# AROW: A V2X-based Automated Right-of-Way Algorithm for Distributed
Cooperative Intersection Management

Ghayoor Shah1, Yaser P. Fallah1, Danyang Tian2, Ehsan Moradi-Pari2 1 Connected
& Autonomous Vehicle Research Lab (CAVREL), University of Central Florida,
Orlando, FL, USA<EMAIL_ADDRESS>Honda Research Institute, Ann Arbor,
MI

###### Abstract

Safe and efficient intersection management is critical for an improved driving
experience. As per several studies, an increasing number of crashes and
fatalities occur every year at intersections. Most crashes are a consequence
of a lack of situational awareness and ambiguity over intersection crossing
priority. In this regard, research in Cooperative Intersection Management
(CIM) is considered highly significant since it can utilize Vehicle-to-
Everything (V2X) communication among Connected and Autonomous Vehicles (CAVs).
CAVs can transceive basic and/or advanced safety information, thereby
improving situational awareness at intersections. Although numerous studies
have been performed on CIM, most of them are reliant on the presence of a
Road-Side Unit (RSU) that can act as a centralized intersection manager and
assign intersection crossing priorities. In the absence of RSU, there are some
distributed CIM methods that only rely on communication among CAVs for
situational awareness, however, none of them are specifically focused towards
Stop Controlled-Intersection (SCI) with the aim of mitigating ambiguity among
CAVs. Thus, we propose an Automated Right-of-Way (AROW) algorithm based on
distributed CIM that is capable of reducing ambiguity and handling any level
of non-compliance by CAVs. The algorithm is validated with extensive
experiments for its functionality and robustness, and it outperforms the
current solutions.

###### Index Terms:

Cooperative Intersection Management, V2X, V2V, Right-of-Way, Stop-Controlled
Intersections, Ambiguity

##  I Introduction

Intersection management is one of the most significant and challenging topics
for safe and efficient driving experience. Intersections can be mainly divided
into two categories, i.e., signalized and unsignalized intersections.
Signalized intersections comprise of traffic lights, whereas the unsignalized
intersections consists of stop or yield signs, or in some instances, no signs
at all. The ever-increasing vehicles on roads can lead to congestion [1],
traffic delays [2], and economic and societal costs due to crashes [3]. In
this context, unsignalized [4] and signalized [5] intersections have been
found to be hazardous and inefficient towards catering large volumes of
traffic. Particularly, in unsignalized intersections, Stop Controlled-
Intersections (SC-I) are a major source of crashes [4].

According to the United States National Motor Vehicle Causation Survey, around
35% of the crashes between 2005 and 2007 occurred on intersections, out of
which, insufficient situational awareness and ambiguity over intersection
priority constituted for 44.1% and 8.4%, respectively [6]. Similarly, it was
reported that in the United States and Europe, around 40% of all traffic
accidents occurred at intersections [7]. Based on the National Highway Traffic
Safety Administration (NHTSA) report [8] conducted in 2015, around 95% of the
total vehicle crashes in the US from 2005 to 2007 were a consequence of human
error, out of which, around 35% occurred due to bad driver decisions. Given
these studies, it is critical to investigate intelligent traffic management
systems.

In this regard, Cooperative Intersection Management (CIM) systems have been a
major source of interest in the research community [9, 10, 11]. CIM systems
are used by Connected and Autonomous Vehicles (CAVs) to improve the overall
driver experience. CAVs employ Vehicle-to-Everything (V2X) communication [12,
13, 14, 15] to enhance their situational awareness and improve safety
standards while making driving decisions. Although there is abundant
literature on CIM for signalized intersections [16, 17, 18], the focus of this
study is on ambiguity mitigation at SC-I which is a subset of unsignalized
intersections.

While numerous studies exist for unsignalized CIM in the space of cooperative
resource reservation [19], trajectory planning [20], and collision avoidance
[21], they are mostly dependent on a centralized Road-Side Unit (RSU) to
function as an intersection manager for passing priorities and information
about nearby CAVs [22, 23], thereby either partially or completely replacing
the functionality of SC-Is. On the other hand, there is sparse literature on
distributed CIM systems where CAVs solely rely on communication with each
other without the presence of any RSU. Although there are some related works
for SC-I in distributed CIM, none of the studies focus explicitly on resolving
ambiguity among CAVs at SC-I.

VanMiddlesworth  _et al._ [24] uses distributed CIM to navigate through SC-I,
however, it is only feasible for a low number of CAVs. Secondly, although the
authors discuss possible CAV non-compliance consideration, however, they do
not provide a mechanism to test it and confirm the robustness of the system.
The most related work is performed by Hassan  _et al._ [25] where they present
a distributed heuristic-based algorithm for cooperative SC-I management that
outperforms the traditional First-in-First-Out (FIFO) approach at SC-I in
terms of average delay, however, the study does not address ambiguity issues
in cases when CAVs arrive at the SC-I at close intervals of each other. Also,
the robustness of the algorithms is not tested under CAV non-compliance by
CAVs.

Therefore, to address this, we propose a distributed CIM algorithm namely
Automated Right-of-Way (AROW) that utilizes an earlier designed and
implemented Driver Messenger System (DMS) [26] based on the relevant source
material [27]. CAVs can employ AROW in SC-I to negotiate SC-I crossing
priorities and avoid any potential for ambiguity. The proposed algorithm is
robust to any non-compliance from CAVs and not only assists in mitigating
ambiguity, but also in promoting fairness when it comes to SC-I crossing, even
for large-scale CAV scenarios.

##  II Driver Messenger System (DMS)

DMS allows CAVs to utilize sensor data and V2X communication to share
application-specific Over-the-Air (OTA) Driver Intention Messages (DIMs)
between Host Vehicle (HV) and Target Remote Vehicles (TVs). DMS is essentially
divided four main components which have been previously explained in detail by
the authors [26]. Relevant details of these components specific to the
application in focus are mentioned in the following.

###  II-A Local Object Map

This is the first module within DMS and it creates and updates a local object
map to localize the HV and the nearby RVs around it. For this paper, the
authors only utilize GPS and V2X communication to create and update the local
object map and localize the CAVs. It is assumed that all participating
vehicles in any scenario are connected and that there are no communication
losses due to congestion or bad resource allocation.

###  II-B Application Detection

This module is tasked with utilizing the updated local object map and deciding
if the HV is currently in one or more of the pre-defined applications within
DMS. Once identified, DMS executes the corresponding application thread for
the next application-specific tasks. In this study, we assume a four-way
allway SC-I where each of the lanes connecting to the SC-I is a singular lane.
However, the logic presented throughout in this study along with the proposed
AROW algorithm can be applied to any kind of SC-I. Figure 1 shows an example
of the SC-I used for this study.

Since only GPS and V2X communication in the form of Basic Safety Messages
(BSMs) are utilized in the creation of the local object map, this study uses a
pre-configured map setting with an SC-I whose location is already known by all
the participating CAVs as ground-truth. Therefore, as CAVs approach the SC-I,
they can utilize the known ground truth location of the SC-I to determine
their distance $(dist)$ from the SC-I and thus, the stop sign. The application
detection block considers a CAV $A$ to be within an SC-I application and
trigger its application block as long as (1) below is satisfied:

$dist_{A}\leq det_{thresh}$ (1)

where $dist_{A}$ is the distance of $A$ from the stop sign in its lane and
$det_{thresh}$ is the SC-I application detecting distance threshold.
$det_{thresh}$ is one of the configurable parameters of SC-I as explained in
later sections.

Another objective for any CAV within the application detection block upon
approaching an SC-I is to detect whether it is the leading CAV in its lane to
reach the stop sign or if it is following another CAV in front of it. As shown
in Figure 1, a CAV $A$ can be described in a typical SC-I scenario as shown in
(2) below:

$A=\begin{dcases*}v_{L}\in V_{L}&if leading, $dist_{A}\leq det_{thresh}$\\\
v_{F}\in V_{F}&if following, $dist_{A}\leq det_{thresh}$\end{dcases*}$ (2)

where $v_{L}$ is the leading CAV in a particular lane while approaching an
SC-I and it satisfies (1) and $V_{L}$ is the current updated set of all
leading CAVs in a SC-I. On the other hand, CAV $v_{F}$ is following another
CAV in front while approaching an SC-I while also satisfying (1) and $V_{F}$
is the set of all following CAVs in an SC-I. Finally, CAV $V_{O}$ may or may
not be the leading CAV however it does not satisfy (1), and thus does not
qualify for SC-I application. As explained in the next section, finding the
state of a CAV and its proximity to an upcoming SC-I as per (2) is significant
to determine its priority in the proposed AROW algorithm, especially in
scenarios where there are queues of CAVs approaching an SC-I.

Figure 1: Bird-eye view of a Stop Controlled-Intersection (SC-I) during
application detection phase.

###  II-C Application Block

Once the application detection block identifies that the HV is approaching an
SC-I (1), DMS triggers the application execution block of SC-I. This block
contains the proposed AROW algorithm whose main goal is to identify fellow
CAVs at the SC-I through the local object map and negotiate SC-I crossing
turns of all CAVs in consideration by a series of DIMs. It should be noted
that all CAVs in this study are assumed to be equipped with DMS and thus the
same AROW algorithm is going to be executed for all CAVs approaching an SC-I.

###  II-D V2X Communication

This block is responsible for transmitting and receiving DIMs to and from the
HV, respectively. DIMs are application-specific and their structure and
content varies for every specific application within DMS. The details of DIM
structure and encoding/decoding procedures are not the focus of this paper and
thus are not included.

##  III Automated Right-of-Way (AROW) Algorithm

AROW algorithm is executed inside the application module of SC-I within DMS
where CAVs can utilize DIMs to assign priorities to cross an SC-I and reduce
ambiguity. The SC-I application module within a HV is executed as soon as it
satisfies (1) and it can be referred to as belonging to either $V_{L}$ or
$V_{F}$ as per (2). On an abstract level, AROW considers the current total
competing vehicles ($V_{T}$) at an SC-I such as that

$n(V_{T})=n(V_{L})+n(V_{F})$ (3)

and it operates by assigning one of the $V_{L}$ as the arbitrator CAV
($V_{arb}$) such that $\mathit{V_{arb}\in V_{L}}$ can assign priorities in the
form of turns to all CAVs within $V_{L}$ to avoid any ambiguity. One of the
main contributions of AROW is that it is equipped to assign distinct crossing
turns such that there is no duplicity and ambiguity. Secondly, it is also
capable of countering situations where some participating CAVs in an SC-I
scenario can turn out to be non-compliant with the rules of AROW and turns
assigned by $V_{arb}$.

AROW comprises of several stages given the involved complexity and the task of
maintaining resolution among multiple independent CAVs. Each stage within AROW
involves transceiving of stage-specific DIMs and/or acknowledgment (ACK)
signals as mentioned in Table I.

TABLE I: AROW DIMs and ACKs AROW1 | SC-I introduction ($S1$)
---|---
AROW2 | $V_{arb}$ announcement ($S2_{2}$)
ACK2 | Acknowledgment of AROW2 ($S2_{3}$)
AROW3 | $V_{arb}$ turn scheduling ($S3_{1}$)
ACK3 | Acknowledgment of AROW3 ($S3_{2}$)
AROW41 | $V_{arb}$ in-turn SC-I exit + assign new $V_{arb}$ ($S4_{1}$)
AROW42 | In-turn SC-I exit ($S4_{2}$)
AROW5 | Out-of-turn SC-I exit ($S2_{2}$,$S2_{3}$,$S3_{1}$,$S3_{2}$)
AROWwait | Request CAVs in $V_{S}$ to wait for current AROW

###  III-A Stage $0$ $(S0)$ \- Not in SC-I

This is the idle stage of AROW and the HV stays in this stage as long as it
does not satisfy (1).

###  III-B Stage $1$ $(S1$) - SC-I Discovery

This is the first step in the execution of AROW where the HV satisfies (1) and
broadcasts a discovery DIM known as AROW1. On a high-level, in addition to
HV’s basic safety and identification data, the contents of this DIM can be
considered to highlight the detection of SC-I by the HV and the initiation of
AROW algorithm within its DMS. Also, this DIM includes information pertaining
to whether currently $\text{HV}\in V_{L}||\text{ HV}\in V_{F}$. Just like the
HV, any CAV starting its AROW process can be assumed to broadcast a similar
AROW1 DIM. After broadcasting AROW1, the HV waits for a pre-configured
timeout/clock-constraint $T1$ to receive any DIMs from other CAVs in $V_{T}$.
The two types of receiving DIMs under focus in this stage are AROW1s from CAVs
that have also just initiated AROW algorithm or AROWwait from $V_{arb}$.

Towards the end of constraint $T1$, if the HV does not receive any DIM, then
it can be considered that there are no fellow CAVs at the SC-I besides the HV
itself. This triggers DMS to effectively terminate AROW and the HV is
instructed by its DMS to cross the SC-I without AROW and switch to $S0$. On
the other hand, if HV receives AROW1(s) from other CAVs but no AROWwait, then
this signifies that there is no $V_{arb}$ present at SC-I but there are fellow
competing CAVs that arrived at the SC-I at similar times as that of the HV,
and that the AROW process should proceed into next stage, i.e. $S2_{1}$.
Finally, if the HV receives AROWwait from $V_{arb}$, this signals that there
is a current AROW process going on where $V_{arb}$ is arbitrating and
negotiating SC-I crossing turns among a group of CAVs ($V_{P}$) that arrived
at the SC-I at least $T1$ time before the HV. AROWwait is sent by $V_{arb}$ to
any CAV $A$ broadcasting AROW1 to signal it to wait for the current AROW
process to end before $A$ can participate for its own turn assignment. As
detailed in the next sub-section, as soon as $V_{arb}$ is assigned in $S2_{1}$
and until all its tasks in AROW are accomplished, $V_{arb}$ maintains two
updating sets in which it divides the CAVs from $V_{T}$ such that:

  * •

$V_{P}$: Set containing primary CAVs that are part of the current AROW
procedure. These are always the leading CAVs.

  * •

$V_{S}$: Set containing secondary CAVs that are instructed to wait for the
current AROW procedure to finish before they can be considered for
arbitration. These can either be following CAVs or leading CAVs that arrive
during an ongoing AROW.

At any time within AROW, arbitration is always performed among CAVs that are
present in $V_{P}$. Therefore, if HV receives AROWwait from $V_{arb}$, then
this indicates that HV needs to move to $SW$ and wait for the current
arbitration to end. In this case, HV is also added to $V_{S}$ as it is not one
of the CAVs considered for the current round of arbitration.

###  III-C Stage $2_{1}$ $(S2_{1})$ \- $V_{arb}$ Selection

In the case that HV receives at least one AROW1 from a fellow CAV but no
AROWwait from $V_{arb}$, AROW enters $S2_{1}$ in which a single CAV from
$V_{L}$ is chosen as $V_{arb}$ for the remainder of the AROW process until
$V_{arb}$ crosses the SC-I on its assigned turn. Based on a fixed heuristic
$H_{1}$ within DMS of every CAV in set $V_{L}$, one of the CAVs is chosen as
$V_{arb}$. To ensure that all participating CAVs in $V_{L}$ choose the same
$V_{arb}$ and there is no duplication, there is a single heuristic stored
within DMS of all CAVs. For this study, the heuristic $H_{1}$ is as follows:

  * •

$H_{1}$: The last arriving CAV denoted from the timestamp at which it entered
SC-I application by satisfying (1) and initiated its AROW, is chosen as
$V_{arb}$. If two or more CAVs arrive at the same timestamp, then their unique
CAV identification numbers can be utilized as tie breaker and the CAV with an
alphanumeric character containing the lowest ASCII value at the first index
with differing characters by process of elimination can be chosen as
$V_{arb}$.

Following this same $H_{1}$, it can be guaranteed that all CAVs in $V_{L}$
will choose the same CAV as $V_{arb}$.

Particular attention needs to be given to the fact that during this process of
$V_{arb}$ selection, only CAVs that are considered are the ones that were a
part of $V_{L}$ up until the end of clock $T1$. In other words, any new CAVs
that entered the SC-I application after the current AROW process considering
CAVs in $V_{L}$ has already moved on from $S_{1}$ would not be considered in
the current arbitration selection process even if it is now a part of $V_{L}$,
since priority is given to CAVs that arrived at similar times in $S_{1}$ and
have already passed to the next stage.

Whoever is chosen as the $V_{arb}$ in this stage as per $H_{1}$, the first
task that it needs to perform is to divide up CAVs in $V_{T}$ into $V_{P}$ and
$V_{S}$, as mentioned in the previous sub-section. All the CAVs as part of the
current arbitrator process in $S2_{1}$ are included in $V_{P}$ whereas all the
CAVs in $V_{F}$ are added to $V_{S}$. Also, if any CAV enters SC-I and its
$S_{1}$ as a $v_{L}$ or $v_{F}$ while the current AROW process is going on in
any stage after $S_{1}$, it would be directly entered in set $V_{S}$ by
$V_{arb}$. At every timestamp throughout AROW, whenever any CAV enters or
leaves SC-I, $V_{arb}$ always updates both $V_{P}$ and $V_{S}$.

Finally, during $S2_{1}$, if the HV is chosen to be the $V_{arb}$ as per
$H_{1}$, then it goes into $S2_{2}$ and all the other CAVs in $V_{P}$ proceed
to their $S2_{3}$. On the other hand, if HV is not chosen to be the $V_{arb}$,
then it proceeds to its $S2_{3}$ along with other CAVs in $V_{P}$ that are
also not chosen as $V_{arb}$ whereas the CAV chosen as $V_{arb}$ goes into
$S2_{2}$.

Figure 2: Example scenario during HV’s $V_{arb}$ announcement in stage
$S2_{2}$. HV had previously broadcasted its AROW2 DIM and the other competing
CAVs in $V_{P}$ are now sending their ACK2 signals.

###  III-D Stage $2_{2}$ $(S2_{2})$ \- $V_{arb}$ Announcement

In $S2_{2}$, the HV broadcasts AROW2 DIM in which it informs all the CAVs in
$V_{P}$ that it has been chosen as $V_{arb}$. After broadcasting AROW2, the HV
waits for constraint $T2$ to receive acknowledgment signal ACK2 from CAVs in
$V_{P}$ as an acceptance of HV as $V_{arb}$. Figure 2 shows an example of AROW
in $S2_{2}$ with HV as $V_{arb}$. After the completion of $T2$, if HV receives
ACK2 from all $V_{P}$, then HV moves to $S3_{1}$, whereas the non-arbitrator
CAVs in $V_{P}$ move to $S3_{2}$. Alternatively, if there is non-compliance
where one or more CAVs other than HV in $V_{P}$ leave the SC-I prematurely,
the other compliant CAVs in $V_{P}$ along with any new CAVs in $V_{L}$ that
are not yet part of $V_{P}$ can re-start AROW by going back to $S1$. The
number of times the compliant CAVs can consecutively repeat a particular round
of AROW in face of non-compliance is determined by the pre-configured
$AROW_{thresh}$, as shown in the equation below:

$AROW_{count}\leq AROW_{thresh}$ (4)

where $AROW_{count}$ is the counter to keep track of the consecutive
repitions. As soon as (4) is not satisfied, DMS within all compliant CAVs in
$V_{P}$ switches to $S0$ and the CAVs can cross the SC-I manually without the
assistance of AROW.

###  III-E Stage $2_{3}$ $(S2_{3})$ \- $V_{arb}$ Acceptance

In $S2_{3}$, since the HV is not chosen as $V_{arb}$, it waits for $T2$ to
receive AROW2 DIM from $V_{arb}$, and upon reception, it needs to send an
ACK2. Towards the end of $T2$, if all CAVs in $V_{P}$ along with HV are
compliant, then AROW moves HV into $S3_{2}$ along with other CAVs in $V_{P}$
that are not $V_{arb}$. At the same time, AROW within $V_{arb}$ moves it from
$S2_{2}$ into $S3_{1}$ as explained in the previous subsection. However, if
there is any non-compliance by a CAV in $V_{P}$ or $V_{arb}$ itself, then the
AROW within HV and other compliant CAVs in $V_{P}$ requires to break the
current AROW process and move to either $S1$ or $S0$ depending on (4), as
explained in the previous subsection.

Figure 3: Non-compliance scenario in AROW with HV as $V_{arb}$. One of the
CAVs in $V_{P}$ has become non-compliant and prematurely exited the SC-I upon
which the DMS within it has broadcasted the AROW5 DIM.

###  III-F Non-Compliance

Non-compliance is a condition within AROW that can occur when a CAV is in any
of four stages defined as $NC_{stages}=\\{S2_{2},S2_{3},S3_{1},S3_{2}\\}$. A
CAV in $V_{P}$ is said to be non-compliant whenever it crosses an SC-I prior
to its assigned turn. Whenever it does, the out-of-turn CAV broadcasts an
AROW5 exit DIM. This DIM is used by $V_{arb}$ and other CAVs in $V_{P}$ to
identify a non-compliant CAV. Figure 3 shows an example of non-compliance
where one of the CAVs in $V_{P}$ decides to leave during $S2_{2}$ where turns
have not even been assigned yet. As soon as AROW within that CAV detects the
untimely exit, it broadcasts AROW5. Usually, DMS would utilize a camera to
identify if it has already passed the SC-I to broadcast AROW5, however, since
we only utilize V2X as the data source for this study, the ground truth data
of the SC-I is utilized for the purpose of identifying an exit from an SC-I
and broadcasting AROW5 DIM. In this study, non-compliance can occur to any CAV
in $V_{P}$ during AROW including $V_{arb}$. The only exception to this is the
HV itself. In other words, we always assume that the HV is always fully
compliant. To evaluate the impact of non-compliance, it is probabilistically
applied ($NC_{prob}$) to each CAV independently when it is in each of the four
stages in $NC_{stages}$.

###  III-G Stage $3_{1}$ $(S3_{1})$ \- Turn Scheduling

HV can arrive in $S3_{1}$ from either the parent stage $S2_{2}$ or $SW$. The
details of switching from the former parent stage are explained later under
the subsection of $SW$. In the case of parent stage $S2_{2}$, if the HV
receives ACK2 signal from all CAVs in $V_{P}$ after its selection as
$V_{arb}$, HV moves into $S3_{1}$ while the other CAVs in $V_{P}$ move to
$S3_{2}$. This is the stage where the HV as $V_{arb}$ assigns turns to all
CAVs in $V_{P}$ to cross the SC-I based on a fixed pre-configured heuristic
$H_{2}$. The main goal behind choosing any heuristic is to ensure that
different turns are assigned to each CAV and that there is no duplication. The
heuristic $H_{2}$ used for this study is defined as follows:

  * •

$H_{2}$: $V_{arb}$ assigns turns based on the arrival timestamp of every CAV
in $V_{P}$ and prioritizes CAVs that arrived earlier at the SC-I. In the
situation where more than one CAV carries identical arrival timestamp,
$V_{arb}$ can randomly assign turns among them.

The turn assignment information is enclosed within AROW DIM and broadcasted.
Once received, the CAVs in $V_{P}$ are required to reply with an ACK3
acknowledgment to confirm the corresponding turn assignment. After
broadcasting AROW3, HV waits for constraint $T3$. Towards the end of $T3$, if
the HV receives ACK3 signals from all relevant CAVs, then it moves towards
$S4_{1}$. On the other hand, if there is non-compliance by any CAV, then
depending on (4), HV either moves to $S1$ to restart AROW or to $S0$ where it
disables AROW to manually pass the SC-I.

###  III-H Stage $3_{2}$ $(S3_{2})$ \- Turn Acceptance

After passing $S2_{3}$, HV moves into $S3_{2}$ where, similar to that in
$S2_{3}$, it waits for $V_{arb}$ to send a AROW3 DIM that contains the turn
assignment for the HV among other CAVs in $V_{P}$. Upon receiving AROW3, HV
sends an ACK3 signal to acknowledge the reception. Once $T3$ is elapsed and
there is no non-compliance, the HV moves into $S4_{2}$. However, just like in
$S2_{3}$, if any CAV in $V_{P}$ or $V_{arb}$ becomes non-compliant, then HV
moves into $S1$ or $S0$ depending on (4).

###  III-I Stage $4_{1}$ $(S4_{1})$ \- Exit SC-I + Assign New $V_{arb}$

$S4_{1}$ is the ultimate stage for HV as $V_{arb}$ in AROW. By the time the HV
arrives in this stage and the other CAVs in $V_{P}$ arrive in the
corresponding $S4_{2}$, the turns have already been assigned to all involved
CAVs along with the HV. HV stays in this stage until the arrival of its turn
to cross the SC-I. Upon exiting the SC-I, the HV needs to perform one last
task in its role as $V_{arb}$ i.e. to choose a new $V_{arb}$ as per a pre-
defined heuristic $H_{3}$. For simplicity, this study uses $H_{1}$ as the
heuristic for choosing new $V_{arb}$, i.e. ($\mathit{H_{3}=H_{1}}$). If there
are any CAVs in $V_{S}$ waiting at the SC-I for the current AROW procedure
involving HV and $V_{P}$ to terminate, then HV as $V_{arb}$ needs to select
one of CAVs in $V_{S}$ to become the new $V_{arb}$. After selecting new
$V_{arb}$, HV crosses the SC-I, and broadcasts AROW41 DIM indicating to all
other CAVs in $V_{T}$ that it is exiting SC-I along with the information
pertaining to new $V_{arb}$. Finally, AROW within HV moves to $S0$ as the idle
stage.

###  III-J Stage $4_{2}$ $(S4_{2})$ \- Exit SC-I

Similar to $S4_{1}$, HV waits for its turn to pass the SC-I. Once it does, it
broadcasts a final AROW42 DIM, indicating to CAVs in $V_{T}$ that it is
leaving the SC-I, and then its AROW moves to $S0$.

###  III-K Stage Wait $(SW)$ \- Wait for current AROW completion

If HV arrives at SC-I by satisfying (1) with an ongoing AROW arbitration
round, then the $V_{arb}$ instructs HV via AROWwait to wait in $SW$ as one of
$V_{S}$. If the current AROW concludes successfully without any non-
compliance, then depending on the set $V_{S}$, the HV can either move to $S0$,
$S3_{1}$, or $S3_{2}$. If HV is the only CAV in $V_{S}$, then AROW is not
required and HV can manually pass the SC-I, thus HV moves to $S0$. In the case
of presence of other CAVs in $V_{S}$, HV can move to $S3_{1}$ if $V_{arb}$ of
the concluding AROW has chosen HV to be the new $V_{arb}$ via AROW41 DIM,
otherwise, it transitions to $S3_{2}$. The process of assigning new $V_{arb}$
assists in optimizing AROW since it avoids the need for CAVs to utilize AROW
from the beginning stage of $S1$. Finally, if there is non-compliance among
competing CAVs in $V_{P}$ while HV is in $SW$ and (4) is not satisfied which
means that all CAVs in $V_{P}$ collectively eliminate AROW and manually pass
SC-I, then HV along with others CAVs in $V_{S}$ move to $S1$ to initiate AROW
from the beginning.

Figure 4: AROW algorithm expressed as a timed automaton

##  IV AROW Implementation as a Timed Automaton

This section provides details into the earlier-introduced stages within AROW
and shows their functionality as distinguishable states. AROW can be modeled
as a timed automaton [28], [29] that allows it to be within a particular state
at any specific time due to timing constraints. Figure 4 represents AROW as a
timed automaton. The automaton consists of nodes called locations and edges
known as switches. Formally, the automaton can be described as a tuple
$\mathcal{M}=\langle S,S^{0},A,X,I,E\rangle$ where

  * •

$S$ is a finite set of all locations within $\mathcal{M}$ and it can be
defined as

$S=\\{SW,S0,S1,S2_{1},S2_{2},S2_{3},S3_{1},S3_{2},S4_{1},S4_{2}\\}$ (5)

Each location in $S$ defines a particular AROW stage which has been explained
in detail in the previous section. Figure 4 provides a description highlight
for each location.

  * •

$S^{0}\subseteq S$ is a set of initial locations. For AROW system,

$S^{0}=\\{S0\\}$ (6)

This is also the location where AROW is typically deactivated which means that
whenever HV is in this location, it is not approaching a nearby SC-I.

  * •

$A$ is a finite set of input symbols,

$A=\\{a_{i}\mid i\in\mathbb{N},0\leq i\leq 24\\}$ (7)

This signifies that the total number of symbols in AROW are equal to 24.

  * •

$X$ is a finite set of clocks. The transition system for AROW only utilizes a
singular clock $T$,

$X=\\{T\\}$ (8)

  * •

$I$ is a mapping that assigns locations within $\mathcal{M}$ with clock
constraints in set $\mathit{\Phi(X)}$. Given that (8) contains only a singular
clock, all the constraints in $\mathit{\Phi(X)}$ are defined for $T$,

$\displaystyle\mathit{\Phi(X)}=\\{\,T1,T1+T2,T1+T2+T3,$ (9) $\displaystyle
T1+T2+T3+T\textsubscript{turn},T\textsubscript{wait}\\}$

These constraints are included in specific locations within the description
blocks as observable in Figure 4. $I$ maps these constraints from
$\mathit{\Phi(X)}$ for clock $T$ on select locations within $\mathcal{M}$ as
mentioned below:

    * –

$S1:T<T1$

    * –

$S2\textsubscript{2},S2\textsubscript{3}:T<T1+T2$

    * –

$S3\textsubscript{1},S3\textsubscript{2}:T<T1+T2+T3$

    * –

$S4\textsubscript{1},S4\textsubscript{2}:T<T1+T2+T3+T\textsubscript{turn}$

    * –

$SW:T<T\textsubscript{wait}$

All locations within $\mathcal{M}$ not mentioned in the mapping above can be
considered as not possessing any clock constraint.

  * •

$\mathit{E\subseteq S\textsc{ x }A\textsc{ x }2^{X}\textsc{ x }\Phi(X)\textsc{
x }S}$ is a set of switches between locations within $\mathcal{M}$. A switch
$\langle s,a,\varphi,\lambda,s^{\prime}\rangle$ represents a transition edge
from location $s$ to $s^{\prime}$ over a symbol $a$. A switch can also
comprise of a timing constraint $\varphi$ over $X$ that specifies when the
transition switch can be used. Also, a switch can also contain the set
$\lambda\subseteq X$ that allows clocks to be reset to a particular value with
this switch.

It should be noted that none of the switches in $E$ have clock constraint
$\varphi$ over $X$. In other words, none of the switches in AROW system
require fulfillment of clock constraint to be executed for a location switch
to occur. However, there exist some switches within $\mathcal{M}$ in which the
clock $T$ is reset. Since $X$ only contains a single clock $T$ throughout
$\mathcal{M}$, therefore $\lambda$ also only comprises of $X$, i.e.

$\lambda=\\{T\\}$ (10)

All such instances are mentioned below where $e\textsubscript{i}\subseteq E$
switches contain a clock $T$ reset:

    * –

$e\textsubscript{1},e\textsubscript{7},e\textsubscript{10},e\textsubscript{13},e\textsubscript{16},e\textsubscript{22}:T=0$

    * –

$e\textsubscript{21},e\textsubscript{23}:T=T1+T2$

Every $i$ in $e_{i}$ mentioned above corresponds to the switch containing an
input symbol $a_{i}\in A$ as in (7).

TABLE II: SUMO simulation parameters Experiment Duration | 50000s
---|---
No. of CAVs ($n_{veh}$) | 4, 8, 16
Car-Following Model | Krauss [30]
Maximum Vehicle Speed | 70 m/s
Vehicle Acceleration | 2.6m/s2
Vehicle Deceleration | 4.5m/s2
Sigma (Driver Imperfection) | 0.5
minGap (Empty space after leader) | 2.5m
CAV length | 5m
Road Topology | Circled Plus
No. of lanes/road segment | 1

$N$ is the transition system of $\mathcal{M}$. State of $N$ can be described
as a pair $(s,v)$ where $s\in S$ denotes the current location and $v$
represents the clock interpretation for $X$ as in (8) such that $v$ satisfies
the constraint of the clock mapped to $s$ by $I(s)$. A transition $N_{p}\in N$
can be described in two ways:

  * •

In the case of self-transition where a transition state returns to itself due
to clock constraint,

$N_{p}:(s_{i},v)\xrightarrow[]{\delta}(s_{i},v+\delta),$ (11)

where the clock increment $\delta$ is such that $v+\delta$ satisfies the clock
constraint set by $I(s_{i})$ mapping. Also, the source and destination
location is $s_{i}$ signifying the self-transition.

  * •

In the case of transition switch from one location $s_{i}$ to another $s_{j}$
based on $e\in E$,

$N_{p}:(s_{i},v)\xrightarrow[]{a}(s_{j},v[\lambda:=y]),$ (12)

where $v$ satisfies $\varphi$, and $a$ is part of the the transition edge $e$.
Also, $s_{i}$ and $s_{j}$ are the source and destination locations,
respectively. $y$ represents the reset of the clock upon reaching the
destination location.

As afore-mentioned, there are multiple reset values set up for the clock $T$
in different locations along with some locations that do not contain any
particular reset. Thus, for simplicity, $v[\lambda:=y]$ will just referred to
as $v^{\prime}$ for this study and the clock constraints for each transition
will not be explicitly mentioned as they can be clearly observed in Figure 4.
This transition system will be repeatedly utilized for analysis in the next
sections. The focus will be on transitions caused by location switches and
will generally be mentioned as
$N_{t}:(s_{i},v)\xrightarrow[]{a_{t}}(s_{j},v^{\prime})$, where $a_{t}$ refers
to symbols in $\mathcal{M}$ as shown in Figure 4 and satisfy (7).

##  V Experimental Results

###  V-A Simulation and AROW Configuration Parameters

To test AROW and provide experimental details regarding its functionality, the
transition system $\mathcal{M}$ defined in the last section is modeled and
tested using the Simulation of Urban Mobility (SUMO) traffic simulator [31].
The simulation parameters specific to SUMO are mentioned in Table II. These
parameters can be configured as per user preference. The road topology used
for this study considers a four-way allway SC-I attached to four single-lane
road segments. Each end of the four road segments from SC-I is about 51.2m in
length and connected to a circular round-about to facilitate CAVs to drive in
an endless loop and repeatedly pass through the SC-I in the center for the
entirety of the simulation. In order for the AROW algorithm to interact in
real-time with SUMO simulation, the authors utilize Traffic Control Interface
(TraCI) [32]. To test a variety of use-cases, the study utilizes different
number of CAVs, i.e. $n_{veh}$ = 4, 8, or 16. Given the road topology, these
values of $n_{veh}$ can be considered as low, medium, and high density
traffic, respectively.

Table III shows the values assigned to the configurable parameters of AROW for
this study. The $det_{thresh}$ is chosen to be 10m with aim to: (i) allow the
CAVs to initiate the process of AROW in advance so that generally the CAV is
assigned its turn to leave SC-I by the time it arrives at the stop sign,
provided there is no non-compliance, and (ii) to allow up to two CAVs per lane
to be included in the AROW process given the CAV length mentioned in Table II.

TABLE III: AROW configurable parameters $det_{thresh}$ | 10m
---|---
BSM Periodicity | {100,600}ms [33]
Resource Reservation Interval | 100ms[34]
$T1$ | 2s
$T2$ | 2s
$T3$ | 2s
Non-Compliance Probability | 0, 0.1, 0.25
$AROW_{thresh}$ | 2

On the other hand, $AROW_{thresh}=2$ to provide compliant CAVs with at most
two consecutive chances to use AROW to eliminate ambiguity in the face of non-
compliance. $AROW_{thresh}$ should not be set to a really high value since it
can then unfairly penalize compliant CAVs for following AROW rules since they
will end up spending more time waiting to pass the SC-I.

As explained earlier, $T1$ is the timeout clock used by a CAV during discovery
stage $S1$ of AROW. $T1$ for this study is set to 2s to allow realistic chance
for one or more CAVs to initiate AROW and these CAVs can then enter in an
arbitration as mentioned in the AROW logic explained in the previous sections.
$T2$ is the timeout clock used to control how long a CAV stays in
$S2\textsubscript{2}$ or $S2\textsubscript{3}$ while undergoing AROW process.
The experimental value of $T2$ is chosen to be 2s for CAVs in $S2_{2}$ and
$S2_{3}$. The realistic duration for $T2$ can be further reduced and optimized
based on the inherent communication latencies of the V2X technology in use.
This optimization is the subject of a future study related to this topic. The
same logic is applied to choosing the duration for $T3$.

TABLE IV: Raw state frequencies from simulations in Figure 5 with full compliance ($NC_{prob}=0$) $n_{veh}$ | $SW$ | $S0$ | $S1$ | $S2_{1}$ | $S2_{2}$ | $S2_{3}$ | $S3_{1}$ | $S3_{2}$ | $S4_{1}$ | $S4_{2}$ | Total
---|---|---|---|---|---|---|---|---|---|---|---
4 | 814 | 1577 | 1577 | 256 | 130 | 126 | 211 | 201 | 211 | 201 | 5304
15.35 | 29.73 | 29.73 | 4.83 | 2.45 | 2.38 | 3.98 | 3.79 | 3.98 | 3.79 | 100%
8 | 1146 | 1159 | 1159 | 12 | 4 | 8 | 400 | 675 | 400 | 675 | 5638
20.33 | 20.56 | 20.56 | 0.21 | 0.07 | 0.14 | 7.09 | 11.97 | 7.09 | 11.97 | 100%
16 | 587 | 588 | 588 | 1 | 0 | 1 | 167 | 421 | 167 | 421 | 2941
19.96 | 19.99 | 19.99 | 0.03 | 0 | 0.03 | 5.68 | 14.31 | 5.68 | 14.31 | 100%

###  V-B Analysis and Results

####  V-B1 AROW Performance under Full Compliance ($NC_{prob}=0$)

The first goal using simulations is to prove the completeness of the logic of
AROW. To achieve this, the simulations using AROW with parameters mentioned in
Tables II and III are run and each state’s frequency and transitions are
independently logged throughout the simulation duration. It should be noted
that the terms ‘state frequency’ and ‘state transitions’ are used instead of
‘location frequency’ and ‘location transition’ to specify that these values
have been collected over time in a simulation whenever the clock constraints
for each transition are fulfilled as mentioned earlier in the description of
the timed automaton $\mathcal{M}$ of AROW. For this set of simulations, all
the participating CAVs are set to be fully compliant, i.e.
$\mathit{NC_{prob}}$ = 0. The results of these simulations are shown in Figure
5 and Table IV. Figure 5 shows the state transitions matrices represented as
heat maps and based on the transition system $N$ of AROW. The x-axis and
y-axis denote the destination and source locations, respectively. In addition
to Figure 5, Table IV provides the state frequency in terms of raw numbers and
percentages for each location.

Figure 5: State transition comparison for simulations with full compliance
($NC_{prob}$ = 0)

For each of the three simulations, Table IV shows state frequency of each
location and the transition matrix provides the outgoing and incoming
transition switches from that location, respectively. For example, for
$\mathit{n_{veh}=}$ 4, $S3_{1}$ has a percentage frequency of 3.98% and the
transition matrix clarifies this frequency by showing that $S3_{1}$ has two
incoming transition switches
$N_{21}:(SW,v)\xrightarrow[]{a_{21}}(S3_{1},v^{\prime})$, and
$N_{9}:(S2_{2},v)\xrightarrow[]{a_{9}}(S3_{1},v^{\prime})$ with frequencies of
1.53% and 2.45%, respectively, that add up to 3.98%, equal to state frequency
of $S3_{1}$ as shown in Table IV. Additionally, the transition matrix also
shows one outgoing transition switch from $S3_{1}$, i.e.
$N_{15}:(S3_{1},v)\xrightarrow[]{a_{15}}(S4_{1},v^{\prime})$ worth 3.98% which
is again equal to the incoming transitions to $S3_{1}$ and also its percentage
frequency. The equality between incoming and outgoing transition switches can
be observed for all locations in all traffic scenarios, except for minuscule
differences due to rounding in percentages. All the transitions in the
matrices can also be observed to be in line with those in the timed automaton
$\mathcal{M}$ and use switches $E$ corresponding to input symbols $A$ in
Figure 4, thereby ensuring that the experimental operation is corresponding to
the AROW theory. Finally, all transitions within each matrix along with the
state frequency percentages in Table IV add up to 100%, barring rounding
errors.

Comparing the three simulations, it can be first observed that as the value of
$n_{veh}$ increases from 4 to 8, the total raw frequency increases by a small
margin as shown in Table IV. This is mainly due to the fact that this higher
number of CAVs in the scenario increases the frequency of HV’s transition to
$SW$ upon its arrival at the SC-I in focus. Furthermore, as $n_{veh}$
increases to 16, there is a sharp reduction in the total raw frequency which
is caused by a reduction in the count of $S_{0}$ and $S_{1}$. This is mainly
because as $n_{veh}$ increases, there is a higher congestion at the SC-I in
focus. Thus, the HV spends more time to get through SC-I and hence, fewer
transitions switches of $N_{1}:(S0,v)\xrightarrow[]{a_{1}}(S1,v^{\prime})$
from $S0$ to $S1$ in the given simulation duration. The percentage equality of
$S0$ and $S1$ in every simulation also attests to the 100% $N_{1}$ transition
from $S0$ to $S1$ as shown in the graph $\mathcal{M}$ in Figure 4.

From $S1$, the transition $N_{2}:(S1,v)\xrightarrow[]{a_{2}}(S0,v^{\prime})$
to $S0$ occurs when the HV is unaccompanied by any fellow competing CAV at the
SC-I, and in this case, the HV passes SC-I without AROW. As expected, the
matrix for $n_{veh}=4$ shows $N_{1}$ transition frequency of 9.56%, which goes
to almost 0% in the case of $n_{veh}=8,16$ since with more CAVs, there is a
lesser probability of HV approaching the SC-I in focus without any
competition. On the other hand, the transition
$N_{3}:(S1,v)\xrightarrow[]{a_{3}}(SW,v^{\prime})$ to $SW$ occurs when HV
initiates AROW in the middle of an ongoing AROW round among CAVs in $V_{P}$.
In this case, $V_{arb}$ instructs HV to wait in $SW$. It can be seen in both
the percentage state frequency and matrices that the frequency of $N_{3}$ is
higher for $n_{veh}=8,16$ because as $n_{veh}$ increases, there is a higher
probability that HV would arrive at SC-I in focus and initiate in the presence
of other CAVs.

One more transition possibility from $S1$ is
$N_{4}:(S1,v)\xrightarrow[]{a_{4}}(S2_{1},v^{\prime})$ to $S2_{1}$. $N_{4}$
occurs when HV is accompanied by other competing CAVs in $V_{L}$ in SC-I and
there is no $V_{arb}$ present. In this case, the CAVs along with HV need to
follow AROW and elect a $V_{arb}$. Again, as $n_{veh}$ increases, there is a
higher probability of a $V_{arb}$ already present upon the arrival of HV, thus
the frequency of $N_{4}$ reduces. This is why $N_{4}$ frequency for
$n_{veh}=4$ is 4.83% whereas it drops to just 0.21% and 0.03% for $n_{veh}=8$
and $n_{veh}=16$, respectively. From $S2_{1}$, the only transitions are
$N_{5}:(S2_{1},v)\xrightarrow[]{a_{5}}(S2_{2},v^{\prime})$ and
$N_{6}:(S2_{1},v)\xrightarrow[]{a_{6}}(S2_{3},v^{\prime})$ to $S2_{2}$ and
$S2_{3}$, respectively. These transitions can be seen in the transition
matrices and for the same afore-mentioned reason of a higher frequency of
$N_{4}$ for $n_{veh}=4$, we can also observe a higher frequency of $N_{5}$ and
$N_{6}$ for $n_{veh}=4$ that sum to the total state frequency of $N_{4}$.
Similarly, the transitions from $S2_{2}$ and $S2_{3}$ are
$N_{9}:(S2_{2},v)\xrightarrow[]{a_{9}}(S3_{1},v^{\prime})$, and
$N_{12}:(S2_{3},v)\xrightarrow[]{a_{12}}(S3_{2},v^{\prime})$ to $S3_{1}$ and
$S3_{2}$, respectively, and carry a higher frequency in the case of
$n_{veh}=4$ as compared to other scenarios. It should be noted that since
$NC_{prob}=0$ in this set of three simulations, the transitions
$N_{8}:(S2_{2},v)\xrightarrow[]{a_{8}}(S0,v^{\prime})$,
$N_{7}:(S2_{2},v)\xrightarrow[]{a_{7}}(S1,v^{\prime})$,
$N_{11}:(S2_{3},v)\xrightarrow[]{a_{11}}(S0,v^{\prime})$,
$N_{10}:(S2_{3},v)\xrightarrow[]{a_{10}}(S1,v^{\prime})$ are all 0%.

For $SW$, the transitions are
$N_{24}:(SW,v)\xrightarrow[]{a_{24}}(S0,v^{\prime})$,
$N_{22}:(SW,v)\xrightarrow[]{a_{22}}(S1,v^{\prime})$,
$N_{21}:(SW,v)\xrightarrow[]{a_{21}}(S3_{1},v^{\prime})$, and
$N_{23}:(SW,v)\xrightarrow[]{a_{23}}(S3_{2},v^{\prime})$ to $S0$, $S1$,
$S3_{1}$, and $S3_{2}$, respectively. $N_{24}$ occurs in the cases when HV is
ready to switch from $SW$ upon the conclusion of current AROW round of other
CAVs in $V_{P}$, however, there is no other waiting CAV besides HV, thus AROW
is not required for HV. As expected, this transition majorly occurs in
$n_{veh}=4$ scenario with less CAVs (12.41%), and the other scenarios with
higher CAVs, the frequency of $N_{24}$ reduces rapidly. The transition
$N_{22}$ is 0% for all scenarios here since all CAVs are fully compliant
($NC_{prob}=0$). The transitions $N_{21}$ and $N_{23}$ occur in the cases when
HV, along with other waiting CAVs in $V_{S}$ is ready to switch out from $SW$
upon the conclusion of the current AROW round and the $V_{arb}$ has chosen on
the CAVs from $V_{P}$ to become the new $V_{arb}$. If HV is chosen as the new
$V_{arb}$, then it follows $N_{21}$, otherwise it uses $N_{23}$ as per AROW
rules. As shown in the Figure 5 transition matrices, these transitions contain
higher frequencies as $n_{veh}$ increases, simply due to the earlier-stated
argument that a higher number of competing CAVs creates a higher probability
of CAVs in $SW$.

Finally, from $S3_{1}$ and $S3_{2}$, the only valid transitions in the case of
$NC_{prob}=0$ are $N_{15}:(S3_{1},v)\xrightarrow[]{a_{15}}(S4_{1},v^{\prime})$
and $N_{18}:(S3_{2},v)\xrightarrow[]{a_{18}}(S4_{2},v^{\prime})$,
respectively. For the same reason, the transitions
$N_{13}:(S3_{1},v)\xrightarrow[]{a_{13}}(S1,v^{\prime})$,
$N_{14}:(S3_{1},v)\xrightarrow[]{a_{14}}(S0,v^{\prime})$,
$N_{16}:(S3_{2},v)\xrightarrow[]{a_{16}}(S1,v^{\prime})$,
$N_{17}:(S3_{2},v)\xrightarrow[]{a_{17}}(S0,v^{\prime})$ are 0%. With the
increase of $n_{veh}$, there are more instances of competing CAVs with HV, and
thus the percentage of $N_{15}$ and $N_{18}$ also rises. Once CAVs
successfully conclude AROW in $S4_{1}$ or $S4_{2}$, AROW is transitioned back
to $S0$ using transitions
$N_{19}:(S4_{1},v)\xrightarrow[]{a_{19}}(S0,v^{\prime})$ and
$N_{20}:(S4_{1},v)\xrightarrow[]{a_{20}}(S0,v^{\prime})$, respectively.

####  V-B2 AROW Performance under Non-Compliance Scenarios

##### Theoretical analysis of Non-Compliance

To increase robustness, AROW considers the occurrence of non-compliance and
allows compliant CAVs to still reduce ambiguity and safely pass SC-I. To show
the impact of non-compliance, this study randomly assigns non-compliance
probability, i.e., $NC_{prob}$, to each CAV except HV every time they engage
in AROW. There are two values used for experimentation purposes, i.e.
$NC_{prob}$ = 0.1, or 0.25. Even higher values can be chosen, but for the
purposes of this paper, these values are sufficient to show the collective
impact of $NC_{prob}$ on AROW. In theory, $NC_{prob}$ is designed to be
independently applied to each CAV during each of the stages in $NC_{stages}$.

To show the collective impact of $NC_{prob}$ on a typical round of AROW, we
use a metric $P(\exists NC)$ which is the probability that at least one CAV
becomes non-compliant throughout a singular round of AROW. Using the law of
total probability $P(X)=\sum_{n}P(X\cap Y_{n})$, we calculate $P(\exists NC)$
below:

$P(\exists
NC)=\sum_{j}^{n_{CV}}\sum_{m}^{j}\sum_{i}^{NC_{stages}}P(HV_{i})P(NC_{m}|HV_{i})P(CV_{j}),$
(13)

where $P(HV_{i})$ is the probability that HV is in stage $i$,
$P(NC_{m}|HV_{i})$ is the conditional probability that there are $m$ non-
compliant CAVs when HV is in stage $i$, and $P(CV_{j})$ is the probability of
HV in the current AROW round with $j$ competing CAVs. $P(CV_{j})$ uses the
outermost sum where $CV\in V_{P}$ and $n_{CV}$ is the total number of
competing CAVs to the HV during a singular round of AROW. Considering the
experimental topology for this study where competing CAVs can be on any of the
single-lane roads of the SC-I, $n_{CV}$ can be ranged as $1\leq j\leq 3$. For
every $j$ in the outermost sum, the inner sum aggregates $P(NC_{m}|HV_{i})$ in
range $1\leq m\leq j$. Finally, over every $m$, the inner-most sum aggregates
$P(HV_{i})$ where $i$ is every location defined in $NC_{stages}$, i.e.
$NC_{stages}=\\{S2_{2},S2_{3},S3_{1},S3_{2}\\}$. As can be observed in (13),
the probability $P(\exists NC)$ is calculated from the perspective of the HV
due to the easiness of calculations. For example, if HV is in $S2_{2}$, we can
already infer that other CAVs in $V_{P}$ will be in $S2_{3}$, or if HV is in
$S2_{3}$, we can then infer that one of the CAVs in $V_{P}$ other than HV has
been chosen as $V_{arb}$ and has proceeded to $S2_{2}$, whereas remaining CAVs
have moved to $S2_{3}$ along with HV. The same logic can be applied for $HV$
being in $S3_{1}$ or $S3_{2}$.

$P(CV_{j})$ is non-deterministic since it is not possible to predict the
specific number of competing CAVs to HV at a specific time, and thus in this
experiment, we rely on simulations to estimate it. On the other hand, when
calculating probability $P(NC_{m}|HV_{i})$ and given the set $NC_{stages}$, it
can be observed that $P(NC_{m}|HV_{S2_{2}})=P(NC_{m}|HV_{S2_{3}})$ and
similarly, $P(NC_{m}|HV_{S3_{1}})=P(NC_{m}|HV_{S3_{2}})$. On a high-level,
$P(NC_{m}|HV_{i})$ can be defined as:

$\small
P(NC_{m}|HV_{i})=\binom{j}{m}*P(NC|HV_{i})^{m}*(1-P(NC|HV_{i}))^{(j-m)}$ (14)

where $\binom{j}{m}=\frac{j!}{m!(j-m)!}$ is the binomial coefficient
representing the different combinations of $m$ non-compliant CAVs,
$P(NC|HV_{i})=NC_{prob}$, $P(NC|HV_{i})^{m}$ is the probability of $m$ non-
compliant CAVs, and $(1-P(NC|HV_{i}))^{(j-m)}$ is the probability of $(j-m)$
CAVs being compliant. Finally, $P(HV_{i})$ is calculated as:

$\small
P(HV_{i})=\begin{cases}(P(N_{4}^{*})+P(N_{3})P(N_{22})P(N_{4}^{+}))P(N_{5})&\text{if
}i=S2_{2},\\\ (P(N_{4}^{*})+P(N_{3})P(N_{22})P(N_{4}^{+}))P(N_{6})&\text{if
}i=S2_{3},\\\ P(HV_{S2_{2}})P_{C}(S2_{2})+P(N_{3})P(N_{21})&\text{if
}i=S3_{1},\\\ P(HV_{S2_{3}})P_{C}(S2_{3})+P(N_{3})P(N_{22})&\text{if
}i=S3_{2}\\\ \end{cases}$ (15)

where

$P_{C}(t)=(1-P(NC|HV_{t}))^{j}$ (16)

Figure 6: Comparison between $P_{T}(\exists NC)$ and $P_{E}(\exists NC)$

As observable in (15), $P(HV_{i})$ yields different values depending on the
specific location and its parent locations. For instance, $P(HV_{S2_{2}})$ or
the probability that HV arrives in $S2_{2}$ is dependent on either the direct
transition $N_{4}^{*}:(S1,v)\xrightarrow[]{a_{4}}(S2_{1},v^{\prime})$ or
sequence of transitions $N_{3}:(S1,v)\xrightarrow[]{a_{3}}(SW,v^{\prime})$,
$N_{22}:(SW,v)\xrightarrow[]{a_{22}}(S1,v^{\prime})$, and
$N_{4}^{+}:(S1,v)\xrightarrow[]{a_{4}}(S2_{1},v^{\prime})$. After considering
the possibilities of HV arriving at $S2_{1}$, the result is multiplied by
$P(N_{5})$ to calculate $P(HV_{S2_{2}})$ where
$N_{5}:(S2_{1},v)\xrightarrow[]{a_{5}}(S2_{2},v^{\prime})$. It should be noted
that $\|N_{4}\|=\|{N_{4}}^{*}\|+\|{N_{4}}^{+}\|$, and these transitions are
separated out due to probability calculations. $P(HV_{S2_{3}})$ is also
similarly calculated for HV in $S2_{3}$. Calculating $P(HV_{S3_{1}})$ and
$P(HV_{S3_{2}})$ is comparatively more complex because in addition to arriving
at $S3_{1}$ or $S3_{2}$ from $S2_{2}$ or $S2_{3}$ using transitions
$N_{9}:(S2_{2},v)\xrightarrow[]{a_{9}}(S3_{1},v^{\prime})$ or
$N_{12}:(S2_{3},v)\xrightarrow[]{a_{12}}(S3_{2},v^{\prime})$, respectively, HV
can also arrive at $S3_{1}$ or $S3_{2}$ from the wait stage $SW$ using
transitions $N_{21}:(SW,v)\xrightarrow[]{a_{21}}(S3_{1},v^{\prime})$ or
$N_{23}:(SW,v)\xrightarrow[]{a_{23}}(S321,v^{\prime})$, respectively. In
addition, in the cases of HV arriving at $S3_{1}$ or $S3_{2}$ from $S2_{2}$ or
$S2_{3}$, it is also necessary for all competing CAVs to HV to be compliant in
the parent locations $S2_{2}$ or $S2_{3}$, respectively. This can be
calculated probabilistically using (16).

Given $j$ which is the number of competing CAVs to HV in the current iteration
of (13), some probabilities in (15) such as $P(N_{5})$, $P(N_{6})$,
$P(N_{21})$, and $P(N_{23})$ can be determined probabilistically, whereas
other remaining probabilities such as $P({N_{4}}^{*})$, $P({N_{4}}^{+})$,
$P(N_{3})$, $P(N_{22})$ are non-deterministic since they totally depend on the
particular scenario. Finally, since we are calculating $P(\exists NC)$ where
it is assumed that $1\leq n_{CV}\leq 3$, thus $P({N_{4}}^{+})$ is always
assumed to be 1.

$n_{veh}$ | $NC_{prob}$ | $P_{T}(\exists NC)$ | $P_{E}(\exists NC)$
---|---|---|---
4 | 0.1 | 0.17 | 0.17
0.25 | 0.39 | 0.35
8 | 0.1 | 0.21 | 0.2
0.25 | 0.49 | 0.46
16 | 0.1 | 0.29 | 0.29
0.25 | 0.68 | 0.68
TABLE V: Tabular comparison between $P_{T}(\exists NC)$ and $P_{E}(\exists
NC)$ Figure 7: State transition comparison for non-compliance scenarios
($NC_{prob}$ = 0.1, $NC_{prob}$ = 0.25)

##### Experimental Analysis of Non-Compliance

Given the parameters in Tables II and III and (13), (14), (15), and (16), we
run a total of six simulations using different values of $n_{veh}$ and
$NC_{prob}$ and compare the theoretical and experimental $P(\exists NC)$, i.e.
$P_{E}(\exists NC)$ and $P_{T}(\exists NC)$, as shown in Figure 6. It should
be noted that the earlier-mentioned non-deterministic probabilities that are
needed to calculate $P_{T}(\exists NC)$ are taken from the simulations for
each scenario as known probabilities. As observable in all simulation results
in Figure 6, $P_{E}(\exists NC)$ converges to $P_{T}(\exists NC)$ as the
simulation moves ahead in time, which proves that AROW correctly considers the
impact of $NC_{prob}$ and the experimental results match with that of the
theoretical concept. This also shows that the simulation duration and logging
data size are sufficient to validate that the AROW algorithm has no deadlocks
among a variation of scenarios. Table V points to the same convergence in
tabular form as $P_{T}(\exists NC)$ and $P_{E}(\exists NC)$ are very similar
to each other towards the end of the simulation duration. For all simulation
scenarios, it can be generally viewed that as expected, an increase in
$NC_{prob}$ results in an increase in the overall $P_{T}(\exists NC)$ and
$P_{E}(\exists NC)$. Secondly, an increase in $n_{veh}$ also increases
$P_{T}(\exists NC)$ and $P_{E}(\exists NC)$ for both values of $NC_{prob}$
since more $n_{veh}$ results in more competing CAVs with HV during every AROW
round. As evident from Table VI, as we increase $n_{veh}$ for both values of
$NC_{prob}$, the percentage of AROW rounds involving HV with a higher number
of competing CAVs rises. For instance, with simulations scenarios where
$n_{veh}=4$, the highest percentage of AROW rounds for HV are with 1 competing
CAV. For $n_{veh}={8,16}$, the highest percentage changes to 2 and 3 competing
CAVs, respectively. Therefore, this explains why $P_{T}(\exists NC)$ and
$P_{E}(\exists NC)$ increase with the increase in $n_{veh}$.

| Percentage of $CVs$
---|---
$n_{veh}$ | $NC_{prob}$ | 1 | 2 | 3
4 | 0.1 | 88 | 10.7 | 1.3
0.25 | 90.6 | 8.8 | 0.6
8 | 0.1 | 25.1 | 57.7 | 17.2
0.25 | 34.4 | 54.8 | 10.8
16 | 0.1 | 0.9 | 29.3 | 69.8
0.25 | 3.3 | 29.7 | 67
TABLE VI: Percentages of competing CAVs ($CVs$) during AROW rounds for non-
compliance scenarios ($NC_{prob}$ = 0.1, $NC_{prob}$ = 0.25)

After establishing the fact that the theoretical impact of $NC_{prob}$ matches
with that of the experimental results, we analyze the effect of $NC_{prob}$ on
AROW performance in terms of the state transitions. For this reason, Figure 7
displays the state transition matrices in the form of heat maps for different
values of $n_{veh}$ and $NC_{prob}$. Most transitions and trends in the heat
maps in Figures 5 and 7 are similar except for the transitions involving
$NC_{stages}$. The first major difference is that the heat maps in Figure 7
contain non-zero transitions in
$N_{8}:(S2_{2},v)\xrightarrow[]{a_{8}}(S0,v^{\prime})$,
$N_{7}:(S2_{2},v)\xrightarrow[]{a_{7}}(S1,v^{\prime})$,
$N_{11}:(S2_{3},v)\xrightarrow[]{a_{11}}(S0,v^{\prime})$,
$N_{10}:(S2_{3},v)\xrightarrow[]{a_{10}}(S1,v^{\prime})$,
$N_{13}:(S3_{1},v)\xrightarrow[]{a_{13}}(S1,v^{\prime})$,
$N_{14}:(S3_{1},v)\xrightarrow[]{a_{14}}(S0,v^{\prime})$,
$N_{16}:(S3_{2},v)\xrightarrow[]{a_{16}}(S1,v^{\prime})$, and
$N_{17}:(S3_{2},v)\xrightarrow[]{a_{17}}(S0,v^{\prime})$, due to $NC_{prob}$,
as opposed to the same transitions which were all 0% in the heat maps in
Figure 5 due to full compliance.

It has been mentioned that in the case of non-zero $NC_{prob}$, AROW within
every compliant competing CAV utilizes $AROW_{thresh}$ so that in the cases of
non-compliance by some other CAV(s), it does not need to withdraw from using
AROW altogether and transition to $S0$ but instead re-attempt AROW until (4)
is being satisfied. This is the reason why the transitions
$N_{5}:(S2_{1},v)\xrightarrow[]{a_{5}}(S2_{2},v^{\prime})$ and
$N_{6}:(S2_{1},v)\xrightarrow[]{a_{6}}(S2_{3},v^{\prime})$ yield higher
percentages with $NC_{prob}$ = 0.25 than $NC_{prob}$ = 0.1, which in turn
yields higher percentages than $NC_{prob}$ = 0. The same reasoning is also
responsible for the increase in percentages of
$N_{9}:(S2_{2},v)\xrightarrow[]{a_{9}}(S3_{1},v^{\prime})$, and
$N_{12}:(S2_{3},v)\xrightarrow[]{a_{12}}(S3_{2},v^{\prime})$ in the cases of
$NC_{prob}$ = 0.25 than $NC_{prob}$ = 0.1.

Next, for any $n_{veh}$ in Figure 7, as $NC_{prob}$ increases, so does the
percentage of non-compliance related transitions from any of the
$NC_{stages}$. For example, it can be observed that $N_{7}$ is higher for
$NC_{prob}=$0.25 as compare to that for $NC_{prob}=$0.1. The same is the case
with $N_{8}$, $N_{10}$, $N_{11}$, $N_{13}$, $N_{14}$, $N_{16}$, and $N_{17}$.
This can also be understood by analyzing that for any $n_{veh}$, the total
non-compliance percentage by taking the sum of $N_{7}$, $N_{8}$, $N_{10}$,
$N_{11}$, $N_{13}$, $N_{14}$, $N_{16}$, and $N_{17}$ increases with the rise
in $NC_{prob}$ according to the $P(\exists NC)$ analysis earlier. Also, as
$n_{veh}$ rises, this denotes that there will be more competing CAVs to HV and
thus the percentages of the above-mentioned transitions increase even further.

In addition, it can also be observed that for $n_{veh}=$ 8, 16, the heat maps
display a higher percentages for $N_{13}$ and $N_{16}$ as compared to $N_{14}$
and $N_{17}$, respectively. As $n_{veh}$ increases, so does the percentage of
$N_{3}:(S1,v)\xrightarrow[]{a_{3}}(SW,v^{\prime})$ since there is a higher
probability that HV would encounter CAVs competing for AROW when it arrives at
the SC-I. This in turn explains the increase in the percentages of
$N_{21}:(SW,v)\xrightarrow[]{a_{21}}(S3_{1},v^{\prime})$ and
$N_{23}:(SW,v)\xrightarrow[]{a_{23}}(S3_{2},v^{\prime})$ where HV goes from
$SW$ directly to $S3_{1}$ or $S3_{2}$ towards the end of the successful
preceding AROW. Recalling the logic behind $AROW_{thresh}$, this means that as
the HV arrives at $S3_{1}$ or $S3_{2}$, its $AROW_{thresh}$ is still 0, and
thus if there is non-compliance and (4) holds true, HV would restart its AROW
and use $N_{13}$ and $N_{16}$ to transition to $S1$ rather than transitioning
to $S0$ and disable its AROW. This behavior can be observed for both non-zero
$NC_{prob}$ values. For the same reason, the percentages of $N_{8}$ and
$N_{11}$ are higher than that of $N_{7}$ and $N_{10}$ because as HV reaches
$S2_{2}$ or $S2_{3}$, it is probable that due to the non-compliance in the
previous AROW round, the $AROW_{count}$ is close to reaching $AROW_{thresh}$,
and thus a non-compliance here would mean that HV would disable its AROW.
These behaviors are not viewable in the case of $n_{veh}$ = 4 simply because
there are not enough CAVs in the scenario to force HV to transition to $SW$
upon arriving at the SC-I.

Finally, Figure 7 also shows that for any $n_{veh}$, the percentage of
$N_{15}:(S3_{1},v)\xrightarrow[]{a_{15}}(S4_{1},v^{\prime})$ and
$N_{18}:(S3_{2},v)\xrightarrow[]{a_{18}}(S4_{2},v^{\prime})$ reduces with the
increase of $NC_{prob}$ and that is a direct consequence of $NC_{prob}$ as it
reduces the probability of a successful AROW completion.

Figure 8: CDF comparison of vehicle clearance time ($T_{clearance}$) between
AROW, traffic light, and allway

####  V-B3 AROW Impact based on Evaluation Metrics

The impact of AROW is evaluated on the basis of ambiguity reduction and
fairness. The main contribution of AROW is to reduce the ambiguity that
drivers may face upon arriving at the SC-I at close time intervals to each
other. This in turn can allow fairness in terms of SC-I crossing priority
assignments. In this regard, the two metrics are mentioned below:

  * •

For ambiguity reduction, we calculate the frequency of ambiguous instances
($n_{amb}$) at SC-I where vehicles arrive at close intervals of each other.
$n_{amb}$ is characterized by the number of false starts by vehicles in
situations where the right-of-way is not clearly evident.

  * •

For fairness-based metric, the vehicle clearance time ($T_{clearance}$) is
calculated for a set of leading competing vehicles $S_{CV}$ at an intersection
that arrive within $T1$ of each other. This is the time difference between the
first vehicle in $S_{CV}$ entering the junction and the last vehicle in
$S_{CV}$ exiting the junction. SC-I junction can be described as the region
within the SC-I past the stop sign. $T_{clearance}$ can be described as:

$T_{clearance}=\max(S_{B})-\min(S_{A})$ (17)

where $S_{A}$ and $S_{B}$ are the sets for the junction arrival and departure
timestamp, respectively.

To avoid any confusion, it should be noted that only those vehicles utilizing
AROW are denoted as CAVs. For $n_{amb}$, AROW is compared to the allway stop
intersection management method from SUMO. This method is similar to the real-
life human behavior at an SC-I. The default rules of allway stop within SUMO
are according to the general right-of-way rules [35]. For AROW, $n_{amb}$ = 0
for all cases since CAVs are always aware of their SC-I passing turn. However,
same is not the case for allway as there are multiple cases where vehicles
have a false start due to ambiguity. Table VII shows the instances of non-zero
$n_{amb}$ in allway method for different values of $n_{veh}$. The column
labeled ‘1’ refers to all the cases where for any group of competing vehicles,
only one vehicle enters the junction at a time, and thus, $n_{amb}$ = 0. As
suggested by the percentages under this column, majority of the cases within
allway occur without ambiguity. However, there are cases where ‘2’ or ‘3’
vehicles out of the competing vehicles enter the SC-I junction due to
ambiguity, thus non-zero $n_{amb}$ as shown in their respective columns in the
table. Additionally, the percentages of $n_{amb}$ for these columns can be
observed to rise with the increase in $n_{veh}$.

In addition to ambiguity reduction, AROW also promotes fairness among
competing vehicles at an SC-I without necessarily causing additional delays.
Figure 8 compares the $T_{clearance}$ CDF of AROW to allway and traffic signal
methods from SUMO, respectively. The results from traffic light based
intersection have been included to serve as a baseline. It is clearly
observable from Figure 8 that AROW does not only outperform traffic lights in
terms of $T_{clearance}$ but it also yields very similar results to allway for
all values of $n_{veh}$. To analyze the differences numerically, consider the
equation below:

$\Delta
A=\int_{a}^{b}T_{clearance_{1}}(t)dt-\int_{c}^{d}T_{clearance_{2}}(t)dt$ (18)

where $\Delta A$ is the difference between the areas under the two CDF curves
of $T_{clearance}$. Using (18), $\Delta A$ between traffic light and AROW is
60.7, 113.7, and 103.5, for $n_{veh}$ = 4, 8, and 16, respectively. On the
other hand, $\Delta A$ between allway and AROW for the same values of
$n_{veh}$ is -1.48, 0.2, 1.93, respectively. Thus, this calculation reiterates
that AROW performs far better than traffic light in terms of $T_{clearance}$
and it is very similar to that of allway.

$n_{veh}$ | Competing Vehicles in Allway SC-I |
---|---|---
| ($n_{amb}$) |
1 | 2 | 3 | Total
4 | 427 (96%) | 17 (3.8%) | 1 (0.2%) | 445
8 | 606 (84.5%) | 106 (14.8%) | 5 (0.7%) | 717
16 | 696 (82.2%) | 143 (16.9%) | 8 (0.9%) | 847
TABLE VII: Tabular representation of allway SC-I scenarios with false-starts
due to ambiguity ($n_{amb}$)

##  VI Conclusion

This study proposes the AROW algorithm to reduce priority-related ambiguity at
SC-Is. The algorithm utilizes a cooperative DMS where vehicles use V2X to
communicate with each other. AROW is deployed to run several simulation
scenarios involving various levels of CAVs and $NC_{prob}$ values of non-
compliance to prove the completeness and robustness of AROW. The paper
iterates the accuracy of the proposed algorithm by showing close similarities
between the theoretical metrics and experimental results. Finally, AROW is
evaluated on the basis of ambiguity mitigation and intersection clearance time
as compared to traffic light and allway-stop based intersections from SUMO
traffic simulator. AROW is observed to outperform traffic lights and allway in
both metrics. As future work, the authors plan to test AROW under real-life
conditions by embedding the DMS and the underlying AROW on to the test
hardware. Secondly, AROW can be stress-tested under varying levels of
congested channels and communication losses to further improve the robustness
of the algorithm. Current study assumes that all CAVs are connected, which can
be relaxed to show the robustness of AROW in corner cases in the presence of
connected and non-connected vehicles. Finally, the timeouts $T1$, $T2$, and
$T3$ can be optimized by conducting analysis on communication latencies using
different V2X technologies. These optimized timeouts can further accelerate
AROW.

## References

  * [1] C. B. Rafter, B. Anvari, and S. Box, “Traffic responsive intersection control algorithm using gps data,” in _2017 IEEE 20th International Conference on Intelligent Transportation Systems (ITSC)_. IEEE, 2017, pp. 1–6.
  * [2] Y. Rahmati and A. Talebpour, “Towards a collaborative connected, automated driving environment: A game theory based decision framework for unprotected left turn maneuvers,” in _2017 IEEE Intelligent Vehicles Symposium (IV)_. IEEE, 2017, pp. 1316–1321.
  * [3] L. Blincoe, T. R. Miller, E. Zaloshnja, and B. A. Lawrence, “The economic and societal impact of motor vehicle crashes, 2010 (revised),” Tech. Rep., 2015.
  * [4] R. A. Retting, H. B. Weinstein, and M. G. Solomon, “Analysis of motor-vehicle crashes at stop signs in four us cities,” _Journal of Safety Research_ , vol. 34, no. 5, pp. 485–489, 2003.
  * [5] M.-k. Shi, H. Jiang, and S.-h. Li, “An intelligent traffic-flow-based real-time vehicles scheduling algorithm at intersection,” in _2016 14th International Conference on Control, Automation, Robotics and Vision (ICARCV)_. IEEE, 2016, pp. 1–5.
  * [6] E.-H. Choi, “Crash factors in intersection-related crashes: An on-scene perspective,” 2010.
  * [7] R. Azimi, G. Bhatia, R. R. Rajkumar, and P. Mudalige, “Stip: Spatio-temporal intersection protocols for autonomous vehicles,” in _2014 ACM/IEEE international conference on cyber-physical systems (ICCPS)_. IEEE, 2014, pp. 1–12.
  * [8] S. Singh, “Critical reasons for crashes investigated in the national motor vehicle crash causation survey,” Tech. Rep., 2015.
  * [9] L. Chen and C. Englund, “Cooperative intersection management: A survey,” _IEEE transactions on intelligent transportation systems_ , vol. 17, no. 2, pp. 570–586, 2015.
  * [10] E. Namazi, J. Li, and C. Lu, “Intelligent intersection management systems considering autonomous vehicles: A systematic literature review,” _IEEE Access_ , vol. 7, pp. 91 946–91 965, 2019.
  * [11] Z. Zhong, M. Nejad, and E. E. Lee, “Autonomous and semiautonomous intersection management: A survey,” _IEEE Intelligent Transportation Systems Magazine_ , vol. 13, no. 2, pp. 53–70, 2020.
  * [12] J. B. Kenney, “Dedicated short-range communications (dsrc) standards in the united states,” _Proceedings of the IEEE_ , vol. 99, no. 7, pp. 1162–1182, July 2011.
  * [13] 3GPP, “Evolved universal terrestrial radio access (e-utra); physical layer procedures (v14.7.0),” vol. 3GPP. TS 36.213, June 2018.
  * [14] G. Shah, R. Valiente, N. Gupta, S. O. Gani, B. Toghi, Y. P. Fallah, and S. D. Gupta, “Real-time hardware-in-the-loop emulation framework for dsrc-based connected vehicle applications,” in _2019 IEEE 2nd Connected and Automated Vehicles Symposium (CAVS)_. IEEE, 2019, pp. 1–6.
  * [15] G. Shah, M. Saifuddin, Y. P. Fallah, and S. D. Gupta, “Rve-cv2x: A scalable emulation framework for real-time evaluation of cv2x-based connected vehicle applications,” in _2020 IEEE Vehicular Networking Conference (VNC)_. IEEE, 2020, pp. 1–8.
  * [16] H.-J. Chang and G.-T. Park, “A study on traffic signal control at signalized intersections in vehicular ad hoc networks,” _Ad Hoc Networks_ , vol. 11, no. 7, pp. 2115–2124, 2013.
  * [17] J.-D. Schmöcker, S. Ahuja, and M. G. Bell, “Multi-objective signal control of urban junctions–framework and a london case study,” _Transportation Research Part C: Emerging Technologies_ , vol. 16, no. 4, pp. 454–470, 2008.
  * [18] D. DeVoe and R. W. Wall, “A distributed smart signal architecture for traffic signal controls,” in _2008 IEEE International Symposium on Industrial Electronics_. IEEE, 2008, pp. 2060–2065.
  * [19] K. Dresner and P. Stone, “Multiagent traffic management: A reservation-based intersection control mechanism,” in _Autonomous Agents and Multiagent Systems, International Joint Conference on_ , vol. 3. Citeseer, 2004, pp. 530–537.
  * [20] L. Li and F.-Y. Wang, “Cooperative driving at blind crossings using intervehicle communication,” _IEEE Transactions on Vehicular technology_ , vol. 55, no. 6, pp. 1712–1724, 2006.
  * [21] H. Kowshik, D. Caveney, and P. Kumar, “Provable systemwide safety in intelligent intersections,” _IEEE transactions on vehicular technology_ , vol. 60, no. 3, pp. 804–818, 2011.
  * [22] F. Perronnet, A. Abbas-Turki, J. Buisson, A. El Moudni, R. Zeo, and M. Ahmane, “Cooperative intersection management: Real implementation and feasibility study of a sequence based protocol for urban applications,” in _2012 15th international IEEE conference on intelligent transportation systems_. IEEE, 2012, pp. 42–47.
  * [23] J. Wu, A. Abbas-Turki, and A. El Moudni, “Cooperative driving: an ant colony system for autonomous intersection management,” _Applied Intelligence_ , vol. 37, pp. 207–222, 2012.
  * [24] M. VanMiddlesworth, K. Dresner, and P. Stone, “Replacing the stop sign: Unmanaged intersection control for autonomous vehicles,” in _Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems-Volume 3_ , 2008, pp. 1413–1416.
  * [25] A. A. Hassan and H. A. Rakha, “A fully-distributed heuristic algorithm for control of autonomous vehicle movements at isolated intersections,” _International Journal of Transportation Science and Technology_ , vol. 3, no. 4, pp. 297–309, 2014.
  * [26] G. Shah, S. Shahram, Y. Fallah, D. Tian, and E. Moradi-Pari, “Enabling a cooperative driver messenger system for lane change assistance application,” in _2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC)_. IEEE, 2022, pp. 4320–4327.
  * [27] S. Rajab, S. Bai, S. Saigusa, J. Keller, A. Pradhan, S. Bao, and J. Sullivan, “Driver to driver (d2d) personalized messaging based on connected vehicles: Concept evaluation via simulation,” 2017.
  * [28] R. Alur and D. L. Dill, “A theory of timed automata,” _Theoretical computer science_ , vol. 126, no. 2, pp. 183–235, 1994.
  * [29] R. Alur, “Timed automata,” in _International Conference on Computer Aided Verification_. Springer, 1999, pp. 8–22.
  * [30] S. Krauß, P. Wagner, and C. Gawron, “Metastable states in a microscopic model of traffic flow,” _Physical Review E_ , vol. 55, no. 5, p. 5597, 1997\.
  * [31] P. A. Lopez, M. Behrisch, L. Bieker-Walz, J. Erdmann, Y.-P. Flötteröd, R. Hilbrich, L. Lücken, J. Rummel, P. Wagner, and E. Wießner, “Microscopic traffic simulation using sumo,” in _The 21st IEEE International Conference on Intelligent Transportation Systems_. IEEE, 2018. [Online]. Available: https://elib.dlr.de/124092/
  * [32] A. Wegener, M. Piórkowski, M. Raya, H. Hellbrück, S. Fischer, and J.-P. Hubaux, “Traci: an interface for coupling road traffic and network simulators,” in _Proceedings of the 11th communications and networking simulation symposium_ , 2008, pp. 155–163.
  * [33] S. International, “Lte vehicle-to-everything (lte-v2x) deployment profiles and radio parameters for single radio channel multi-service coexistence,” Society of Automotive Engineers, Standard J3161, 04 2022.
  * [34] B. Toghi, M. Saifuddin, H. N. Mahjoub, M. O. Mughal, Y. P. Fallah, J. Rao, and S. Das, “Multiple access in cellular v2x: Performance analysis in highly congested vehicular networks,” in _2018 IEEE Vehicular Networking Conference (VNC)_. IEEE, 2018, pp. 1–8.
  * [35] U.S. Department of Transportation, Federal Highway Administration, “Manual on uniform traffic control devices (mutcd),” Online, 2003, accessed on March 26, 2023. [Online]. Available: https://mutcd.fhwa.dot.gov/htm/2003r1/part2/part2b1.htm#section2B04

|  Ghayoor Shah is a Ph.D. candidate at the University of Central Florida. He
received the B.Sc. degree in Computer Engineering from University of Illinois
at Urbana-Champaign in 2018. He has previously worked as a mobility
engineering intern at Phantom Auto and as a research intern at Ford Motor
Company. His research interests include Connected and Autonomous Vehicles
(CAVs), scalability analysis of V2X, and applications of artificial
intelligence to cooperative driving.
---|---
|  Yaser P. Fallah is an Associate Professor in the ECE Department at the
University of Central Florida. He received the Ph.D. degree from the
University of British Columbia, Vancouver, BC, Canada, in 2007. From 2008 to
2011, he was a Research Scientist with the Institute of Transportation
Studies, University of California Berkeley, Berkeley, CA, USA. His research,
sponsored by industry, USDoT, and NSF, is focused on intelligent
transportation systems and automated and networked vehicle safety systems.
---|---
|  Danyang Tian earned her Ph.D. degree in electrical engineering from the
University of California, Riverside, in 2018. She is currently a scientist at
Honda Research Institute USA, Inc. Her research interests include connected
and automated vehicles, vehicular communication systems, and driver behavior
modeling, application design and development of connected and automated
vehicles, vehicle-to-everything (V2X) communication technologies. She serves
as chair in the SAE International V2X Vehicular Applications Technical
Committee.
---|---
|  Ehsan Moradi-Pari is a lead principal scientist and communication/data
research group lead at Honda Research Institute (HRI-US). His current research
is focused on vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I)
communications based on short-range communication and cellular technologies.
He serves as Honda lead and representative for V2V and V2I precompetitive
research such as Vehicle-to-Vehicle Systems Engineering and Vehicle
Integration Research for Deployment, Cooperative Adaptive Cruise Control, and
5G Automotive Association (5GAA). He has spearheaded Honda’s efforts and
preparations to accelerate connected automated vehicle deployment in the
United States and the state of Ohio where he led the team to design and deploy
the first-of-its-kind smart intersection concept in Marysville, Ohio. Dr.
Moradi-Pari has several publications in internationally refereed journals,
conference proceedings, and book chapters in the area of designing
communication protocols and applications for connected and automated vehicles
and modeling/analysis of intelligent transportation systems
---|---