1. Improving the left-turn flow at McKellips and Scottsdale Rds. IEE 545 Discrete Event Simulation December 6, 2011 Yousef Dashti Kevin O'Connor Serhan S. Alshammari Min Choi

2. Problem & Objective Problem –waiting time for left-turn cars on N. Scottsdale road is unreasonably high Objective—to compare two policies (current and proposed) and choose a better one o Current: Left turn at green arrow o Proposed: Left turn at green light with caution

3. Data Collection Data collected 5pm on a work day (rush hour) over a 15min period South bound: o 242 straight: 86.1% o 39 left : 13.9% o Mean inter arrival time was 3.202 seconds North bound: o 338 straight : 93.9% o 24 left: 6.1% o Mean inter arrival time was 2.325 seconds

4. Low Rate Data Data collected 11pm Collected actual IAT of 149 cars over 26 min period North bound: o Mean inter arrival time was 10.537 seconds

5. H 0 : data fits an exponential distribution with mean of 10.537 H 1 :data does not fit an exponential distribution with mean of 10.537 Input Modeling— Equal size bins

6. Input Modeling— Equal prob bins

7. BinFrequencyEi(Oi-Ei)^2/Ei 0.9208912.41670.94016 1.92951912.41673.49049 3.0444712.41672.36298 4.29091312.41670.0274 5.7041012.41670.47036 7.3354912.41670.94016 9.26481812.41672.51063 11.62631512.41670.53747 14.67071112.41670.16163 18.96161212.41670.01398 26.2971512.41670.53747 More1112.41670.16163 Xo^212.15436 Input Modeling— Equal prob bins

9. BinFrequencyEi(Oi-Ei)^2/Ei 0.54044157.450.805704698 1.1101177.450.027181208 1.71234897.450.322483221 2.35110787.450.040604027 3.03110467.450.282214765 3.75803377.450.027181208 4.53885767.450.282214765 5.38221177.450.027181208 6.29898977.450.027181208 7.30320547.451.597651007 8.413315127.452.77885906 9.654312117.451.691610738 11.0612497.450.322483221 12.6854267.450.282214765 14.6064177.450.027181208 16.9575267.450.282214765 19.9886297.450.322483221 24.2607297.450.322483221 31.5639377.450.027181208 More77.450.027181208 Xo^29.523489933 Input Modeling— Equal prob bins

10. We failed to reject the null hypotheses that our data fits an exponential distribution with mean of 10.537 Input Modeling Conclusion

11. Model Basics Entity: cars Attribute: arrival time Activities: crossing the intersection (straight & turn) Resources: sections of roads that must be cleared to cross the intersection (straight & turn)

12. Overview-Current System South Bound Cars Traffic Light Pattern

13. Model - Current System 1 lane for turning left 3 lanes for going straight (equal probability)

14. Model - Current System The left-turn lane (South bound) One of the three lanes going straight (South bound) 0.139

15. Model Validation The observed average waiting time of North bound cars turning left was 24.88 in our sample The confidence interval of average waiting time of north bound left-turn cars generated by our model: NLW_C 23.575 25.808 24.954 23.464 25.691 27.74 23.043 27.686 25.579 27.315 25.072 23.605 27.626 27.089 26.119

16. Proposed Model Keeping track of the cars going straight and turning left using global variables

17. Proposed Model The left-turn lane (North bound) One of the three lanes going straight (South bound)

18. Proposed Model Freeing the resource for left-turn cars

19. Output Analysis Pared t-test for average waiting time for cars going North and turning left NLW_CNLW_P2d_n2 23.57519.7143.861 25.80818.1787.63 24.95416.6148.34 23.46416.4527.012 25.69118.187.511 27.7417.23510.505 23.04318.9574.086 27.68619.2988.388 25.57917.5098.07 27.31517.7469.569 25.07217.7857.287 23.60517.3366.269 27.62618.3629.264 27.08916.72610.363 26.11917.119.009

20. Output Analysis Pared t-test for average waiting time for cars going South and turning left SLW_CSLW_P2d_s2 33.78126.1447.637 31.66226.1685.494 32.5927.1875.403 33.7326.0927.638 34.3927.5466.844 30.8532.201-1.351 34.00425.38.704 32.51227.9374.575 30.4126.5993.811 31.28325.1866.097 32.76228.0044.758 31.14726.1175.03 33.40426.2667.138 33.1925.7787.412 34.12427.9176.207

21. Conclusion Our simulation analysis shows that the proposed solution (removing the left-turn arrow) significantly reduce the average waiting time of the cars turning left (both North and South bounds)

22. Questions ?