2016년 한국통신학회 하계종합학술발표회
Formulation of Vehicular Traffic Flow Maximization problem
based on real-time traffic data at an intersection
Lee Sook Young, Lee Mee Jeong*
Ewha Womans University
Abstract
Research work in controlling vehicle traffic congestion and maximizing traffic throughput in urban areas has
been growing and thus various adaptive traffic light control algorithms have been proposed. However, no previous
work has been performed to model the traffic throughput maximization problem considering real-time road
conditions. In this paper, considering incoming vehicles have different outgoing directions depending on the
itinerary, we formulate vehicular traffic flow maximization problem considering real-time condition at an
intersection where traffic lights that we desire to control locate as a maximum integer multi-commodity flow
problem with lower bounds.
Ⅰ. Introduction
Ⅱ. Formulation of TFM
Due to rapid urbanization, a variety of vehicular
traffic management (VTM) issues in urban areas have
received growing attention. In order to resolve such
problems as traffic congestion, delayed travel time,
safety, fuel consumption, etc, the transportation
system in urban areas has been advanced as the
intelligent transportation system (ITS) which manages
traffic using communication-based information such as
traffic light signal control (TLC) system. Recently,
various wireless communication technologies have
been introduced in ITS and thus vehicular ad-hoc
network (VANET) has been emerged and rapidly
growing in the industry as well in the academic
sectors [1].
Popular VTM strategies designed for improving
traffic condition can be categorized into two groups.
The first group focuses on traffic data collection using
VANET and applying re-routing algorithms which
detour vehicles based on the data [2-4]. The
approaches vary based on when to respond to changes
in the traffic pattern and how to determine the detour
paths. Meanwhile, research in the second group [5-8]
explores adaptive TLC and some take advantage of
advances in wireless communication technologies and
computing resources to enable the real-time traffic
conditions of each road to be taken into consideration
[7-8]. The focus of most TLC work has been mainly
on increasing traffic throughput while considering a
single intersection; only few studies consider multiple
intersections for the traffic flow maximization.
Moreover, no efforts have been devoted to modeling
the TLC as a traffic flow maximization problem. Unlike
prior work, this paper formulates the vehicular traffic
flow maximization problem while considering realtime condition at an intersection which includes traffic
lights that we desire to control (TFM) as seen in
Figure 1-(a) as a maximum integer multi-commodity
flow problem with lower bounds (MCF-LB).
In this paper, we assume vehicles are equipped with
its own on-board unit and communicate with another
vehicle or a road-side unit (RSU) attached at each
traffic light using VANET. Thus RSU can recognize
the driving direction of vehicles waiting for a green
light at a particular intersection
and also can count
the number of vehicles that have departed from . In
addition, assuming a grid road network as seen in
Figure 1-(a), the considered intersections include a
target intersection
where traffic lights that we
finally desire to control locate and its four adjacent
intersections in the north, south, west and east
direction of
,
hereafter denoted
,
,
, and
as
respectively.
Then
we
represent the road
network as a flow
network
via
a
directed graph G =
(V, E) where V and
E
include
five
(a)
intersections and
driving
roads
respectively.
Based on G we
represent
the
monitored
realtime traffic stream
condition around at
as demands of a
vertex v
V and
lower bounds of a
capacity
of
an
edge e
E as
(b)
seen in Figure 1- Figure 1. TFM problem is
formulated as MCF-LB via a
(b).
directed graph.
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2016년 한국통신학회 하계종합학술발표회
Due to assumption of knowing the expected
forwarding direction of vehicles at an intersection, it
is also known that how many vehicles are coming into
from each of the four directions and vice versa.
Then we define a flow of vehicles FoVi = (
,
,
ni) that pass throughout the target intersection
towards the direction of the flow, i.e., a flow of
vehicles from
to
where
,
{ , ,
,
} and
≠
. Then each FoVi can be
mapped into an individual commodity Ki in a flow
network, Ki = (si, ti, di), where si, and ti, is a source
and sink of commodity i and di is the demand, each of
,
, and
respectively.
which is mapped into
Based on G and FoVi, we prove that for i FoVi TFM
satisfies the following three constraints that MCF-LB
holds.
① Capacity constraints: In G, the accumulated flow,
i.e., the sum of FoVi’ s on an edge e
E cannot be
more than a full capacity or upper bound of a capacity
denoted as Ubs(e), which is usually a fixed value
defined by the physical infrastructure, e.g., number of
lanes of e , namely,
.
② Flow conservation at : TFM opts to serve all
vehicles in every FoV coming into
for the desired
direction. Therefore, the sum of the FoVs entering
must equal that of the FoVs exiting , namely TFM
holds flow conservation of MCF-LB.
Ⅲ. Conclusion and Future work
In this paper, we formulate vehicular traffic flow
maximization problem based on real-time condition at
an intersection as a maximum integer multicommodity flow problem with lower bounds. Future
work includes development of a novel adaptive traffic
light control algorithm using the formulation.
ACKNOWLEDGMENT
This research was supported by Basic Science Research
Program through the National Research Foundation of
Korea(NRF) funded by the Ministry of Education
(2015R1D1A1A01057095). This work was also supported by
Institute for Information & communications Technology
Promotion(IITP)
grant
funded
by
the
Korea
government(MSIP)
(No. B0126-16-1051, A Study on
Hyper Connected Self-Organizing Network Infrastructure
Technologies for IoT Service)
참 고 문 헌
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Vehicular Applications and Inter-Networking
Technologies,” Wiley’ s, UK, February 2010.
[2] M. Milojevic and V. Rakocevic, “ Distributed road
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th
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“ STIP: Spatio-Temporal Intersection Protocols
for Autonomous Vehicles ”
ACM/IEEE 5th
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③ Demand satisfaction: Finally, TFM complies
demands satisfaction of multi-commodity flow
problem, namely, a sum of incoming FoVs to G via
{ ,
,
,
} must be equal to that of
outgoing FoV’ s from G via
{ , ,
,
},
namely for each i, the following equation holds.
,
In addition, we consider real-time traffic data,
namely traffic volume already occupied in the road e
and waiting for a green light for departing from , i.e.,
a lower bound of a capacity of an edge e hereafter
denoted as Lbs(e). Lbs(e) may vary depending on road
traffic condition. Finally, our objective which is to
maximize the total flow into
can be formulated as
following:
Maximize
subject to
,
, and
on
Cyber-Physical
[4] Hult, R., Campos, G., Falcone, P., and Wymeersch,
H., “ An approximate solution to the optimal
coordination problem for autonomous vehicles at
intersections, ” In American Control Conference,
pp. 763~768. Chicago, IL, USA, 2015.
[5] F. Ahmad, S. Mahmud, G. Khan, and F. Yousaf,
“ Shortest remaining processing time based
schedulers for reduction of traffic congestion,” in
the Proceedings of the International Conference on
Connected Vehicles and Expo (ICCVE), Las Vegas,
Nevada, December 2013.
[6] K. Pandit, D. Ghosal, H. Zhang, and C.-N. Chuah,
“ Adaptive traffic signal control with vehicular ad
hoc networks, ” IEEE Transactions on Vehicular
Technology, Vol. 62, No. 4, pp. 1459– 1471, May
2013.
[7] S. Kwatirayo, J. Almhana, and Z. Liu, “ Adaptive
traffic light control using VANET: A case study,”
th
in the Proceedings of the 9 International Wireless
Communications and Mobile Computing Conference
(IWCMC 2013), pp. 752– 757, July 2013.
[8] Faye, S., Chaudet, C., Demeure, I., “ A distributed
algorithm for multiple intersections adaptive traffic
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networking, ACM, pp. 13-18, 2012.
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