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NEW VOLUME DELAY FUNCTION Wacław Jastrzębski

NEW VOLUME DELAY FUNCTION Wacław Jastrzębski. The Overcapacity Problem. Volume>>Capacity. Problem. Using standard VDF functions, sometimes the forecasted demand results in volumes greater than capacity, whereas the actual capacity may in fact be sufficient .

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NEW VOLUME DELAY FUNCTION Wacław Jastrzębski

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  1. NEW VOLUME DELAY FUNCTIONWacław Jastrzębski Scott Wilson Ltd – Poland Branch

  2. The Overcapacity Problem Volume>>Capacity Scott Wilson Ltd – Poland Branch

  3. Problem Using standard VDF functions, sometimes the forecasted demand results in volumes greater than capacity, whereas the actual capacity may in fact be sufficient . Scott Wilson Ltd – Poland Branch

  4. Model – representation of human behaviors using the language of mathematic • To travel or not to travel…. ? • To the city center or closer to home ? • By car or by transit ? • Which route? Scott Wilson Ltd – Poland Branch

  5. Four Step Model Scott Wilson Ltd – Poland Branch

  6. Reality vs. Model Curves capacity Scott Wilson Ltd – Poland Branch

  7. Mathematical Conditions for VDF Function - F(x) is a strictly increasing function for the variable between 0 and + (F’(0)>0) - F(0) = T0, where T0 is the free-flow time; - F’(x) existing and is strictly increasing – that means that function is convex – this last condition is not essential but desirable;The calculation time for the new function should not use more CPU time than BPR function, Scott Wilson Ltd – Poland Branch

  8. Behavioral Conditions • Time spent in traffic congestion weights much more for the traveler than the travel time at the acceptable speed; • Within the range of 0.2-0.8 of capacity, the average speed of traffic shows little sensitivity to the volume of traffic. After reaching the capacity level the travel time increases substantially; • Traveler chooses a path based on previous experience • Traveler can adjust the path as new information on traffic situation is acquired. Scott Wilson Ltd – Poland Branch

  9. The Modeling Conditions • The function should „force” the algorithm to seek additional paths in order to minimize the number of links with volume greater then capacity; • The free-flow-speed is the actual average speed as determined through the surveys (regardless of legal limitations such as speed limits). • The function takes into account that traffic lights decrease the average speed; Scott Wilson Ltd – Poland Branch

  10. Various Mathematical Formulas for VDF Scott Wilson Ltd – Poland Branch

  11. Various Mathematical Formulas for VDF Scott Wilson Ltd – Poland Branch

  12. Various Mathematical Formulas for VDF Scott Wilson Ltd – Poland Branch

  13. Surveys’ Results Scott Wilson Ltd – Poland Branch

  14. Surveys’ Results t Scott Wilson Ltd – Poland Branch

  15. Surveys’ Results Scott Wilson Ltd – Poland Branch

  16. New Function b – odd integer >1 Scott Wilson Ltd – Poland Branch

  17. Mathematical Condition b – odd integer >1 so b –1 is even Scott Wilson Ltd – Poland Branch

  18. Continuity Scott Wilson Ltd – Poland Branch

  19. New Function Scott Wilson Ltd – Poland Branch

  20. What Does it Mean “free flow speed”? Scott Wilson Ltd – Poland Branch

  21. Function and Surveys Scott Wilson Ltd – Poland Branch

  22. EMME Implementation a fd27 =el1 * (1 + 1.35 * ((volau / el2) ^ 9) + .65 * volau / el2) + .2 * (volau .gt. el2) * (volau - el2) a fd30 =el1 * (1 + 100 * ((volau / el2 - .44) ^ 7 + .44 ^ 7) + .45 * volau / el2) + .4 * (volau .gt. el2) * (volau - el2) a fd31 =el1 * (1 + 90 * ((volau / el2 - .43) ^ 7 + .43 ^ 7) + .44 * volau / el2) + .4 * (volau .gt. el2) * (volau - el2) a fd32 =el1 * (1 + 70 * ((volau / el2 - .4) ^ 7 + .4 ^ 7) + .3 * volau / el2) + .4 * (volau .gt. el2) * (volau - el2) a fd33 =el1 * (1 + 28 * ((volau / el2 - .42) ^ 5 + .42 ^ 5) + .28 * volau / el2) + .4 * (volau .gt. el2) * (volau - el2) Scott Wilson Ltd – Poland Branch

  23. Equilibrium Assignment Scott Wilson Ltd – Poland Branch

  24. Equilibrium Assignment Scott Wilson Ltd – Poland Branch

  25. HowDoes It Work? - capacity 700 pcu/h - free flow speed 70 km/h - speed on the capacity limit 20 km/h - practical capacity 0,65 capacity - speed on the practical capacity limit ~ 45 km/h Scott Wilson Ltd – Poland Branch

  26. Various Functions Scott Wilson Ltd – Poland Branch

  27. Results for Various Functions Scott Wilson Ltd – Poland Branch

  28. Matrix Reduction to Eliminate Overcapacity Scott Wilson Ltd – Poland Branch

  29. NO FUNCTION IS PERFECT! Scott Wilson Ltd – Poland Branch

  30. Disadvantages ASSIGNMENT 2035 ~132000 min Scott Wilson Ltd – Poland Branch

  31. Reason? No alternative paths Scott Wilson Ltd – Poland Branch

  32. Solution • Check network carefully and add new possible links – even local to add extra capacity • Add extra capacity or additional centroid connector Scott Wilson Ltd – Poland Branch

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