Saturation flow as the rate of queue discharge

flow definition



There are various definitions of a concept of
saturation flow. (Mohammed Ibrahim, 2017)describes it as
“macro performance measure of intersection operation. They also claim it is “an
indication of the potential capacity of an intersection when operating under
‘ideal’ conditions” and ‘ideal’ conditions can be understood in a definition by
Webster and Cobbe (1996) that describes saturation flow rate as the “flow which
would be obtained if there was a constant queue of vehicles and they were given
a 100 percent green time”. The (Highway Capacity Manual, 1985) describes the
saturation flow rate as the flow, in vehicles per hour per lane, that can be
accommodated by the lane assuming that the green phase is always available to
the approach. (Australian Road Research Board, 1981) defines saturation flow as
the maximum constant departure rate from the queue during the green period,
expressed in through-car units per hour (tcu/hr). (Canadian Capacity Guide, 1984)
defines saturation flow as the rate of queue discharge from the stop line of an
approach lane, expressed in passenger-car units per hour of green (pcu/hr

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 All of
the definitions agree that the saturation flow may differ due to various
conditions as well as geometric and traffic configurations. ARRB report, The
HCM and CCG highlight importance of factors that modify the saturation flow
such as lane width, environment, pedestrians, discharge space, weather
conditions, parking interference or duration of the green interval. All three
documents have a fundamental difference of understanding the traffic
composition. CCG considers all the vehicle types such as passenger cars,
lorries, public buses as a homogenous entity and converts all the vehicle types
into passenger car units. HCM and the ARRB report look into the basic
saturation flow in the green light period making later adjustments based on
geometric design and traffic conditions. All three definitions consider turning
vehicles from shared lanes in the calculations in order to provide more
accurate results. Final comparison of the three measuring results is based on
following rules applied in each of the documents. HCM uses an adjustment factor
(FHV) which is taken from table 9-6 of the HCM and it calculates the
percentage of heavy vehicles in the traffic. CCG converts all of the surveyed
vehicles into passenger car unit equivalent in order to process the data. On
the other hand, ARRB Report 123 combines variety of vehicle types and their
turning movements which results give the traffic composition factor (Fc).










techniques & methods



There is a variety of methods of collecting
data in order to measure the saturation flow, some of them are carried out
manually and there are others more complex and automatic techniques.

Measurement method should be chosen for the type of study being conducted and
depend on availability of a workforce, cost of a study, ease of analysis and it
should provide researcher with a data for further analysis.


are three fundamental techniques that are used for the calculation of a
saturation flow: The Road Note 34 Method (1963) defined by Williams et al.

(1987) is a method that consists of taking classified counts of vehicles
crossing the stop line, within the approach width, in six seconds intervals
during the green and amber period of the cycle under saturated flow condition.

In the application of the RN34 to cyclists, the first interval starts when the
green period begins. Then the average height of the saturated intervals gives
the saturation flow (Sebastian Seriani et al, 2015). Headway method
(Greenshields et al. ; TRB 1997) estimates the average time headway between the
vehicles discharging from queue as they pass the stop-line.  Time headway of a vehicle is measured as the
time between vehicles as they cross the stop line by the rear bumper of the
vehicle preceding it, and its own rear bumper. (Scraggs, 1964) Regression
technique is used to develop an equation involving saturated green time, number
of vehicles in various categories, and lost time. A regression analysis yields
the saturation flow, the lost times, and the passenger car equivalents for
vehicles other than passenger cars. (Branston and Gipps; Kimber et al.; Stoke
et al.)






There are numerous methods of collecting data
for measuring saturation flow. It can be conducted manually where a person can
use either electronic hand held or record the data uses a tally sheet. Tests
that have been carried out claim that manual vehicle counting is 99 percent
accurate (Windmill Software Ltd , 2016). The other method of
data collection is video vehicle counting. This method requires less labour as
there are systems that make it possible to analyse the video pictures as cars
are passing underneath. It has been also very popular to count vehicles using
pneumatic road tube. (Windmill Software Ltd , 2016)


Proved to be the most popular method of
recording traffic flow (Methods for Measuring Saturation Flow, No Date), video tape recorded
method provides satisfactory results and will be used in this study. “During
the data collection at the site the portable video recording camera and number
generator is used to super impose the time based on the recorded traffic
events. Nowadays cameras with a built-in time base recording are available,
that can measure the time in fraction of a second” (Methods
for Measuring Saturation Flow, No Date).








Although there are many studies regarding
vehicle flow there is a very limited knowledge and research conducted on
bicycle flows. (Rui Jiang et al, 2016) Due to the growing number of bicycles
used in the present times such studies are essential. “There are now more than
670,000 cycle trips a day in London, an increase of over 130 per cent since
2000” (Tranport for London, 2017) There is a stronger
need to design more functional and safer routes for cyclists. This can be
carried out by measuring saturation flow on already existing bicycle lanes. (Tranport for London, 2017) presents the Cycle
Network Model for London, known as Cynemon, developed model that estimates
cycling routes, journey times and flows at strategic level across London.

According to Allen et al (1998) there are different studies that calculate the
capacity of cycle lanes. HCM (2000) defines 1600 bicycles per hour per lane as
the capacity for two-way facility and 3200 bicycles per hour per lane for
one-way facility. However (Sebastian Seriani et al, 2015) states that there
are different values for the capacity of cycle lanes and there is no clear
references to identify which one is correct capacity for a traffic signal
approach, hence the importance of this project. The principal method of
measuring vehicle saturation at traffic signals presented by The RN34 is to divide
saturated portion of each green period into short intervals of time and and to
average the flows in those saturated interval which are free from ‘lost time’
effects, to give a measure of the saturation flow. (Sebastian Seriani et al, 2015) suggest that “in
order to get the same conditions at cycle lanes traffic signal unrestraint
discharges of cyclist must be studied.” As this study focuses on cycle lanes in
London, there are factors that should be considered while conducting this
project. “It must be noted that in London before the green period starts there
is an amber time to prepare cyclist for the discharge process”



of bicycle lanes


Over the world countries have different average
bicycle lane capacity (bicycle/h-lane); Sebastian Seriani et al. (2015)
provides the following data:



·      Sweden – 1.2m lane = 1500 bicycle/h-lane

·      Canada – 1.25m lane = 5000 bicycle/h-lane

·      China – 1.00m lane = 1800-2100 bicycle/h-lane

·      Germany – 1.00m lane = 3200 bicycle/h-lane



Sebastian Seriani et al
provides the following:


Measurements were carried out in London at
Tavistoke Square where it was found a capacity of 1000 bicycle/h-lane on the
peak (morning and afternoon) hour with the width of 1m per lane. Whereas in
Santiago in Chile the capacity is 900 bicycle/h-lane in the morning and 1300 bicycle/h-lane
afternoon. (Sebastian Seriani et al, 2015)


Experiments in the controlled environment at
cycle-track, in order to simulate a junction with constant queue, it was made
experiments with different lane widths. In scenario A (1.0–m lane) one lane of
cyclists formed and the saturation flow reached 2070 bicycle/h-lane. As the
width increased for scenario B to 1.25 m (25%) the saturation also increased
25% with the flow of 2587 bicycle/h-lane. Scenario C (1.5-m lane) saturation
was 3442 bicycle/h-lane, and scenario D (2.0-m lane) it increased to 2.5 bigger
than scenario A, reaching the number of 4657 bicycle/h-lane. It is almost a
linear relationship between the lane width and the discharge if the junction. (Sebastian Seriani et al, 2015)


Rui Jiang et al, (2016) in a different
experiment used an oval shaped circuit with 29 m straight sections joined by 14
m circular curves, the total length was 146 m, width of 0.8 m and bicycles were
not allowed to overtake. The experiment took place in 3 different days and also
3 different weather conditions. For the firs experiment, the capacity was
estimated to be 3000 bicycles per hour. The second experiment the capacity is
smaller which is around 2700 per hour and the experiment the capacity is
considerably smaller due to the rain. (Rui Jiang et al, 2016)


Previous studies indicated the following expectations;
2,600 bicycles per hour per 1 m lane(Homburger, W.S 1976), 3,000 to 3,500 bicycles
per hour per 0.78 m lane(Botma, H & Papendrecht, H 1991); 4,500 bicycles
per hour per 2.4 m lane (Raksuntorn, W & Khan, S.I. 2003) and 10,000
bicycles per hour per 2.5 m lane (Navin, F.P.D. 1994).


It is noticeable the lack of consistency among
the results. Although the experiments are run in different ways, one would should
have a more precise number on what to expect for the capacity of lanes for a
given width. There are some factors that could have influenced the results in
some of the experiments such as different gender constitution of riders,
weather condition, the fact that the volunteers for the experiment are not real
commuters, ground surface grip, information points or distraction points. A common
fact among these papers is the acknowledgment about the lack of measurements
out there, proving once again the importance of this project.


















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