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Scott Wilson Ltd – Poland Branch NEW VOLUME DELAY FUNCTION Wacław Jastrzębski.

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Presentation on theme: "Scott Wilson Ltd – Poland Branch NEW VOLUME DELAY FUNCTION Wacław Jastrzębski."— Presentation transcript:

1 Scott Wilson Ltd – Poland Branch NEW VOLUME DELAY FUNCTION Wacław Jastrzębski

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

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

4 Scott Wilson Ltd – Poland Branch 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?

5 Scott Wilson Ltd – Poland Branch Four Step Model

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

7 Scott Wilson Ltd – Poland Branch 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,

8 Scott Wilson Ltd – Poland Branch 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.

9 Scott Wilson Ltd – Poland Branch 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;

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

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

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

13 Scott Wilson Ltd – Poland Branch Surveys Results

14 Scott Wilson Ltd – Poland Branch Surveys Results t

15 Scott Wilson Ltd – Poland Branch Surveys Results

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

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

18 Scott Wilson Ltd – Poland Branch Continuity V00C T--0+++ T++++++ TToTo INCREASE

19 Scott Wilson Ltd – Poland Branch New Function

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

21 Scott Wilson Ltd – Poland Branch Function and Surveys

22 Scott Wilson Ltd – Poland Branch 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)

23 Scott Wilson Ltd – Poland Branch Equilibrium Assignment

24 Scott Wilson Ltd – Poland Branch Equilibrium Assignment

25 Scott Wilson Ltd – Poland Branch How Does 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

26 Scott Wilson Ltd – Poland Branch Various Functions

27 Scott Wilson Ltd – Poland Branch Results for Various Functions linkVatzek wykładnicza Overgaarda Generalised BPR ConicalS logitINRETSOslo 1 7007057097011212701711 2 700703709701745701711 3 700713704701656701703 4 700698699700872700697 5 700699697699474700699 6 689690698473698690 7 700692 700467699689 iterations 3341192848921 overcapacity traffic 02122746825 vehicle-hours 2522245325932452231224522449 average time 30,8830,0331,7530,0228,3130,0229,98 average speed 19,4319,9818,9019,9821,1919,9920,01

28 Scott Wilson Ltd – Poland Branch Matrix Reduction to Eliminate Overcapacity Vatzek expotential Overgaarda BPR generalised ConicalS logitINRETSOslo Trip matrix 4900480348374871420948274817 [%]100,0098,0298,7199,4185,9098,5198,31

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

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

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

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


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