Congestion?

Congestion Congestion occurs mainly as a result of occurs mainly as a result of increased number of pedestrians and increased number of pedestrians and vehicles competing for the limited vehicles competing for the limited spacespace of a corridor or roadway segmentof a corridor or roadway segment. .

Empirical ModelEmpirical Model

The service rate (speed) decays within a corridor

Since there is a finite Since there is a finite amount of available amount of available space within each space within each corridor, the density of corridor, the density of pedestrians reaches an pedestrians reaches an upper limit upper limit (jam density(jam density).).

•Performance MeasuresPerformance Measures

Flow (q) Output volume or throughput Density Density (k)(k)the number of customers or the number of customers or

vehicles travelling over a unit lengthvehicles travelling over a unit length Pedestrian Speed Pedestrian Speed (()) Time Time (t)(t)

Design VariablesDesign Variables

LengthLength (L) (L) of the corridor or highway of the corridor or highway segmentsegment

Width (Width (WW) of corridor or ) of corridor or highway segment.highway segment. Capacity Capacity (C) = 5 LW(C) = 5 LW Other variables of interest e.g. Other variables of interest e.g.

• pavement materials, patterns, etc.pavement materials, patterns, etc.• grades, stairs, etc.grades, stairs, etc.• geometric curves, etc.geometric curves, etc.

Contextual VariablesContextual Variables

Input Volume Input Volume (()):=:= total number of total number of pedestrians that enter a circulation pedestrians that enter a circulation segment during a given time intervalsegment during a given time interval

Other contextual variablesOther contextual variables• obstacles,obstacles,• weather conditionsweather conditions• climateclimate• wind conditionswind conditions

Building Blocks MethodologyBuilding Blocks Methodology

Public BuildingsPublic Buildings• AirportsAirports• CourthousesCourthouses• HospitalsHospitals• MallsMalls

CampusesCampuses FreewaysFreeways

LinearLinear ModelModel

A:= average pedestrian or vehicle A:= average pedestrian or vehicle speedspeed

C: capacity of the corridor or highway C: capacity of the corridor or highway segment C = f(L,N)segment C = f(L,N)

)1( nCC

A

ExponentialExponential ModelModel

:= scale parameter:= scale parameter := shape parameter:= shape parameter

])/)1((exp[ nA

Empirical Curves of Pedestrian Stairwell Empirical Curves of Pedestrian Stairwell Flows (after Fruin)Flows (after Fruin)

General Models of Pedestrian General Models of Pedestrian FlowsFlows

Representation of FacilitiesRepresentation of Facilities

Floor Plan/Section Graph RepresentationFloor Plan/Section Graph Representation

Newton Wellesley Hospital Newton Wellesley Hospital CampusCampus

Typical Hospital FloorTypical Hospital Floor

Routes of Pedestrian TravelRoutes of Pedestrian Travel

Routes of Pedestrian TravelRoutes of Pedestrian Travel

3d representation of the Campus3d representation of the Campus

Pedestrian Route AnalysisPedestrian Route Analysis

SynthesisSynthesis

Optimal Routes of Pedestrian Optimal Routes of Pedestrian TravelTravel

Optimization of the networkOptimization of the network

Engineered Polymers Inc.Engineered Polymers Inc.

Warehouse capacity analysisWarehouse capacity analysis Dynamic material handling designDynamic material handling design

• Layout Layout and equipment needsand equipment needs• ForecastForecast space utilization over time space utilization over time• BottleneckBottleneck analysis analysis

Over to Simulation model animations …Over to Simulation model animations …

Volume of BoxesVolume of Boxes

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Warehouse CapacitiesWarehouse Capacities

Raw materials Semi-FinishedRaw materials Semi-Finished

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Total Warehouse CapacityTotal Warehouse Capacity

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Average Turnaround TimeAverage Turnaround Time

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Equipment UtilizationEquipment Utilization

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Extruder UtilizationExtruder Utilization

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Holyoke Power and LightHolyoke Power and Light

Pedestrian vehicular layout alternativesPedestrian vehicular layout alternatives• Horseshoe Counter with 1 ATM Horseshoe Counter with 1 ATM • Horseshoe Counter with 2 ATMsHorseshoe Counter with 2 ATMs• Linear CounterLinear Counter• L-Shaped CounterL-Shaped Counter

Animations of different alternativesAnimations of different alternatives Summary of resultsSummary of results

1: Horseshoe Counter Layout 1: Horseshoe Counter Layout with one and two drive-upswith one and two drive-ups

2:2: Horseshoe Counter LayoutHorseshoe Counter Layout

3:3: Linear Counter Layout with Linear Counter Layout with two drive-upstwo drive-ups

4: L-Shaped Layout4: L-Shaped Layout

Basic DataBasic Data CashiersCashiers

• 128128 drive-ups /day, Ave Time: 1 min 9 sec drive-ups /day, Ave Time: 1 min 9 sec• 290290 walk-ins /day, Ave Time: 1 min 18 sec walk-ins /day, Ave Time: 1 min 18 sec

CreditCredit• 1212 walk-ins /day, Ave Time: 6.42 min walk-ins /day, Ave Time: 6.42 min• 27 27 call-ins / day, Ave Time: 3.78 mincall-ins / day, Ave Time: 3.78 min

Customer AccountsCustomer Accounts• 36 36 walk-ins /day, Ave Time: 4.30 minwalk-ins /day, Ave Time: 4.30 min• 3737 call-ins /day, Ave Time: 2.54 min call-ins /day, Ave Time: 2.54 min

Water Dept: 5% of 8100 customers /monthWater Dept: 5% of 8100 customers /month

AssumptionsAssumptions 70%70% customers enter via parking lot, customers enter via parking lot, 30%30% enter enter

via Suffolk Streetvia Suffolk Street If cashiers are backed up, computer entries are If cashiers are backed up, computer entries are

postponed until they are freepostponed until they are free Cashiers operate on the policy of First-Come-Cashiers operate on the policy of First-Come-

First-Served when serving both walk-ins and First-Served when serving both walk-ins and drive-upsdrive-ups

With Water Dept, an additional cashier is With Water Dept, an additional cashier is available, and all cashiers handle all types of available, and all cashiers handle all types of customerscustomers

Simulation ExperimentsSimulation Experiments

Results analyzed over Results analyzed over 3030 independent independent days of operationdays of operation

Simulation programs written in Simulation programs written in SIMANSIMAN and animations developed in and animations developed in ARENAARENA

Animations shown for each alternative Animations shown for each alternative over 1 day (8 hours) of operationover 1 day (8 hours) of operation

Over to animations .....Over to animations .....

Average Time in SystemAverage Time in System

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Hoseshoe 1Dup

Horseshoe 2Dups

Linear 2Dups

L, 2 Dups &Water

Parked CustDriveup CustSuffolk Cust

Maximum Times in SystemMaximum Times in System

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Horseshoe 1Dup

Horseshoe 2Dups

Linear 2Dups

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Parked CustDriveup CustSuffolk Cust

Maximum Drive-up QueueMaximum Drive-up Queue

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Maximum Cashier QueueMaximum Cashier Queue

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Customers in BuildingCustomers in Building

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Linear 2 Dups L, 2 Dups &Water

AverageMaximum

Average Server UtilizationsAverage Server Utilizations

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CashierCreditC_Accnt

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Methodology SummaryMethodology Summary

RepresentationRepresentation• Step Step 1.01.0: Define Customer Classes: Define Customer Classes• Step Step 2.02.0: Define Routing vectors: Define Routing vectors• Step Step 3.03.0: Define Distance and Flow Matrices : Define Distance and Flow Matrices

AnalysisAnalysis• Step Step 4.04.0: Topological Diagrams: Topological Diagrams• Step Step 5.05.0: Layout Alternatives: Layout Alternatives• Step Step 6.06.0: Flow Analysis: Flow Analysis

SynthesisSynthesis• Step Step 7.07.0: Evaluation of Alternatives: Evaluation of Alternatives• Step Step 8.08.0: Synthesis: Synthesis• Step Step 9.09.0: Implementation: Implementation

Summary and ConclusionsSummary and Conclusions

Dynamic Pedestrian Dynamic Pedestrian FlowsFlows

Fundamental PrinciplesFundamental Principles• Travel Speed vs. DensityTravel Speed vs. Density• C = 5LWC = 5LW

Case StudiesCase Studies System OptimizationSystem Optimization