Ieeepro techno solutions 2013 ieee embedded project person-based traffic responsive signal control optimization

1278 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 14, NO. 3, SEPTEMBER 2013
Person-Based Traffic Responsive
Signal Control Optimization
Eleni Christofa, Ioannis Papamichail, and Alexander Skabardonis
Abstract—This paper presents a person-based traffic respon-
sive signal control system for transit signal priority (TSP) on
conflicting transit routes. A mixed-integer nonlinear program
(MINLP) is formulated, which minimizes the total person delay
at an intersection while assigning priority to the transit vehicles
based on their passenger occupancy. The mathematical formula-
tion marks an improvement to previous formulations by ensur-
ing global optimality for undersaturated traffic conditions and
intersection design and traffic characteristics that lead to convex
objective functions in reasonable computation time for real-time
applications. The system has been tested for a complex signalized
intersection located in Athens, Greece, which is characterized
by multiple bus lines traveling in conflicting directions. Testing
includes cases with deterministic vehicle arrivals at the inter-
section and emulation-in-the-loop simulation (EILS) tests that
incorporate stochasticity in the vehicle arrivals. The results show
that the proposed person-based traffic responsive signal control
system reduces the total person delay at the intersection and
effectively provides priority to transit vehicles, even when perfect
information about the auto and transit arrivals at the intersection
is not available.
Index Terms—Mathematical model, person delay, traffic signal
control, transit signal priority (TSP).
I. INTRODUCTION
TRAFFIC congestion is one of the biggest problems that
urban areas are facing. Conflicts among multiple modes
that share the same infrastructure further complicate the system
and exacerbate this problem. However, multimodal systems are
essential for achieving more efficient, sustainable, and equi-
table transportation operations. If properly optimized, traffic
signal systems hold potential to achieve efficient multimodal
traffic operations while mitigating congestion and its negative
externalities in urban networks. These systems are tradition-
ally optimized by minimizing total delays for vehicles. Such
vehicle-based optimization can lead to unfair treatment of pas-
sengers in high occupancy vehicles.
Manuscript received October 18, 2012; revised February 22, 2013; accepted
April 7, 2013. Date of publication May 16, 2013; date of current version
August 28, 2013. The Associate Editor for this paper was W. Fan.
E. Christofa is with the Department of Civil and Environmental Engineering,
University of Massachusetts, Amherst, MA 01003 USA (e-mail: christofa@ecs.
umass.edu).
I. Papamichail is with the Department of Production Engineering and Man-
agement, Technical University of Crete, Chania 73100, Greece (e-mail: ipapa@
dssl.tuc.gr).
A. Skabardonis is with the Department of Civil and Environmental Engineer-
ing, Institute of Transportation Studies, University of California, Berkeley, CA
94720 USA (e-mail: skabardonis@ce.berkeley.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TITS.2013.2259623
Transit vehicles contribute less to congestion and pollution
per passenger, but their users often experience higher overall
travel costs than auto users. There is a need for granting
priority to transit vehicles at bottlenecks, such as signalized
intersections, which are responsible for a significant portion of
their delay. Prioritizing transit vehicles through improvements
in facility design (e.g., bus lanes) is not always feasible be-
cause of geometric or spatial restrictions. Transit signal priority
(TSP) is an operational strategy that facilitates efficient transit
operations by providing priority to transit vehicles at signalized
intersections, and it has been incorporated in several real-
time signal control systems. These systems use detection of
vehicular traffic at some point upstream and/or downstream of
an intersection to predict the traffic conditions and adjust the
signal settings in real time. Using the available information,
the signal settings are optimized on a decision horizon equal
to one cycle or a few minutes (traffic responsive systems) or on
a rolling horizon (adaptive systems). Recently, an arterial-level
adaptive signal control system has been developed, which opti-
mizes signal settings using mobile sources, but its success de-
pends on the existence of high market penetration of equipped
vehicles [1].
The literature provides several examples of real-time (i.e.,
adaptive and traffic responsive) traffic signal control systems
that incorporate TSP with various levels of success under
different traffic conditions. Despite the number of systems that
have been designed, there are still several issues that have not
been successfully addressed. First of all, the majority of the
existing systems do not provide priority in a systematic way
to transit vehicles traveling in conflicting directions. Existing
work has dealt with this issue either by predetermining the rela-
tive priority level of the transit routes [2], [3] or by constraining
the implementation of the system to networks that include only
transit vehicles traveling in nonconflicting directions [4]–[6].
Moreover, transit priority is often unconditionally provided,
without considering specific criteria, such as passenger oc-
cupancy and schedule delay [7]. Such criteria could ensure
improvement in the operations of transit vehicles while pro-
tecting cross streets from reaching oversaturated conditions. In
addition, the existing systems do not account for the difference
in the passenger occupancy of autos and transit vehicles, instead
optimizing their systems on a per-vehicle basis [4], [8], [9]. The
provision of priority is often rule based [10], and as a result, it
is not explicitly included in the optimization process.
Recently, a traffic responsive signal control system with TSP
has been developed and tested by the authors [11], [12]. The
objective of this system is to optimize the signal timings at an
intersection, such that conditional priority is granted to transit
1524-9050 © 2013 IEEE

CHRISTOFA et al.: PERSON-BASED TRAFFIC RESPONSIVE SIGNAL CONTROL OPTIMIZATION 1279
vehicles based on their passenger occupancy. Conditional pri-
ority is used as a way to assign priority when two or more
transit vehicles from conflicting directions are expected to
arrive at the intersection at approximately the same time and
to compete for priority. In addition, the impact of TSP on the
auto delays is taken into account by using the total person delay
in the objective function for all of the vehicles present at the
intersection. The system is based on data from readily available
sensing systems to predict vehicle arrivals. It has been tested
for a variety of undersaturated and oversaturated conditions for
deterministic vehicle arrivals at an isolated intersection. The
results indicate that the system leads to significant reductions
in the transit users’ delay and the total person delay at the
intersection for a wide range of operating conditions.
This paper introduces a significant extension of our pre-
vious work by presenting an improved formulation of the
mathematical program for undersaturated traffic conditions and
isolated intersections, which ensures global optimality, as long
as the objective function for the specific intersection is convex
(which is the case for the intersections tested). It does this in
sufficiently short computation time for real-time applications.
In addition, this paper presents the development and application
of an emulation-in-the-loop simulation (EILS) approach, which
allows for realistic evaluation of the proposed system and
calculation of several performance measures that cannot be
easily and analytically assessed, e.g., emissions. This paper also
demonstrates the robustness of the proposed system through
the simulation experiments. The system is shown to improve
transit operations and to reduce total passenger delay at a
signalized intersection, even when perfect information on the
actual arrivals of autos and transit vehicles is not available.
The paper is organized as follows. First, we describe the
mathematical program that minimizes person delays for all
users traveling through the intersection. Then, the study site
used for testing the proposed person-based traffic responsive
signal control system is presented. The results from the tests
that are performed with deterministic vehicle arrivals and the
results from the simulation tests that incorporate stochastic ve-
hicle arrivals follow. Finally, the study findings are summarized,
and ongoing and future research works are outlined.
II. MATHEMATICAL MODEL
A mathematical model that minimizes total person delay at
an intersection has been formulated for undersaturated traffic
conditions. Minimization of the total person delay is achieved
by weighting delays for both autos and transit vehicles by
their respective passenger occupancies. This way, the issue of
providing priority when conflicting transit routes are present is
also addressed.
The mathematical model is formulated based on the as-
sumption that perfect information is available about the vehicle
arrivals, passenger occupancies, and lane capacities at the inter-
section. Auto vehicle arrivals are assumed to be uniform since
the focus is on isolated intersections for which vehicle arrivals
do not depend on the signal settings of upstream intersections
and are considered to be deterministic for delay estimation
purposes. For the analysis period, the cycle length is assumed
to be constant, and the sequence of the phases and the phase
design are predetermined and fixed. In addition, all of the
phases that serve a specific lane group1
are assumed to be
consecutive within each cycle, and the phase yellow times are
assumed to be known. It is also assumed that the capacity for
each approach at the intersection is fixed and not affected by
traffic operations, which means that the saturation flow for each
of the lane groups is constant. Finally, the model is formulated,
assuming that transit vehicles travel on mixed-use traffic lanes
along with autos. However, the formulation of the mathematical
model holds even when dedicated lanes for transit vehicles
exist.
The mathematical program minimizes the total person delay
at the intersection by changing the green times for each phase
i, i.e., gi, T , within the cycle under consideration (indexed by
T), constrained by minimum and maximum green times and a
fixed cycle length C. The mathematical program is run once for
every cycle, and the generalized formulation that optimizes the
signal settings for any design cycle T is as follows:
min
AT
a=1
oada, T +
BT
b=1
obdb, T (1a)
s.t. gi min ≤ gi, T ≤ gi max (1b)
lj
i=kj
gi, T +
lj −1
i=kj
yi ≥ gj min (1c)
I
i=1
gi, T + L = C (1d)
where
a auto vehicle index;
b transit vehicle index;
AT total number of autos served by the intersection
during cycles T and T + 1;
BT total number of transit vehicles present at the inter-
section during cycle T;
oa passenger occupancy of auto a [passengers/vehicle];
ob passenger occupancy of transit vehicle b [passen-
gers/vehicle];
da, T delay for auto a for cycle T [seconds];
db, T delay for transit vehicle b for cycle T [seconds];
gi, T green time allocated to phase i in cycle T [seconds];
gi min minimum green time for phase i [seconds];
gi max maximum green time for phase i [seconds];
kj first phase in a cycle that can serve lane group j;
lj last phase in a cycle that can serve lane group j;
yi yellow time for phase i;
gj min minimum green time for lane group j [seconds];
I total number of phases in a cycle;
L lost time [seconds];
C cycle length [seconds].
1A lane group is defined per the Highway Capacity Manual 2000 [13] as one
or more adjacent lanes at each intersection approach that can be served by the
same phases.

Fig. 1. Queueing diagram for lane group j.
The objective function consists of the sum of the delay
for auto passengers that are served by the intersection during
the design cycle T and during the next cycle T + 1 and the
transit passengers that are present at the intersection during the
design cycle T. Delays for autos and transit vehicles depend
on the green times gi, T , which are the decision variables for
the mathematical program. In fact, the auto and transit vehicle
delays, i.e., da, T and db, T , respectively, also depend on the
green times of the previous and the next cycles, the yellow
times, and numerous other input parameters, which are either
prespecified by the user or collected with the use of surveillance
technologies. The delays of both autos and transit vehicles
are weighted by their respective passenger occupancies in the
objective function to make this a person-based optimization.
Three constraints are introduced for the decision variables.
The green times of each phase i are constrained by their
minimum and maximum green times [see constraint (1b)]. Min-
imum green times gi min are necessary to ensure safe vehicle
and pedestrian crossings. In addition, they guarantee that no
phase is skipped. Note that, if the user wants to allow a phase
to be skipped, the corresponding minimum green time can
be set equal to zero. Maximum green times gi max are used
to restrict the domain of solutions for the green times of the
phases and to reduce computation times. Phase green times are
further constrained by minimum lane group green times gj min
to ensure undersaturated traffic conditions for each lane group
[see constraint (1c)], i.e., gj min = Cqj/sj. The phase green
times are also constrained, such that the sum of the green times
for all phases at each intersection and the lost time adds up to
the cycle length [see constraint (1d)], which is kept constant for
every cycle in the analysis period. Lost time L is assumed to be
the summation of the yellow times for each phase, i.e.,
L =
I
i=1
yi. (2)
Note that the yellow times do not have to be constant across all
phases.
A. Auto Delay
The person delay for the auto passengers included in the
objective function is the sum of two terms: 1) the person delay
that corresponds to the autos that are served during the design
cycle T and 2) an estimate of the delay for those that will be
served during the next cycle T + 1. This second delay estimate
is included in the objective function to account for the impact
that the design of the signal timings for T will have on the
delays of T + 1. If this second delay estimate was not included,
the optimized signal timings for the design cycle would provide
the minimum green times to all of the phases apart from the last
one, and this would substantially increase the auto delay for the
next cycle.
Based on the deterministic component of Webster’s delay
formula [14], the total delay for all vehicles in a lane group
j and for one cycle, which is denoted by Dj, is calculated as
a function of the red time interval Rj, during which the queue
grows; the rate at which vehicles arrive qj; and the rate at which
vehicles are served sj; as follows:
Dj =
1
2
qjR2
j
1 −
qj
sj
. (3)
Fig. 1 shows the delay for the vehicles of a lane group j
and the cumulative number of vehicles of that lane group served
by an intersection during cycle T or T + 1. Note that the
cumulative count for each cycle restarts at the end of the green
phase that serves the subject lane group in the previous cycle.
The cycle length for each lane group can be split into three
components, which are functions of the phase green times.
The first component is the red time from the start of the
cycle to the beginning of the green time for the subject lane
group R
(1)
j (gi, T ), the second component is the duration of the
effective green time itself Ge
j(gi, T ), and the third component is
the red time from the end of the green time until the end of the
cycle R
(2)
j (gi, T ). These components are shown in Fig. 1 and
can be calculated as follows:
R
(1)
j (gi, T ) =
kj −1
i=1
gi, T +
kj −1
i=1
yi (4a)
Ge
j(gi, T ) =
lj
i=kj
gi, T +
lj −1
i=kj
yi (4b)
R
(2)
j (gi, T ) =
I
i=lj +1
gi, T +
I
i=lj
yi. (4c)

Note that, to simplify the illustration, the yellow time intervals
have not been marked on the time axis but are considered to be
included at the end of each phase.
The shaded area between the solid lines represents the total
delay experienced by the autos of lane group j that are served
during the design cycle T, and it is denoted by Dj, T . The
shaded area between the dashed lines represents the estimate
of the total delay experienced by the autos of lane group j that
are served during the next cycle T + 1, and it is denoted by
ˆDj, T +1. The delay for a lane group j for cycle T is counted
from the end of the green phase that served j in cycle T − 1
until the end of the corresponding green phase in cycle T. As a
result, the signal timings for the previous cycle T − 1 must be
known to determine the delays of the vehicles that arrive at the
intersection during cycle T − 1 but will be served during the
design cycle T. Such queueing diagrams can be drawn for each
lane group to estimate the delay for autos under the assumption
of first-in–first-out queueing discipline. The calculation of auto
delays for cycles T and T + 1 is presented in the following.
Auto Delay for Cycle T: The total delay for all autos of lane
group j that are served during cycle T, i.e., Dj, T , is derived
from (3) as follows:
Dj, T =
1
2
qj
1 −
qj
sj
R
(2)
j (gi,T −1) + R
(1)
j (gi, T )
2
. (5)
Auto Delay for Cycle T + 1: The estimate of the total delay
for all autos that will be served during cycle T + 1, i.e.,
ˆDj, T +1, is derived from (3) as follows:
ˆDj, T +1 =
1
2
qj
1 −
qj
sj
R
(2)
j (gi, T ) + R
(1)
j (gi next)
2
(6)
where gi next is a user-specified value for the green time of
phase i during cycle T + 1. Base case signal timings, optimal
fixed signal timings that have been determined offline, or the
optimal green times obtained from the optimization of cycle
T − 1 can be used as the phase green times for the next cycle
without significantly affecting the performance of the system.
Equation (6) is also based on the assumption that the arrival
rate for the next cycle is the same as for the design cycle and is
therefore equal to qj.
As a result of these delay components, the first part of the
objective function (auto person delay) becomes
AT
a=1
oada, T = ¯oa
J
j=1
(Dj, T + ˆDj, T +1) (7)
where J is the total number of lane groups at the intersection.
Dj, T and ˆDj, T +1 depend on the decision variables gi, T , as
shown in (5) and (6). An average value of passenger occupancy
per auto ¯oa is used because the total auto delay is collectively
calculated rather than accounting for each vehicle separately.
However, the delays experienced by any individual auto could
be easily estimated with the use of queueing diagrams such as
that in Fig. 1, given that the arrival time of the vehicle at the
back of the queue is known. This approach is used to estimate
transit vehicle delays, as shown in the following.
B. Transit Delay
The person delay for the transit passengers included in the
objective function is the sum of two terms: 1) the person
delay that corresponds to the transit vehicles that are served
during the design cycle T and 2) an estimate of the delay
for those that arrive in cycle T but will be served during
the next cycle T + 1. Under the assumption that the arrival
times of transit vehicles at the intersection are known only
for the design cycle, transit vehicles that arrive at the inter-
section during cycle T + 1 are not taken into account. The
exclusion of such vehicles is not expected to significantly affect
the performance of the system because these vehicles will
be considered when the signal timings for cycle T + 1 are
optimized.
Transit vehicles travel in mixed-use traffic lanes with the
autos; therefore, the delay of a transit vehicle b that arrives at
the back of its lane group’s queue at some time tb is the same
as an auto that arrives at the same time at the back of that lane
group’s queue. The delay for a transit vehicle that belongs to a
lane group j can be calculated by the same queueing diagrams
used for auto delay estimation (see Fig. 1). The estimation of the
transit delay used in the optimization of each cycle T depends
on the actual arrival time of the transit vehicle tb relative to
the end of the last phase that can serve its lane group j in cycle
T − 1, which is denoted by τj, T −1, and the end of the last phase
that can serve j in T, which is denoted by τj, T , where
τj, T = (T − 1)C + R
(1)
j (gi, T ) + Ge
j(gi, T ). (8)
The possible cases are summarized in the following.
Case 1—Arrival Before the End of Green Time in T: If a
transit vehicle b that belongs to lane group j has arrived in the
previous cycle T − 1 at some time after the end of the last phase
that can serve j (tb > τj, T −1) or arrives in the design cycle
T before the end of the phases that can serve it (tb ≤ τj, T ),
its delay for cycle T, which is denoted by db, T , depends on
its arrival time tb and phase green times gi, T . This delay is
expressed as
db, T = (T − 1)C + R
(1)
j (gi, T ) +
qj
sj
(tb − τj, T −1) − tb. (9)
If the transit vehicle arrives before or at the clearance of its lane
group’s queue, (9) will give a nonnegative delay. Define this as
time interval α, i.e.,
α = τj, T −1 < tb ≤ τj, T | db, T ≥ 0 . (10)
However, if the transit vehicle arrives after the clearance of that
queue and at a time within the phases that can serve it, (9)
will give a negative delay, which implies that the true delay for
such a transit vehicle will be zero. Define this as time interval
β, i.e.,
β = τj, T −1 < tb ≤ τj, T | db, T < 0 . (11)
Therefore, the transit vehicle delay db, T for this case is ex-
pressed as
db, T = max{db, T , 0}. (12)

Case 2—Arrival After the End of Green Time in T: If a
transit vehicle b that belongs to lane group j arrives during cycle
T after the last phase that can serve j (tb > τj, T ), the transit
vehicle will be served during the next cycle T + 1. Define this
as time interval γ, i.e.,
γ = {tb > τj, T }. (13)
In this case, the transit delay consists of the delay experienced
until the end of cycle T, denoted by db, T , and an estimate
of the delay that the transit vehicle will experience until it is
served during the next cycle, denoted by ˆdb, T +1. The delay
experienced until the end of cycle T, i.e., db, T , is expressed as
db, T = TC − tb (14)
and the estimate of the delay that such a transit vehicle
will experience during the next cycle T + 1, i.e., ˆdb, T +1, is
expressed as
ˆdb, T +1 = R
(1)
j (gi next) +
qj
sj
(tb − τj, T ) (15)
where the user-specified phase green times for the next cycle
gi next are the same as those used in the auto delay estimation.
Therefore, the transit vehicle delay db, T for this case is
expressed as
db, T = db, T + ˆdb, T +1
= TC + R
(1)
j (gi next) +
qj
sj
(tb − τj, T ) − tb. (16)
C. Mathematical Program Formulation
As described by the earlier equations, the mathematical pro-
gram that minimizes the person delay for auto and transit users
at a signalized intersection for one cycle can be formulated
as a mixed-integer nonlinear program (MINLP). The integer
variables are introduced due to the different delay formulas
that correspond to each of the three time intervals in which a
transit vehicle could possibly arrive (α, β, γ). As a result, for
each transit vehicle b considered in the optimization, there are
three binary variables introduced, i.e., wα
b , wβ
b , and wγ
b , where
wf
b = 1 if tb ∈ f or wf
b = 0 if otherwise, for f ∈ {α, β, γ}. A
summary of the formulation is shown in the following.
Objective Function (person delay component for autos):
¯oa
1
2
J
j=1
qj
1 −
qj
sj
R
(2)
j (gi,T −1) + R
(1)
j (gi, T )
2
+ R
(2)
j (gi, T ) + R
(1)
j (gi next)
2
(17)
Objective Function (person delay component for transit):
BT
b=1
ob wα
b (T − 1)C+R
(1)
j (gi, T )+
qj
sj
(tb − τj, T −1) − tb
+ wγ
b TC + R
(1)
j (gi next) +
qj
sj
(tb − τj, T ) − tb (18)
Constraints:
(T − 1)C + R
(1)
j (gi, T )
+
qj
sj
(tb − τj, T −1) − tb ≥ − (1 − wα
b )M1 ∀b (19)
(T − 1)C + R
(1)
j (gi, T )
+
qj
sj
(tb − τj, T −1) − tb ≤ wα
b M1 ∀b (20)
(1 − wγ
b ) tb ≤ τj, T ∀b (21)
(1 − wγ
b ) M2 + wγ
b tb ≥ τj, T ∀b (22)
Ge
j(gi, T ) ≥
qj
sj
C ∀j (23)
I
i=1
gi, T +
I
i=1
yi = C (24)
gi, T ≥ gi min ∀i (25)
gi, T ≤ gi max ∀i (26)
wα
b + wβ
b + wγ
b = 1 ∀b (27)
wα
b , wβ
b , wγ
b ∈ {0, 1} ∀b (28)
where M1 and M2 are big numbers that can be set equal to C
and TC, respectively. The constraints are described as follows.
• Constraints (19)–(22) ensure that the correct delay formula
will be added to the objective function for each of the tran-
sit vehicles present at the intersection during the design
cycle T.
• Constraint (23) ensures undersaturated conditions for each
lane group.
• Constraint (24) ensures that the green times for each phase,
which will be the outcome of the optimization, and the
sum of the yellow times (i.e., lost time) add up to the cycle
length.
• Constraints (25) and (26) set the upper and lower bounds
for the continuous decision variables gi, T .
• Constraints (27) and (28) ensure that only one binary
variable will be equal to one.
Note that the formulation of the given mathematical pro-
gram leads to bilinearities (i.e., nonconvexity in the objective
function) due to the multiplication of the continuous variables
gi, T with the integer variables wα
b , wβ
b , and wγ
b . To avoid this
problem, three new continuous variables gα
i, b, gβ
i, b, and gγ
i, b are
introduced for each phase and for each of the transit vehicles
whose delays are included in the objective function [15]. The
initial continuous decision variables gi, T are now defined as
gi, T = gα
i, b + gβ
i, b + gγ
i, b ∀i, b (29)
where
gβ
i, b = gγ
i, b = 0 ∀i, b if tb ∈ α (30)
gα
i, b = gγ
i, b = 0 ∀i, b if tb ∈ β (31)
gα
i, b = gβ
i, b = 0 ∀i, b if tb ∈ γ. (32)

Equation (29) is an extra constraint added to the initial math-
ematical program. To avoid the bilinear terms, i.e., nonlinear
terms that are nonconvex, in the transit person delay component
of the objective function, we use the substitution of (29) to
rewrite (18) as follows:
BT
b=1
ob
⎡
⎣wα
b
⎛
⎝(T − 1)C +
kj −1
i=1
yi +
qj
sj
(tb − τj, T −1) − tb
⎞
⎠
+ wγ
b
⎛
⎝TC + R
(1)
j (gi next) − tb
+
qj
sj
⎛
⎝tb − (T − 1)C −
lj −1
i=1
yi
⎞
⎠
⎞
⎠
+
kj −1
i=1
gα
i, b −
qj
sj
lj
i=1
gγ
i, b
⎤
⎦ (33)
and replace constraints (25) and (26) by
gf
i, b ≥ wf
b gi min ∀i, b, ∀f ∈ {α, β, γ} (34)
gf
i, b ≤ wf
b gi max ∀i, b, ∀f ∈ {α, β, γ}. (35)
III. INPUT REQUIREMENTS
The formulation and implementation of the proposed person-
based traffic responsive signal control system is based on the
availability of real-time information about auto and transit
vehicle arrivals and passenger occupancies. The required in-
formation can be provided by surveillance and communication
technologies that are currently deployable in many urban net-
works worldwide.
Traffic demand can be obtained in real time by inductive loop
detectors placed far enough upstream of the intersection so that
the vehicle arrivals are measured under free-flow conditions.
The detectors provide information on average arrival flows per
cycle that can be used to predict vehicle arrivals at the subject
approach. When located at the downstream end of a link,
detectors can also provide information on the turning ratios
of the different movements that are necessary to predict the
demands for the different lane groups.
Transit vehicle arrival times can be predicted using data
from automated vehicle location (AVL) systems, commonly
employed in transit fleets. AVL systems continuously track
the location and speed of transit vehicles in real time. Such
information can be used as input to arrival prediction models,
e.g., in [16], to obtain the arrival time of a transit vehicle at the
intersection.
Real-time information about auto passenger occupancies is
currently not available, and only historical data can provide
estimates of average occupancy per auto. Given that such
estimates vary slightly from day to day for a specific time of
day, an average value should be sufficient. A typical range
of values is 1.2 to 1.5 passengers/vehicle. Transit passenger
occupancies are expected to be more variable, and since the
proposed signal control system depends highly on the number
of people on board to provide priority, real-time information
is highly desirable. Such information can be obtained with the
use of automated passenger counter systems that provide the
number of passengers boarding and alighting at transit stops
and are currently used by many transit agencies.
IV. APPLICATION
The performance of the person-based traffic responsive sig-
nal control system has been tested with data from the real-
world intersection of Mesogion and Katechaki Avenues located
in Athens, Greece. Two types of tests have been performed:
1) deterministic arrival tests and 2) stochastic arrival tests.
Deterministic arrival tests correspond to cases where perfect
information is available for the auto and transit vehicle ar-
rivals and passenger occupancies. Stochastic arrival tests have
been performed through simulation under the assumption of
exponentially distributed auto arrivals. The simulation exper-
iments have been performed with the microscopic simulation
software AIMSUN [17] using EILS. EILS consists of using an
application programming interface that models traffic control,
so that the signal control system is tested in an environment
that emulates its operation in a real-world setting [18]. In a
nutshell, EILS has been used to test the performance of the
proposed signal control optimization in more realistic traffic
conditions, where vehicles do not arrive deterministically and
where errors exist in the prediction of the auto and transit
vehicle arrivals. The formulation of the mathematical program
used for the optimization is still based on the assumption of
perfect information for the input. As a result, stochastic arrival
tests examine how well the system performs when estimates
or predictions are used as input to the optimization in the
case that perfect information is not available. The simulation
has the additional advantage of evaluating the system on the
basis of several performance measures that would be hard to
assess analytically, such as average speed, number of stops, and
emissions.
Both types of tests include evaluation of two different op-
timization scenarios for 1 h of traffic operations: Scenario 1,
when only vehicle delay is minimized (i.e., vehicle-based
optimization where vehicle delays are not weighted by their
respective passenger occupancies), and Scenario 2, when the
total person delay for both transit and auto passengers is mini-
mized (i.e., person-based optimization where vehicle delays are
weighted by their respective passenger occupancies). In addi-
tion, we have tested the performance of optimized fixed-time
signal settings obtained using TRANSYT-7F [19] (Scenario 0).
For each scenario, a warm-up period equal to one cycle length
is used. In addition, each scenario is evaluated ten times to
account for the effect of variations in vehicle arrivals at the
intersection. The resulting average values of the ten replications
are presented. The site used to test the proposed system and
its performance under both types of tests are presented in the
following.

Fig. 2. Layout and bus routes for the intersection of Katechaki and Mesogion Avenues.
A. Test Site
The intersection of Katechaki and Mesogion Avenues is a
busy intersection of two main signalized arterials located in
Athens, Greece. This test intersection has been selected because
of the high traffic volumes on all approaches, its complicated
phasing scheme, and the existence of multiple conflicting bus
routes.
The intersection’s layout is shown in Fig. 2. As the figure
shows, this is a complex intersection with through and turning
traffic in all directions (the main through movement is on
Katechaki Avenue). Fig. 3 shows the lane groups (on the right
labeled 1–8r), phasing, and green and yellow times for the
intersection during the morning peak. The intersection signal
operates on a fixed six-phase cycle. Auto volume data are
available at a rate of once per second from loop detectors placed
40 m upstream of the intersection on each approach. Measured
traffic volumes during the morning peak hour (7:00–8:00 A.M.)
are used as a representative demand. These volumes correspond
to an intersection flow ratio of Y = 0.9.2
For the signal’s
current cycle length of C = 120 s and lost time of L = 14 s,
this indicates nearly saturated traffic conditions.
Nine bus routes travel through the intersection in mixed-use
traffic lanes with headways that vary from 15 to 40 min for each
route. This corresponds to 43 buses in the morning peak hour.
2Intersection flow ratio is defined as the sum of flow ratios (the ratio of
demand to saturation flow) for each critical lane group per signal phase at the
intersection [13].
The numbers next to the directional arrows in Fig. 2 indicate
the different bus routes. The bus routes run in four conflicting
directions with 70% traveling on the northeast–southwest ap-
proaches (Mesogion Avenue) and the rest on the northwest–
southeast approaches (Katechaki Avenue). Their bus stops are
located nearside (i.e., upstream of the intersection). The bus
stop on the southwest approach is not shown in the figure
because of its longer distance from the stop line, which also
diminishes its impact on the traffic operations of the intersec-
tion. However, the impact of all bus stops on the operation of
the intersection is ignored. Information about the bus sched-
ule is available at the Athens Urban Transport Organisation’s
website [20].
B. Deterministic Arrival Tests
The first type of tests have been performed under the as-
sumption that autos arrive deterministically at a constant rate
using data from the test site described earlier. For these tests,
it is assumed that perfect information is available about the
arrival rates of autos and the arrival times of buses at the
intersection. The auto arrival rates are set as the average flow
during the morning peak hour for the intersection of Katechaki
and Mesogion Avenues. In addition, the average auto occu-
pancy ¯oa is assumed to be 1.25 passengers/vehicle. Bus arrival
times at the intersection are simulated based on a shifted
normal distribution around their scheduled arrival times since
no information is available about the real distribution of their
schedule deviation. For the buses, the passenger arrivals at

Fig. 3. Lane groups, phasing, and green and yellow times for the intersection of Katechaki and Mesogion Avenues.
the bus stops are assumed to be deterministic and constant
because headways are short enough that people do not rely on a
published schedule. As a result, the bus occupancy is a function
of the time between the actual arrivals at the intersection of two
consecutive buses of the same route. This means that the buses
are assumed to operate as if they arrive empty at the bus stop
just upstream of the intersection under consideration; therefore,
a larger headway would lead to a higher number of passengers
on board. The passenger occupancy of a bus b when arriving at
the intersection is
ob = pm(tb, m − tb−1, m) (36)
where pm is the passenger demand rate for bus route m, and
tb, m is the actual time that bus b belonging to route m arrives at
the back of its queue at the intersection under consideration.
Despite the fact that the schedule delay of the buses is not
directly considered, it is implicitly taken into account in the
optimization process through the higher passenger occupancy
expected of late buses. For the initial testing of the signal con-
trol system, an average bus occupancy of ¯ob = 40 passengers/
vehicle is assumed.
The user-specified gi next that are used as the phase green
times for the next cycle are set to be the same as the fixed
optimal signal timings provided by TRANSYT-7F for the spe-
cific traffic conditions. In addition, the upper bounds for the
green times of the phases gi max are set equal to C − I
i=1 yi.
Nonzero lower bounds for the phase green times gi min are
also introduced to ensure that all phases are allocated some
minimum green time. A total minimum green time of 7 s is
assigned to each of the left-turn phases and 10 s to each of the
through phases.
The MINLP, which is described in Section II-C, has a
quadratic objective function and linear constraints. As long as
the objective function remains convex, the global optimum can
be easily found using the branch-and-bound method utilized
for solving mixed-integer linear programs. Indeed, the Hessian
matrix of the objective function is positive definite for all
tested scenarios; therefore, the objective function is convex.
The MINLP is solved in MATLAB [21] using the branch-and-
TABLE I
PERSON DELAYS FOR Y = 0.90 AND ¯ob/¯oa = 40/1.25
(DETERMINISTIC ARRIVAL TESTS)
bound method through a recursive function programmed by
the authors. The MATLAB fmincon function is used to solve
each subsequent nonlinear mathematical program. The absolute
optimality tolerance is set to 10−6
, and the computation time
for the optimization of signal timings for one cycle is between
5 and 10 s for the tests performed.3
Table I shows the person delays for autos, buses, and
the total number of users obtained by the three scenarios
tested for an intersection flow ratio of Y = 0.90. A com-
parison of the person-based optimization with the vehicle-
based one indicates that the former can achieve a reduction
of 5% in the total person delay at the intersection by re-
ducing the delay of bus users by 26% and increasing auto
user delay by 2%. This translates into a reduction in average
bus delay of 9 s and an increase in average auto delay of
only 1 s. Comparing the delays obtained from the vehicle-
based optimization with those delays from implementing
the optimized fixed timings obtained from TRANSYT-7F, one
observes that the vehicle-based optimal signal timings result
in lower auto, bus, and overall passenger delays. As a result,
evaluation of the person-based traffic responsive signal control
system is performed by comparing the person delays from the
person-based optimization with those from the vehicle-based
optimization because the latter provides the lowest delays that
can be achieved for autos.
3All tests, both for deterministic and stochastic arrivals, were performed on
an Intel Core i5 2.4-GHz processor with memory of 4 GB.

Fig. 4. Percent change in person delay for different intersection flow ratios
and ¯ob/¯oa = 40/1.25 (deterministic arrival tests).
The performance of the system has been tested for different
intersection flow ratios that vary from 0.4 to 0.9 for average
occupancies of 40 passengers per bus and 1.25 passengers per
auto. The results, which are shown in Fig. 4, indicate consistent
patterns in the person delay changes for all intersection flow
ratios that have been tested. The higher the intersection flow
ratio, the lower the benefit for bus users and for all users
traveling through the intersection, and as a result, the lower
the increase in auto user delay. This is expected due to the
fact that higher intersection flow ratios imply higher auto traffic
demand and, consequently, lower flexibility to change the signal
timings while maintaining undersaturated conditions. For very
high intersection flow ratios, the vehicle-based optimization
and person-based optimization converge to the same optimal
signal timings and the same person delays since the high
auto flow outweighs the higher occupancies of the buses. The
figure also shows the 95% confidence intervals of the percent
changes for person delays of autos, buses, and all travelers at
the intersection. The plotted confidence intervals indicate that
these percent changes are significantly different than zero.
Tests have also been performed for different average bus to
auto passenger occupancy ratios to investigate how changes
in bus ridership affect the provision of priority. The average
auto occupancy is kept constant for all tests and equal to
1.25 passengers/vehicle. Fig. 5 shows the results obtained by
comparing the person delays from the person-based optimiza-
tion with those from the vehicle-based optimization for an
intersection flow ratio of Y = 0.5. The figure indicates that,
for very low average occupancy ratios, the collective benefits
to all passengers diminish along with the benefits to the bus
passengers. The converse is also true; the higher the passenger
occupancy of buses, the higher the savings for their passengers
and the higher the delays for auto users compared with the
person delays from vehicle-based optimization. This outcome
is expected since a higher bus passenger occupancy leads to a
larger weight for the bus delays, and given that the intersec-
tion is undersaturated and there is spare time, more priority
is provided to serve the buses. However, for high average
bus to auto passenger occupancy ratios, the system eventually
converges toward one set of signal timings and the benefit to bus
passengers levels off once the system has reached the maximum
Fig. 5. Percent change in person delay for different average bus to auto
passenger occupancy ratios and Y = 0.5 (deterministic arrival tests).
amount of transit priority that it can provide for the specific
traffic conditions.
Similar patterns as those observed in Fig. 5 are obtained
for all intersection flow ratios tested. However, tests for other
intersection flow ratios have shown that the benefits level off
at different occupancy ratios. The higher the intersection flow
ratio, the lower the spare capacity at the intersection and the
lower the occupancy ratio at which benefits for transit users
level off.
Tests performed for another real-world intersection of San
Pablo and University Avenues in Berkeley, CA, USA, show a
similar behavior. The percent changes for different intersection
flow ratios are different between the two test sites because they
depend on multiple factors such as the intersection’s layout, the
phase sequence, and the frequency of the buses.
C. Stochastic Arrival Tests
Stochastic arrival tests have been performed under the as-
sumption that auto interarrival times follow an exponential
distribution. To predict the auto demand for each cycle using
the same method that would be required in reality, detectors are
located approximately 100 m upstream from the intersection
on each approach. Detectors are also located at the exits of
each of the approaches to measure the exit flow for each lane
group and cycle. To predict the demand of the respective lane
group for the design cycle, exponential smoothing is used on
the measured flows of both sets of detectors during the previous
cycle. The predicted arrival rate ˆqj, T is a weighted average
of the prediction ˆqj, T −1 and the observed value qj, T −1 of the
previous cycle and is given by
ˆqj, T = eqj, T −1 + (1 − e)ˆqj, T −1 (37)
where e is a factor between 0 and 1 that determines how much
weight is placed on the most recent observation. A value of
e = 0.2 has been used in the performed tests. The maximum of
the two smoothed flows from the two sets of detectors is used
as an input for the optimization of the next cycle to account for
cases that signal timings in the previous cycle are not able to
serve all of the incoming demand.

Fig. 6. Percent change in person delay for different intersection flow ratios
and ¯ob/¯oa = 40/1.25 (stochastic arrival tests).
The timetable of the bus arrivals at the entry links of the
network is fixed and based on the same headways as in the
deterministic arrival tests. To predict the arrival time of buses
at the intersection for the traffic signal optimization, detectors
are placed upstream on entry links at distances equivalent to
a travel time of one cycle length from the intersection. The
bus arrivals at the approaches are predicted using an average
nominal speed of 45 km/h. The average passenger occupancy
for the autos is assumed to be 1.25 passengers/vehicle, whereas
each transit vehicle is assigned a random number of passengers
with an average value of 40 passengers/vehicle.
The green times for the next cycle gi next and the upper and
lower bounds gi max and gi min, respectively, are defined as
in the deterministic arrival tests. Ten replications have been
performed for each of the intersection flow ratios tested before
(Y = {0.4, 0.5, . . . , 0.9}), which allow for variation in the auto
and bus arrivals at the intersection. As in the deterministic
arrival tests, the Hessian matrix of the objective function is
positive definite for all tested cases; therefore, the problem can
be solved using the branch-and-bound method, as described
earlier. The computation time for the optimization of signal
timings for one cycle remains between 5 and 10 s, which is
promising for real-time implementations. The optimization is
run once per cycle during the first phase of the cycle. If that
first phase is chosen to be one with a minimum green time that
is greater than the computation time, then the proposed signal
control system can be implemented in real time.
The results from the simulation tests are shown in Fig. 6.
A comparison of the results from the simulation with those
from the deterministic arrival tests indicates that, for the same
intersection flow ratio, the percent benefit achieved in per-
son delay for the whole intersection is on the same order of
magnitude. The same holds for the percent increase of auto
passenger delay. Since no delay at bus stops is considered in
the simulation tests, the differences between the results of the
deterministic and stochastic arrival tests can be attributed only
to the variations in the prediction of auto and bus arrivals, which
are not accounted for in the first type of tests. This results in
a reduction in the benefit that is achieved for bus users and all
travelers at the intersection, compared with the test for the same
traffic demand with perfect information (deterministic arrivals).
For example, for an intersection flow ratio of Y = 0.6, a 31%
reduction in person delay for transit users is observed, but
the reduction assuming perfect information is 46%. Since the
optimization relies on predictions of arrival rates for autos and
arrival times for transit vehicles that contain errors, it cannot
provide the optimal phase duration as it would with perfect
information.
When the intersection flow ratio is Y = 0.9, the person-based
optimization does not reduce the total person delay and the bus
passenger delay for all replications compared with the vehicle-
based optimization. In addition, the person-based optimization
reduces auto passenger delay on average compared with the
vehicle-based optimization. These inconsistencies are caused
by errors in vehicle arrival predictions, which can lead to signal
timings that cause oversaturated traffic conditions for certain
intersection approaches. This results in less accurate predictions
of auto arrival rates and bus arrival times for the subsequent
cycle, which further impede the operation of the signal control
system. Furthermore, the proposed system is used to optimize
one cycle at a time (accounting for the impact on the next cy-
cle), which does not guarantee global optimality for the whole
hour. Since the optimal signal timings may differ between the
two optimization scenarios even for the first cycle, the inputs
for the second cycle are not necessarily the same and may
differ substantially for all subsequent cycles. Therefore, the two
optimization cases are not always equivalent for comparison.
Simulation tests also allow for evaluation of the system
with several additional performance measures that are directly
provided from the simulation software output, such as those
shown in Table II. The results shown in the table for an inter-
section flow ratio of Y = 0.6 indicate that there is a decrease
in the number of stops for buses of 14% and an increase in
the average speed for buses of 8.5% when using person-based
optimization compared with the vehicle-based optimization. At
the same time, the number of stops for autos increases by 2%,
which leads to a slight increase in CO emissions of 0.1%.
However, the signal timings from person-based optimization
lead to a substantial reduction in the CO emitted by buses
of 7%. Overall, the higher the auto traffic demand, the lower
the benefit achieved with the proposed system in terms of
improving bus speeds and reducing stops per bus.
V. CONCLUSION
A person-based traffic responsive signal control system with
TSP has been developed and tested at an isolated intersection.
The optimization method explicitly accounts for the passenger
occupancy of autos and transit vehicles to assign priority in
an efficient way, even when transit vehicles travel in conflict-
ing directions. The proposed traffic responsive signal control
system is generic and offers flexibility to weigh the relative
merit of the passenger and vehicle delays since it allows for
different tradeoffs between auto and transit delays by adjusting
the passenger weights in the objective function.
The results from testing the proposed system on a real-world
intersection show that it can reduce the overall person delay and
transit passenger delay, and it can effectively provide priority to
transit vehicles while increasing the auto passenger delay by

TABLE II
PERFORMANCE MEASURES FOR DIFFERENT INTERSECTION FLOW RATIOS AND ¯ob/¯oa = 40/1.25 (STOCHASTIC ARRIVAL TESTS)
only a small amount. The optimization is shown to be effective
in reducing total person delay at the isolated intersection for
a wide range of auto traffic demands and transit passenger
occupancies. The deterministic arrival tests show that an in-
crease in the auto traffic demand lowers the benefits for both
the total and the transit passengers and reduces the negative
impact on auto users. For very high auto traffic demand, person-
based optimization and vehicle-based optimization converge
to the same outcome. Sensitivity analysis with respect to the
transit passenger occupancy shows that, in general, the higher
the passenger occupancy of a transit vehicle, the higher the
priority provided to it, and the higher the benefit for transit
users. However, there is a limit to the amount of priority that
can be provided to transit vehicles that depends on the traffic
conditions at the intersection and the operating characteristics
of the transit system.
Comparison of the performance of the system through sim-
ulation with the tests performed under the assumption of per-
fect information shows that it improves transit operations and
reduces total passenger delay even without incorporating the
prediction errors in auto demand and transit vehicle arrival
times in the formulation of the mathematical model. Although
the benefit to transit users is lower due to errors in the predic-
tions, the system still achieves significant delay reductions for a
range of auto traffic demands. Accounting for the uncertainty
of arrivals in the delay calculation and developing improved
prediction algorithms for vehicle arrivals can reduce errors in
the system and lead to improved performance.
The proposed person-based traffic responsive signal control
system is particularly beneficial for major signalized intersec-
tions where multiple transit lines with small headways run in
conflicting directions. This is a common phenomenon at transit
transfer locations, such as subway stations, that are served by
many buses. The results are promising for improving transit
reliability of urban networks. Ongoing and future work includes
improving the robustness of the system by accounting for
input inaccuracy in the mathematical program and developing
improved prediction algorithms. In addition, we plan to include
pedestrian delays in the objective function and extend the
system to signalized arterials and grid networks by taking into
consideration that autos will be arriving in platoons, whose size
and arrival times depend on the signal settings of upstream
intersections. Heuristic algorithms will also be developed, if
needed, to ensure computation times that are sufficiently small
for real-world implementations. This is part of a major effort
to develop TSP strategies to improve transit operations and the
person capacity of arterials and grid networks for a wide range
of operating conditions.
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Eleni Christofa was born in Mytilene, Greece, in
1984. She received the Diploma in civil engineering
from the National Technical University of Athens,
Athens, Greece, and the M.Sc. and Ph.D. degrees
in civil and environmental engineering from the
University of California, Berkeley, CA, USA.
She is currently an Assistant Professor with the
Department of Civil and Environmental Engineering,
University of Massachusetts, Amherst, MA, USA.
She is the author and coauthor of multiple tech-
nical papers in scientific journals and conference
proceedings. Her research interests include intelligent transportation systems,
traffic operations and control, public transportation, and incident detection and
management.
Dr. Christofa received the Eugenidi Foundation scholarship for postgraduate
studies (2007–2008), the Gordon F. Newell Memorial Fellowship (2007–2008),
and the Dwight David Eisenhower Transportation Fellowship (2009–2011).
Ioannis Papamichail was born in Toronto, ON,
Canada, in 1976. He received the Dipl.-Eng. (honors)
degree in chemical engineering from the Na-
tional Technical University of Athens, Athens,
Greece, in 1998 and the M.Sc. degree in pro-
cess systems engineering (with distinction) and the
Ph.D. degree in chemical engineering from Imperial
College London, London, U.K., in 1999 and 2002,
respectively.
From 1999 to 2002, he was a Research and Teach-
ing Assistant with the Center for Process Systems
Engineering, Imperial College London. From 2003 to 2004, he served his
military service in Greece as a Chemical Engineer. Since 2009, he has been
an Assistant Professor with the Department of Production Engineering and
Management, Technical University of Crete, Chania, Greece, where he was an
Adjunct Lecturer from 2004 to 2005 and a Lecturer from 2005 to 2009. He is
the author and coauthor of several technical papers in scientific journals and
conference proceedings. His research interests include automatic control and
optimization theory and its applications to traffic and transportation systems.
Dr. Papamichail received the Eugenidi Foundation scholarship for postgrad-
uate studies (1998–1999) and the Transition to Practice Award from the IEEE
Control Systems Society in 2010.
Alexander Skabardonis was born in Athens,
Greece, in 1954. He received the Diploma in civil
engineering from the National Technical University
of Athens, Athens, Greece, and the M.Sc. and Ph.D.
degrees in transportation engineering from the Uni-
versity of Southampton, Southampton, U.K.
He is currently a Professor with the University
of California, Berkeley, CA, USA, and a former
Director with Partners for Advanced Transporta-
tion Technology (PATH), Institute of Transportation
Studies, University of California, Berkeley. He is an
internationally recognized expert in traffic flow theory and models, traffic man-
agement and control systems, design, operation and analysis of transportation
facilities, intelligent transportation systems, energy, and environmental impacts
of transportation. He is the author of over 275 papers and technical reports.
He has worked extensively in the development and application of models and
techniques for traffic control, performance analysis of highway facilities, and
applications of advanced technologies to transportation.
Dr. Skabardonis is a Member of the Traffic Flow Theory, Freeway Op-
erations, Highway Capacity, and Traffic Signal Systems Committees of the
Transportation Research Board. He serves as a member of the editorial board
for the Intelligent Transportation Systems Journal and as a Reviewer for several
archival journals in transportation.

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