# NEW VOLUME DELAY FUNCTION Wacław Jastrzębski

## Presentation on theme: "NEW VOLUME DELAY FUNCTION Wacław Jastrzębski"— Presentation transcript:

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

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

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 . Scott Wilson Ltd – Poland Branch

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? Scott Wilson Ltd – Poland Branch

Scott Wilson Ltd – Poland Branch
Four Step Model Scott Wilson Ltd – Poland Branch

Reality vs. Model Curves
capacity 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, 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 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

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

Various Mathematical Formulas for VDF
Scott Wilson Ltd – Poland Branch

Various Mathematical Formulas for VDF
Scott Wilson Ltd – Poland Branch

Various Mathematical Formulas for VDF
Scott Wilson Ltd – Poland Branch

Scott Wilson Ltd – Poland Branch
Surveys’ Results Scott Wilson Ltd – Poland Branch

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

Scott Wilson Ltd – Poland Branch
Surveys’ Results Scott Wilson Ltd – Poland Branch

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

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

Scott Wilson Ltd – Poland Branch
Continuity V 0<V<C*s V=C*s C*s<V<C V=C V>C T’’ - + T’ T To INCREASE Scott Wilson Ltd – Poland Branch

Scott Wilson Ltd – Poland Branch
New Function Scott Wilson Ltd – Poland Branch

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

Scott Wilson Ltd – Poland Branch
Function and Surveys Scott Wilson Ltd – Poland Branch

Scott Wilson Ltd – Poland Branch
EMME Implementation a fd27 =el1 * ( * ((volau / el2) ^ 9) * volau / el2) + .2 * (volau .gt. el2) * (volau - el2) a fd30 =el1 * ( * ((volau / el ) ^ ^ 7) + .45 * volau / el2) + .4 * (volau .gt. el2) * (volau - el2) a fd31 =el1 * ( * ((volau / el ) ^ ^ 7) + .44 * volau / el2) + .4 * (volau .gt. el2) * (volau - el2) a fd32 =el1 * ( * ((volau / el2 - .4) ^ ^ 7) + .3 * volau / el2) + .4 * (volau .gt. el2) * (volau - el2) a fd33 =el1 * ( * ((volau / el ) ^ ^ 5) + .28 * volau / el2) + .4 * (volau .gt. el2) * (volau - el2) Scott Wilson Ltd – Poland Branch

Equilibrium Assignment
Scott Wilson Ltd – Poland Branch

Equilibrium Assignment
Scott Wilson Ltd – Poland Branch

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 Scott Wilson Ltd – Poland Branch

Scott Wilson Ltd – Poland Branch
Various Functions Scott Wilson Ltd – Poland Branch

Results for Various Functions
link Vatzek wykładnicza Overgaard’a Generalised BPR Conical S logit INRETS Oslo 1 700 705 709 701 1212 711 2 703 745 3 713 704 656 4 698 699 872 697 5 474 6 689 690 473 7 692 467 iterations 33 41 19 28 48 9 21 overcapacity traffic 22 468 25 vehicle-hours 2522 2453 2593 2452 2312 2449 average time 30,88 30,03 31,75 30,02 28,31 29,98 average speed 19,43 19,98 18,90 21,19 19,99 20,01 Scott Wilson Ltd – Poland Branch

Matrix Reduction to Eliminate Overcapacity
Vatzek expotential Overgaard’a BPR generalised Conical S logit INRETS Oslo Trip matrix 4900 4803 4837 4871 4209 4827 4817 [%] 100,00 98,02 98,71 99,41 85,90 98,51 98,31 Scott Wilson Ltd – Poland Branch

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

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

Reason? No alternative paths
Scott Wilson Ltd – Poland Branch

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 Scott Wilson Ltd – Poland Branch

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