Saturation flow using Motorcycle Unit (MCU) 60 

The second research named ‘’Saturation flow and vehicle equivalent factors in traffic dominated by motorcycles’’ of Hien Nguyen and Frank Montgomery, which was published by TRB in 2007 shall be discussed. This research was then developed by the same authors with the title ‘’Different models of saturation flow in traffic dominated by motorcycles’’ and published by the

t1 = a1.n1

t1 = a2.n2

Chapter 5: Calculation of Signal Program Elements for MDCs Saturation flow

Institute for Transport Studies of the University of Leeds in 2007. This research is the doctoral dissertation of Hien Nguyen, too.

This research also used the regression analysis, and collected data at twelve approaches in Hanoi at which road gradient is less than 1%, approach width varies from 3.9 m to 13 m, the traffic stream was composed of private cars, light van, minibus, bus, coach, motorcycle and bicycle, but motorcycle proportion is from 80 % to 95 %. In this traffic condition, the authors decided to use the concept of ‘’homogeneous motorcycle saturation flow rate’’, and other vehicles are converted into motorcycle unit (MCU).

According to the Road Note 34 method (Webster, 1963), when observing the saturation flow rate the number of vehicles is recorded in every consecutive 6 seconds of the green time. However, Hien Nguyen and Frank Montgomery decided to count in every consecutive 4 seconds in case traffic dominated by motorcycles because they found that a period of 4 s was found to be more useful, and the potential variation of saturation flow and MCU value during the green time could be explored more easily.

Regarding the regression function, at first, they assumed that S is the homogeneous motorcycle saturation flow rate during a certain period of time T (for example, 4 s). Now, if M motorcycles are taken out and replaced by Nc passenger cars, then the saturation flow will be (Nmc = S-M)

remaining motorcycles and Nc passenger cars. If calling MCU is equivalent factor of one

passenger car into motorcycles, then:

S = Nmc + MCU*Nc (8)

⇒ Nmc = S – MCU*Nc (9)

Assuming that MCU may vary linearly depending on the number of cars Nc, therefore:

MCU = m + n*Nc (10)

Substituting (10) in (9), gives:

Nmc = S – m*Nc – n*Nc2 (11)

Hien Nguyen and Frank Montgomery proposed a model to estimate the homogeneous motorcycle saturation depending on the approach width, turning radii, proportion of turning motorcycles, and the position of the time period within the saturated green time as follows:

ε

δ

δ

δ

δ

δ

+

+

+

+

+

+

+

+

−

+

=

*(

3.5)

*

*

*P

*P

*P

*P

*P

R

P

d

R

P

c

w

b

a

S

Where: w, Prt, Plt, Rrt, Rlt = approach width, proportion of right and left turning motorcycles,

right and left turning radii,

Chapter 5: Calculation of Signal Program Elements for MDCs Saturation flow

ε = the error term.

Substituting (12) in (11), then using regression analysis with five models as follows:

Model 1: The traffic stream contains only motorcycles and passenger cars, in which passenger

cars drive straight-on only.

Model 2: Similar to model 1, but passenger cars can turn right or left.

Model 3: Traffic stream contains all types of vehicles, and all vehicles can go straight-on, turn

right or left.

Model 4: Based on the model 2 with longer period of green time counting. Model 5: Based on the model 3 with longer period of green time counting.

Note that model 4 and model 5 are developed respectively from the model 2 and model 3 with the longer periods of the saturated green time. They counted traffic volume based on the green of the cycle time, then converting the data based on 4 seconds by dividing their own period length and multiplying by 4. Then, they achieved the results.

The results of the regression analysis show that the coefficients of N2 in formula (11) were insignificant, and all equations were shown to be accurate with R2 value varying from 76% to 86%. The summarized results are shown in Table 21 and Table 22 as follows:

Table 21: Saturation flow and effects of factors at different traffic combinations

Model 1 Period-based Cycle-base

Model 2 Model 3 Model 4 Model 5 Saturation flow (MCU / 4s) 12.08 12.44 12.75 12.32 12.28 Period 3 -0.44 -0.48 Period 4 -0.82 -0.86 Period 5 -1.02 -1.02 Period 6 -0.81 -0.73 Periods >6 -0.68 -0.54 w-3.5 2.13 2.03 2.04 2.12 2.15 Prt/Rrt 47.12 37.23 41.66 66.68 62.60 Plt/Rlt 36.15 40.46 40.59 38.26 34.05

Chapter 5: Calculation of Signal Program Elements for MDCs Saturation flow

Table 22: Comparison of MCU values at different traffic combinations

MCU value Period-based Cycle-based

Model 1 Model 2 Model 3 Model 4 Model 5

Straight-on car 3.67 3.04 3.19 4.58 3.81

Right turning car 4.61 4.56 4.69 5.70

Left turning car 4.63 4.88 5.55 5.81

Straight-on van 5.01 4.82

Right turning van 6.82 8.56

Left turning van 6.44 6.67

Straight-on bus 8.43 7.96

Right turning bus 8.73 9.07

Left turning bus 9.40 10.21

(Hien Nguyen and Frank Montgomery, 2007)

From Table 21, it can be seen that if the lane width is 3.5 m wide, the standard motorcycle saturation flow can be set approximately 12 MCUs per 4 seconds (approximately 11.000 MCU/h) and the saturation flow increases by more than 2 motorcycles in every 4 seconds (approximately 2.000 MCU/h) for each 1.0 m approach width increasing.

Throughout the methodology and the results of Hien Nguyen and Frank Montgomery, it can be seen that the concept of homogeneous motorcycle saturation flow is quite acceptable in case of a high proportion of motorcycles in traffic streams, and other types of vehicle should be converted into motorcycle unit (MCU) by the respective equivalent factors shown in Table 22.

Furthermore, all assumptions of this methodology were suitable and close to the reality, and they did not show any suspicion. However, there is a limitation of this research, that is, it covered only the range of lane width from 3.5 m to 13 m. It did not give the results with the lane width of 3.0 m and 2.75 m, which are used very often in urban intersection design. However, from the saturation flow result of 11.000 MCU/h for the lane width of 3.5 m, and the saturation flow increases 2000 MCU/h for each 1.0 m, it can be assumed that the saturation flow is 10.000 MCU/h for the lane width of 3.0 m, 9.500 MCU/h for the lane width of 2.75 m, and 13000 MCU/h for the lane width of 4.5 m.

Chapter 5: Calculation of Signal Program Elements for MDCs Saturation flow