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# Bicycle rental system simulation analysis

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Assignment for module: cs5233.
Presented on Apr/2017

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### Bicycle rental system simulation analysis

1. 1. CS5233 - SIMULATION AND MODELLING TECHNIQUES Assignment 2 Group 18: Hariharan Chandrasekar A0163105U Mannu Malhotra A0163158A Punna Reddy Gangasani A0163115R
2. 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. 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. 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. 5. Model Atrributes: Variables:
6. 6. Model
7. 7. 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
8. 8. 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.
9. 9. 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
10. 10. 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
11. 11. 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.
12. 12. Thank you