Information and Communication Technology Seminar, Vol. 1 No. 1, August 2005
ISSN 1858-1633 2005 ICTS 152
towards the inner city’s highway, whereas a slow rate is usually expected e.g. in the very early morning or at
holidays. The processing time determine how long a vehicle
would stay in the queue. In case of the vehicle queue at the toll-gate this processing time is dependent on
the speed of the processing machine or people handling the vehicle’s arrival and the reliability of the
supporting software behind.
Fig 2: A model of simple queuing system
However in this step we don’t take into account all of those parameters. In this development step, to
simplify the problem of modeling only the arrival’s rate r of the vehicle is used to determine the traffic
flow in this paper. The characteristics of the queues are described by the parameters l for the queue’s
length and t for the processing time fig. 2. However this model is also provided to model a more complex
queuing system which is characterized by the lanes m before the gate, the lanes g in the gate and the lanes n
after the gate [5]. Therefore our model of simple queuing system is determined by parameters of r, l, t,
m
, n, and g.
Fig 3: The very simple graphical user interface of the software tool
Basically, by using the appropriate data structure and algorithms, we can simulate the vehicle queues at
the toll-gate on the computer. The independent appearance of the vehicles in the queues is realized by
using the principles of the object-oriented method. To get an easy run of the software tool a simple user
interface is of great importance. A very simple graphical user interface is shown in fig. 3.
3. SIMULATION RESULTS
The traffic flow at the toll-gate in Tomang area, West Jakarta, can be used as a special case of the
simulation fig. 4. It can be modeled as a simple m
,g,n queuing system. The traffic condition can be described as follows: To use the Jakarta’s inner-ring
toll-road system the incoming vehicles have to join in the queues of m lanes before gate. Next, there exist g
lanes of gates, in which an incoming vehicle has to pay the toll and wait for t seconds. Then, from there, a
vehicle can get one of n lanes after gate to continue the journey along the inner-ring road.
Fig. 4: A toll-gate in Tomang area of scale 1:15,000
After defining the queuing system the arrival’s rate is set to r ranging from 0.0 to 1.0. In this paper various
r are set to get a comprehensive comparisons. For this
purpose the traffic in- and outflows are compared at various values of r. Additionally, the measurements of
the traffic densities are also performed to describe the traffic condition more precisely. The simulation
results are presented in the following fig. 5-7.
a
b Fig 5: Traffic densities for the arrival’s rate of 0.45 a and 0.15 b
A Simple Queuing System to Model the Traffic Flow at the Toll-Gate: Preliminary Results – Wahju Sediono Dwi Handoko
ISSN 1858-1633 2005 ICTS 153
a
b Fig. 6: Traffic densities for various processing time. The processing
time in b is about 2.5 times longer than a in average
Fig. 7: Change of traffic densities blue curve by opening two additional gates
4. DISCUSSION
The model of simple queuing system is created in accordance with an existing toll-gate in Tomang area,
West Jakarta. In a series of computer simulations we have examined several traffic conditions that can
happen at the toll-gate. These examinations are carried out by varying parameter values relevant to the real-
existing condition on-site. In this case a simple 2,4,2 queuing system is used to model the real-existing
situation. Figure 5 shows the difference of the normalized
traffic densities on two different arrivals rates of the vehicle at the toll-gate. The traffic density is defined
as the ratio between the number of vehicles and the capacity of the queue in a certain interval time. It can
be shown that a higher arrival’s rate fig. 5a will result in a higher traffic density.
Another important aspect of a queuing system is the length of the processing time. This processing time
includes the elapsed time since a vehicle enters a gate until it leaves the gate again. It is shown in fig. 6 that a
longer processing time can be indicated by the higher traffic densities before gate red curve.
In fig. 7 we can clearly recognize the increasing traffic density in the gate blue curve after the half
time of the measurement interval. This simulation result shows that the change of the operating toll-gate
gives an influence on the traffic density in the gate.
From a series of the above simulations we can see that the traffic density is an important index can be
used to characterize the traffic conditions at a toll- gate. The traffic density itself is determined by the
combination of at least three factors: the arrival’s rate r
, the processing time t at the gate and the number g of the simultaneous operating gates.
5. CONCLUSION
