Assignment for module: cs5233. Presented on Apr/2017

1. CS5233 - SIMULATION AND MODELLING TECHNIQUES
Assignment 2
Group 18:
Hariharan Chandrasekar A0163105U
Mannu Malhotra A0163158A
Punna Reddy Gangasani A0163115R

2. Problem Description
● Singapore theme park has 4 attractions A, B, C and D
● Each has a bicycle station with Bicycles and Docks
● Tourist arbitrarily comes and visits all attractions
● They rent bicycles to travel to other stations
● To build a model representing bicycle rental system
● Simulate the model to analyse the customer satisfaction
Assumption: Tourists follow one of the following order
A→ B→C→D
B→C→D→A
C→D→A→B
D→A→B→C

3. Events and States
Type of Simulation: Non- Terminating
Events: Arriving at Attraction(A/B/C/D), Get Cycle, Give Dock,Transfer To Next Attraction
States:
❏ Number of Bicycles in a Bicycle Station,
❏ Number Of Free Docks in a Bicycle Station
❏ Number Of Tourists waiting to return a Bicycle
❏ Number Of Tourists waiting to get a Bicycle
❏ Number Of Tourists in the Theme Park

4. Input Data Analysis
Identified statistical distribution using Chi-Square test
Level of significance = 0.05
Speeds(m/s) : Triangular(Min Value=10,Mode=19.8,Max Value=30)
Time Spent (min): Normal (For A: μ=29.9,σ2=5.11)
Arrivals (min): Exponential( For A:μ=8.65)

5. Model
Atrributes:
Variables:

7. Model

8. Verification and Validation
Verification: Plugged different inputs to ensure we built the model right
Validation:
● Since there is no real system in place, we validated using Face Validity
● Ensured all assumptions are met
● Consistent results across Replications

9. Output Analysis: Finding warm-up time
▪ 24 Hours Running system: Non terminating simulation
▪ Replication method over subinterval and regenerative method.
▪ Challenge: Point estimator Bias.
▪ Output Analyzer for 5 replications : warm up phase and data collection phase
▪ Conclusion: warm up time = 15 hours.

10. Output Analysis: Finding number of replications required
▪ Point estimator : Mean total time spent
▪ R0 (Number of initial replication) : 5
▪ Calculated: R > (Z 𝞪/2 * S)2/ε2
R 3 4 5 6
(t 𝞪/2, R-1 * S)2/ε2 7.91 5.139 4.219 3.769
t 2.920 2.353 2.132 2.015

11. Results Obtained
Confidence = 90% and error range = .04
▪ Warm up period: 15 hours
▪ Avg. Total time spent:
▪ Replications ran : 5
▪ Replications required: 5
▪ Point estimator: 2.80721
▪ Confidence interval: [2.77037 , 2.84405]
▪ Avg. waiting time:
▪ Replications ran: 5
▪ Total replications required: 14
▪ Point estimator: 3.02148
▪ Confidence interval: [2.577, 4.1278]
▪ Number of required docks and bicycles: 78 bicycles and 80 docks

12. Learnings
▪ How to model a real life system in Arena and understanding the various modules/tools available in
Arena
▪ Understanding the parameters of the different probability distributions, their PDF/PMF functions and
see how to fit them with a given set of observations.
▪ How to find the number of replications required.
▪ Calculating the warm up time for non terminating simulation using output analysis.
▪ How difficult it is to work in a team.

13. Thank you