Chapter - IV

Topological Model approach to Traffic Management

Section A: Topological Graph Theory Model for Traffic Management at Intersection.

Section B: Planar Graph Theory Model of Traffic Management at Pedestrian Crossing.

Section C: Data Based Management Systems approach to Load of Pedestrian for Pedestrian safety.

Chapter-IV  

82

Chapter-IV Topological Model for Traffic Management at Urban Centres

Urban road structure is a combination of wide roads and

intersections allowing two way traffic. An intersection has 4 legs. The

Pedestrian crossing is meant for use by both Vehicles and Pedestrian. They

facilitate mobility of Vehicles in two directions and for pedestrian to cross

the road safely. While Intersections are popular for Vehicle-Vehicle

Accidents and Jam, the pedestrian are most sufferers of accidents, while

crossing the road.

Traffic signals are said to be introduced to regulate traffic, both at

intersections and Pedestrian Crossings. The purpose of traffic signal at

intersection is to avoid traffic jam and accident and the signal at pedestrian

crossing is to safeguard pedestrian against accident.

The number of conflict points (where commuters’ path intersects) at

intersection are attributed to incidence of accidents or jam. That means the

Crossing Number of graph of intersection being high is attributed to Jam

and Accidents. If the Graph is Planar (there are no edge crossings), there

would be least possibility for accidents. The Graph of intersection records

16 Conflict Points, while the Pedestrian Crossing records Four.

The traffic signal at intersection permit commuter of four legs by

turns stops commuters of other three legs to permit commuters of each leg.

Thereby, each leg commuters are required to wait for three phases of the

signal (out of the four phases in a cycle). This results in Loss of time to

Chapter-IV  

83

vehicular commuters and hence, their average speed falls drastically. At

any point of time three leg commuters are present at the intersection.

During this waiting period, most of the vehicles do not switch off the

engine and allowed it to idle, resulting in wastage of fuel (for a duration of

three phases of the signal). The Passers by are exposed to this vehicular

emission contributed by three leg commuters (intensity), for a duration of

three phases of the signal (duration), suffering health hazard.

The signal at Pedestrian Crossing operates in two phases. In one

phase, the Pedestrian are stopped and Vehicles use the road (both ways). In

second phase, vehicles of two directions are stopped and Pedestrian are

allowed to cross the road. The Pedestrian and Vehicles wait for duration of

one phase of the signal. There by the loss of time equivalent to one phase of

the signal.

The Vehicles do not switch off the engine resulting in Loss of fuel

for duration of one phase of signal. Passerby are exposed to Vehicular

emission for a duration of one phase of the signal. Vehicles driving in both

the directions contribute pollution resulting in health problems. After roads

are widened, pedestrian take longer time to cross the road and hence the

duration of the phase is lengthy, thus the average speed of vehicles has

fallen drastically.

While Traffic Jam and Accidents are attributed to the number of

conflict points encountered, the loss of time and fuel, is now attributed to

Chapter-IV  

84

large time that the commuters are stopped at Traffic Signals, The traffic

signals are found to be used as a restraint measure rather to a facilitating

one. This has a side effect of commuters suffering pollution.

To control accidents we need to simplify traffic Management.

Devise methods to facilitate commuters pass the area without encountering

others. The Traffic Signals so used, should stop the commuters for a least

possible time. Several Administrative approaches are said to have been

tried by our Engineering Faculties, including restraint measures of One-

way, No-right turn, imposing user charges in peak hours, Cap on new

vehicles purchase etc. Engineering approaches of building flyovers,

infrastructure at intersections, Pelican signal, Intelligent Traffic

Management System, Widening of Roads, Road Dividers and many more.

Some countries have also tried, speedy mobility solutions of Light Rail,

BRTS, Multi-Model Transport System, Metro Rail, Elevated Roads, Local

Rail to provide speedy transport. Not much work has been done from

Mathematics approach. Since Intersections and crossings form Road

structure of Urban Centres, we wish to discuss the problem by the

Topological Graph Theory approach in three sections:

a. Topological Graph Theory Model to Traffic management at 4-leg (2-

way) intersection.

b. Planar Graph Theory Model for Traffic Management at Pedestrian

Crossing.

c. Data Based Management System for Pedestrian Load Assessment

for supervising last mile transport and safe crossing by Pedestrian.

 

Sim

legs

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Fig. 1

f four legs

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Chapter-IV

85

Traffic

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and cross-

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e scope for

Chapter-IV

86

ot in use)

points are

of Conflict

s or to save

o forced to

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.

Chapter-IV  

87

The Intersection records 16 Conflict Points.

To minimize accidents a Round-about (traffic island – circular)

which recorded 8 conflict points was tried. However, as traffic volume

increased and more capable mobility modes (Van, Bus, multiple wheeled

vehicles) are available, the road space being limited more jams and

accidents resulted and hence this was dispensed with. Again round-about

were not possible in old cities and feasible for newly planned cities, also the

cost acquiring land was large, the same was discouraged and introduction

of Traffic Signals were followed.

The Traffic signals at 4-leg intersection work in four phases,

allowing one leg commuters to pass, in each phase (to change the leg),

while other three leg commuters are stopped. Thus time loss and fuel loss

are encountered. The average speed of commuting falls drastically.

Thereby, commuters of each leg will be stopped for a duration of 3

phases of the signal.

At any point of time, three leg commuters will be present at the

intersection. And only one leg commuter will be passing the intersection in

each phase.

The loss of time of each leg commuters is equivalent to 3 Phases of

the signal. This is the time they are not permitted to travel, whereby the

average speed falls drastically.

Chapter-IV  

88

During the period they are stopped, the vehicular commuters do not

switch off the engine and prefer to idle the engine, thereby the vehicular

exhaust continues to emit. Thereby, commuters present at the intersection

(of three legs) are exposed to vehicular exhaust for a duration of three

phases of signal and suffer health hazards due to pollution.

“A whooping 67% of emission in Bangalore is caused by the

transport sector. Over the past decade, dozens of global studies have shown

that spending time in close proximity of heavy traffic, especially diesel

truck traffic, is associated with a wide range of morbidity effects, as well as

increasing mortality”.

During the three phases of stopping, vehicles are idling, resulting in

fuel wastage, if saved and used for travel, would improve fuel efficiency

In all vehicles are wasting fuel during their wait for 3 phases of signal .

Commuters feel that traffic signals are hampering their speed and

their average speed has fallen drastically after signals are introduced. There

are reports that the pollution level at intersection alarming, affecting health,

which is attributed to vehicular exhaust. Commuters are put to health

problems, including the police personnel manning the intersection.

Commuters also say that the fuel spent for idling is also burden to them,

which can be better utilized.

This disadvantage of this system is large waiting time at the traffic

signals. The signals are working out more as an restraint measure than

Chapter-IV  

89

facilitator. Indirectly, they are causing congestion (One commuter forcing

other to slow-down or stop) for unduly long duration.

The operation of signals in four phases is shown in the figure 4

Fig.4

Chapter-IV  

90

Note on Graph of Intersection and Signal operation:

Cause for Accidents:

a. Graph constitutes 8 vertices, 12 edges and record 16 Conflict points

thereby large number of accidents and traffic jams occur.

Cause for Time loss

b. Traffic signal operates in 4 phases. Commuters are made to wait at

signals(idling),to permit passing of commuters of other three legs.

There by each leg commuters are at loss of Time equal to three

phases of the signal.

Fuel loss

c. Traffic signal operates in 4 phases. Commuters are made to wait at

signals(idling),to permit passing of commuters of other three legs.

There by each leg commuters are at loss of fuel for three phases of

the signal.

Exposure to vehicular pollution

d. At any point of time commuters of 3-legs will be present at

intersection thereby commuters are exposed to exhaust of 3-leg

commuters(Intensity of pollution)

e. Each leg commuters is exposed to vehicular pollution for 3 phases of

the signal (Duration of exposure).

Thereby each one is exposed to vehicular emission 3-leg pollution

for a duration of 3 phases of the signal.

Chapter-IV  

91

As each commuter is made to stop for three phases of the signal, His

Average Speed of vehicles is quite low due to time lost at traffic

signal.

Simplification of Traffic Management at Intersection:

The objectives of this study being, to control traffic jam and

accidents; save time and fuel of the commuters and to minimize the

exposure to vehicular emission in duration and intensity of exposure, we

propose to simplify the traffic management at intersection.

We will refer the vehicles approaching intersection as outward traffic and

those entering the leg as inward traffic (Fig.5)

Fig.5

 

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tersection,

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be represe

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Chapter-IV

92

d that the

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fic) would

r right leg)

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‘a’ to ‘x’),

Chapter-IV

93

ntersection

ict points).

, 12 edges

V

3

n

.

s

Chapter-IV  

94

There are 16 Crossing edges (Crossing Number of the Graph).

Set of vertices V = {a,b,c,d, ………..x} , The edge set E

={1,2,3,………12}

Vertices Set of Leg A ={a,b,c,d,e,f}

Vertices Set of Leg B = {g,h,i,j,k,l}

Vertices Set of Leg C = {m,n,o,p,q,r}

Vertices Set of Leg D = {s,t,u,v,w,x}

Description of Edges (with reference to Vertices – showing direction)

Edge From to

1 x a

2 q b

3 j c

4 d u

5 e n

6 f g

7 w h

8 p i

9 k t

10 l m

11 v o

12 r s

Description of Intersection in Graph Theory terms:

Each leg has six Vertices represent 6 lanes; three outward and three

inward (from left to right).

Chapter-IV  

95

The intersection is represented by graph of 24 vertices (‘a’ through’

x’) and 12 edges (nos.’ 1 ‘though ‘12’), there are 16 conflict points ( edge

crossings). Hence the crossing number of the digraph is “16”.

Note: Earlier researchers have referred edge by Vertices, which is felt to be

tedious; hence, we wish to refer them by their number.

To compute the Crossing Number of Intersection, we will first

record it in Matrix Form (edge-crossing matrix), since each edge crossing

(intersection) is recorded twice in the Matrix, we will omit the lower

diagonal iteams (Because the Matrix is Symmetric and Diagonal terms are

all Zeros (No self-loops for Traffic)), the Number of 1’s gives the Crossing

Number of the Graph,here it is ‘16’. Representation of Graph in Matrix

Form and recording edge-crossings (Conflict Points). Edge Crossings

Matrix (with edges as rows and columns) of the 4-leg intersection defined

by

E (I,j) = 1 if edge-i intersects with edge-j

= 0 otherwise.

Each row represent an edge, the items of the column is ‘0’ (if edge

represented by column does not cross it); and is ‘1’ when crosses it. This

Chapter-IV  

96

results in a 12 x 12 matrix (Fig.8):

1 2 3 4 5 6 7 8 9 10 11 12

1 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 0 1 0 0 1 0 1 0 1 0

3 0 0 0 1 1 0 1 1 0 0 0 0

4 0 1 1 0 0 0 1 0 0 0 1 0

5 0 0 1 0 0 0 1 1 1 0 0 0

6 0 0 0 0 0 0 0 0 0 0 0 0

7 0 1 1 1 1 0 0 0 0 0 0 0

8 0 0 1 0 1 0 0 0 1 0 1 0

9 0 1 0 0 1 0 0 1 0 1 0 0

10 0 0 0 0 0 0 0 0 0 0 0 0

11 0 1 0 1 0 0 0 1 1 0 0 0

12 0 0 0 0 0 0 0 0 0 0 0 0

Fig.8

On omitting the 1’s below diagonal we get (Fig.9).

1 2 3 4 5 6 7 8 9 10 11 12

1 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 0 1 0 0 1 0 1 0 1 0

3 0 0 0 1 1 0 1 1 0 0 0 0

4 0 0 0 0 0 0 1 0 0 0 1 0

5 0 0 0 0 0 0 1 1 1 0 0 0

6 0 0 0 0 0 0 0 0 0 0 0 0

7 0 0 0 0 0 0 0 0 0 0 0 0

8 0 0 0 0 0 0 0 0 1 0 1 0

9 0 0 0 0 0 0 0 0 0 1 0 0

10 0 0 0 0 0 0 0 0 0 0 0 0

11 0 0 0 0 0 0 0 0 0 0 0 0

12 0 0 0 0 0 0 0 0 0 0 0 0 Fig. 9

Chapter-IV  

97

‘1’ occurs 16 times reflecting Crossing Number of the Graph, which

corresponds to 16 conflict points encountered at Intersection.

Simplification of Graph:

A special feature of Graph Theory is that, a Graph In question can be

redrawn by altering the shape of the edges and to re-order label of vertices

or altered their position, without altering the property of the graph

(Incidence). The revised graph is said to be an Isomorphs of Original

Graph. (1-1 correspondence between edges and vertices, preserving

incidence relation). If the revised graph is of lesser in thickness, or lesser

Crossing Number the Scope for accidents will be less. Adopting the graph

for traffic management results in safety.

Our objective of this study is to convert the graph in to least

Crossing Number (Conflict Points, to control accidents) by altering the

shape of the edge (path of commuting). If the Graph can be made a Planar

(No edges cross, Crossing Number ZERO – assures least scope for

accidents or jam). There will be no need for construction of flyovers, Road

over bridges, Underway, and an accident free road system results. If the

Thickness of the Graph is greater than zero, the Graph is non-planar, it

means, it is not possible to draw the Graph on a plane without edges

crossings and hence Graph requires more than one plane for embedding.

That means, it is impossible to manage traffic without flyover, walk-way,

sub-way (infrastructure) or some sort of restraint measure of using traffic

signal.

 

Sim

Ste

The

E(B

1.

2.

3.

4.

disj

is P

mplificatio

p I. Colle

e edges co

BC), E(CD)

E(AB)

E(BC)

E(CD)

E(DA)

Observ

joint and P

Planar. (Fig

n of the G

ct all edge

onnecting

), E(AD) r

– edges c

--- set of e

--- set of

--- set of e

ve that ea

Planar (edg

g. 10)

Graph of In

s connectin

adjacent l

espectively

connecting

edges conn

edges conn

edges conn

ch of E(A

ges non-int

ntersection

ng Adjacen

legs (A,B)

y.

legs A an

necting legs

necting leg

necting leg

AB),E(BC)

tersecting),

Fig.10

n:

nt Legs to m

),(B,C),(C,

nd B.

s B and C

gs C and D

gs D and A

),E(CD),E(

, hence the

make a sub

D),(D,A)a

E(AB) =

E(BC)

. E(CD)

A E(DA)

(AD) is n

eir Union m

Chapter-IV

98

bgraph E1

s E(AB),

= { 6,3}.

= {10,8}.

)={12,11}.

)= {1,4}

non empty,

making E1

V

8

,

.

,

1

 

Ste

E(B

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Observ

nar.

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Hence

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ve to accep

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ect edges c

tively

--- set of e

--- set of e

ve that both

ver, the Gr

ossings. He

E= E1 U

raph of E i

pt some Re

s, we have

onnecting

edges conn

edges conn

h E(AC), E

raph of E2

ence non-p

E2 is also

in a Plane

estraint Me

revised th

Opposite L

necting legs

necting legs

E(BD) are

2 is non-Pla

planar.

Fig.11

o non-plan

without e

easure. Fina

e Graph of

Legs A, C

s A and C

s B and D

non-empt

anar. The G

nar. Hence

edge crossi

ally, as we

f E2 (Fig.1

C and B,D

E(AC)

E(BD)

ty and disj

Graph of E

e, it is imp

ng. That

e can merg

2)

Chapter-IV

99

as E(AC),

) = {5,2}

)={7,9}

oint, each

E2 (fig. 11)

possible to

means, we

ge or delete

V

9

,

h

)

o

e

e

 

Wh

Fin

hose thickn

nally, the G

ness is ONE

Graph of E i

E

is as shown

Fig.12

n in figure

Fig.13

13

Chapter-IV

100

V

0

Chapter-IV  

101

The revised graph is as follows

Fig.14

Graph has 8 Conflict points 4 at intersection, other 4, one each on 4 legs

When adopted to Traffic Management at Intersection, the system

works in two phases, as shown in figure 15 and 16, (using signals operating

in two phases)

 

ope

The rev

erated with

vised Grap

h simplifie

Phas

Phas

ph is accep

ed signal

se I (Fig.15

se 2(Fig.16

ted for traf

system w

5)

6)

ffic manag

which oper

gement at in

rates in tw

Chapter-IV

102

ntersection

wo phases

V

2

n

.

Chapter-IV  

103

Hence the Topological Graph Theory Model for traffic management at

intersection.

The Topological Graph Theory Model of Traffic Management at Intersection as achieved the following : Before Now Result -------------------- ------------- -----------------

1. Accident / Traffic Jam Control :

Conflict Points / Edge Crossings Of Graph 16 8 Reduced

2. Loss of Time and Fuel:

No. of Phases of Traffic Signal 4 2 Reduced a. Time Loss 3 Phases 1 Phase Time

saved two Phases.

b. Fuel Wastage (idling) 3 Phases 1 Phase Fuel saved

Two phases.

3. Exposure to Vehicular Pollution : Intensity of pollution 3 leg 2 leg Reduced Duration of exposure 3 Phases 1 Phase Reduced

Both Intensity of pollution and duration of exposure are reduced. Duration, by two phases of the signal and intensity of one leg commuters.

Chapter-IV  

104

Other benefits accrue a. Reduces scope of accidents or Jam.

b. Saves commuters time, the time saved when invested for travel

would improve the Average Speed.

c. Reduces fuel wastage. The saved fuel used for travel would improve

fuel efficiency.

d. The exposure to vehicular pollution both in intensity and duration.

Earlier the passer by were exposed to exhause of 3 leg commuters

for 3 Phase of the signal. Now, they face exhaust of 2 leg

commuters for 1 Phase of the signal.

e. Facility, Earlier only one leg commuters were passing the

intersection. Now, two leg commuters will be passing in each phase.

Chapter-IV  

105

Section B: Planar Graph Theory Model for Traffic

Management at Pedestrian Crossing.

Introduction :

A Pedestrian crossing or crosswalk is a road where pedestrian are

facilitated to cross the road without accident from Vehicles playing in two

directions. They keep pedestrian together to be seen by motorists and can

cross safely across the flow of vehicular traffic. Marked pedestrian

crossing are in use at intersections or at other places, where it is unsafe to

the pedestrian. They are introduced considering the number, speed or road

width. Very frequently used at busy centers where large number of

pedestrian cross the road, near schools, function halls, malls, hospital etc.,

They are also referred to as Zebra Crossing, alternate white and

black strips painted on the road surface, where pedestrian have priority of

using the road and vehicles are required to stop. In some countries,

pedestrian may not have priority, but is an offence to cross the road, other

than at Zebra Crossing. In some countries, a special signal with lamp or

light emitting diode panel are fitted, permitting pedestrian to use the road

and traffic is to stop.

In some cases, Pedestrian operated signals are fitted where,

Pedestrian will push the button to stop the traffic and use the road. In

some countries, vehicles are prescribed with speed limits, to ensure safety

of pedestrian, although they are not stopped, for the sake of pedestrian

safety.

Chapter-IV  

106

The Traffic Signals at Pedestrian Crossing work in two phases,

permitting Vehicles and Pedestrian to use the road alternately in each

phase. Vehicles of both directions are stopped for one Phase of the Signal,

they idle and hence, the passer by are exposed to vehicular exhaust of two

direction vehicles, for One phase duration.

The number of accidents faced by Pedestrian is alarming.

Why do people crossing the Road? To attend works on other side of

the Road. In view of increased fuel cost (which is imported), planners have

recommended use of Public Transport (Bus/Train, Car pooling). How far

has it helped is the question.

We will discuss the use of public transport. A person leaving the

residence for work, approaches the main road for Public Transport. If his

destination is towards left, he will take the transport and leave. However, if

his destination is towards right, he will cross the road and take the Public

Transport (Left hand drive system). On reaching the destination, he will

attend the work if his is work place is on the left side, else he will cross the

road and attend the work This shows his crossing the road depends on the

work place.

In the return trip, he will catch the Public Transport operating in

opposite direction (towards his residence). Hence, he will take Public

Transport running opposite direction of his earlier journey. He will cross

the road, if he did not cross earlier, he will not cross if he did cross earlier.

Chapter-IV  

107

The same thing happens at his originating place. In summary, each

commuter taking Public Transport, will cross the road two times in a trip.

Inference : Each Public Transport user will cross the road two times in a

trip. As Public Transport Users increase, Pedestrian crossing the road

increase (by double).

Accordingly, safety at Pedestrian Crossing gains importance.

Definition of the problem:

The road is used by vehicular commuters in two directions. The

Pedestrian use it for crossing the road. Thereby 4 conflict points are

recorded. To regulate traffic, traffic signals are used, which operate in two

phases. In one phase, Pedestrian are stopped and vehicles are permitted in

two directions. In second phase, the vehicles are stopped and pedestrian are

allowed to cross the road.

This results in loss of time to both pedestrian (each have to wait for

time of one phase); Fuel is wasted during the waiting time. The vehicles

emit exhaust during the waiting time, which all those present are exposed

to.

Analysis of Traffic operation at Pedestrian Crossing:

The Vehicles ride along the road, the pedestrian use it for crossing.

The vehicles move in two directions, pedestrian cross the road both ways..

There are 4 conflict points at the spot. The Graph of the pedestrian crossing

is drawn. Signals are operated to allow pedestrian cross the road safely.

The signals operate in two phases. In one phase the vehicles are stopped

Chapter-IV  

108

and pedestrian use the road. In the second phase, pedestrian are stopped

and vehicles use the road.

Thereby, each of the commuter groups wait for signal for one

phase of the signals. Suffer loss of time, equivalent to one phase of the

signal. The vehicles spend fuel for idling for one phase duration. They are

exposed to vehicular pollution during this time. Their average speed falls.

Time and Fuel loss at Pedestrian Crossing Singal is for One Phase of the

Signal.

The following figure shows the road used by Vehicles and Pedestrian

Fig 1

The arrows show the path of Vehicles and Pedestrian. Vehicles and

Pedestrian cross one others path at 4 points (Marked) where pedestrian are

likely suffer accident or hit by vehicles.

Chapter-IV  

109

Fig 2

The Graph of Pedestrian Crossing can be represented (Digraph),

where Vertices show starting and ending points of Vertices and

Pedestrian. The line joinging them (path followed ) by the Edges (with

direction).

Vertices Set = {a,b,c,d,e,f,g,h} denote starting and ending point of

vehicles

and pedestrian

Edges Set = {1,2,3,4} show the path of commuting

Mapping Edge-1 = (a,b)

Edge-2 = (c,d)

Edge-3 = (e,f)

Edge-4 = (g,h) are ordered pairs with direction.

The edges intersect (cross) at four points are Edge Crossings

(represent conflict points) Presence of edge crossing infer that the Graph is

non-planar. The objective of this study is to eliminate the edge crossing to

make it a Planar Graph, to eliminate accidents.

3 4

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110

The Crossing edges matrix is as follows:

1 2 3 4

1 0 0 1 1

2 0 0 1 1

3 1 1 0 0

4 1 1 0 0

As each edge crossing is reflected twice by `1’in the matrix, and the

matrix is symmetric, we will make the sub-diagonal terms to zero. The

resulting matrix shows four entities of `1’, which is non-zero. Hence the

Graph of the Pedestrian Crossing s non-planar.

1 2 3 4

1 0 0 1 1

2 0 0 1 1

3 0 0 0 0

4 0 0 0 0

There are four 1’s in the matrix, which shows the Crossing Number

of Pedestrian Crossing Graph is FOUR. Hence, Non-Planar.

Improvement of Pedestrian Crossing by Topological Graph Theory

Approach

The property of the Graph (Planarity), will not change by adding or

removing parallel edges and inserting and deleting vertices. We will modify

the Graph.

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Construction :

Draw an Edge Parallel to edge-1 connecting vertices ‘a’ to ‘b’ and

denote it by ‘3’ and mark direction,

Draw an Edge parallel edge-2 connecting vertices ‘c’ to ‘ ‘d and

denote it by “4”.and mark direction.

Add one vertex between ‘e’ and ‘f’ and denote it by ‘ i’

Add one vertex between ‘g’ and ‘h’ and denote it by ‘j’

Note: Drawing or removing Parallel edges and Adding or deleting Vertex

would not affect planarity of the Graph.

The Revised Graph is as follows: Fig 3

Fig 3

The Shape of the edges can be varied suitably to partition the Graph

into two isomorphic sub graph and Planar. So that the whole graph can be

made Planar.

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Variation of shape of the edges is carried as shown in the figure 4

Fig 4

We decompose the graphs G1 and G2 as follows

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113

The Subgraphs G1 with edges 1,2,5,8 and G2 with edges 3,4,6,7

and non-empty and Planar (No edges cross or Crossing Number is ZERO),

and G1 is Isomorphic to G2graph, ( there vertices have one-to-one

correspondence, one-to-one correspondence between their edges and the

incident relationship is also preserved) and are connected by Vertices i and

j. Hence a 2-Connected.Graph.

Vertices being starting and ending point of vehicles and pedestrian

in the direction shown. When G1 and G2 are adopted two phases, results

in accident free Zone.

Process of using G1 and G2 in Two Phases

The exchange of Vehicular and Pedestrian commuters will be in two

phases.

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Phase I, the Sub-graph G1 is operational and in Phase II, the Sub-graph G2

is operational.

Phase I (G1)

Fig 5

In Phase I The Vehicles at vertex ‘a’ drive by edge -1 to reach vertex b’

and Vehicles from vertex ‘ c’ drive by edge-2 to reach vertex ‘d’

Simultaneously , Pedestrian at’ e’ walk by edge- 5 to reach’ I’ and

Pedestrian at ‘j’ walk by edge- 8 to reach’ h’.

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115

In Phase II (They Follow Subgraph G2)’

Vehicles at vertex ‘ a’ drive by edge- 3 to reach ‘b’

Vehicles from vertex ‘c’ drive by edge- 4 to reach vertex ‘d’

Simultaneously, Pedestrian at’ i ‘walk by the edge- 6 to reach ‘f ‘ and

Pedestrian at’g’ walk by the edge - 7 to reach ‘j’.

This completes one cycle, and the cycles will be repeated.

In one cycle the Vehicular commuters at ‘a’ reach ‘b’, while those at ‘ c’

will reach ‘d’; simultaneously the pedestrian at ‘e’ reach ‘f’ and those at

‘g’ will reach ‘h’, safely.

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116

Summary of Results :

The model to be referred as a Planar Graph Model for traffic

management at pedestrian crossing, devised involves, signals operating in

two phases. While, the vehicular commuters will pass the spot, without

stopping, thereby wastage of time is controlled. Pedestrian will cross the

road safely. Hence, there is no waiting time at pedestrian crossing and

hence the commuters are not exposed to vehicular emission.

In all, the Traffic Management Model devised, has minimized the

conflict points encountered, thereby reducing scope of accidents; The

simplified traffic signal system operates as a facilitator than a restraint one.

The connected problems of exposure to vehicular pollution, there by health

hazards are minimized, that too, without much Engineering Support.

Benefits: The Pedestrian and Vehicles will pass the pedestrian crossing

without being stopped.

a. The accidents are eliminated, as conflict points are eliminated.

b. The pedestrian and vehicles save waiting time of one phase duration.

c. Vehicles save fuel of waiting at the signal.

d. Vehicles save time of waiting at signal.

e. The average speed of vehicles improves.

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Summary of benefits :

1. The Pedestrian Crossing zone is free from edge crossings (conflict

points), hence scope for accidents reduced.

2. The time loss which of one phase of signals, is removed.

3. The time saved when invested for travel, improves average speed of

commuting.

4. The fuel loss during one phase idling is removed, resulting in fuel

economy.

5. Exposure to vehicular emission for a duration of one phase of signal,

has been removed.

Results :

1. The Scope of Accidents is reduced – Crossing Number of revised

Graph is ZERO (Planar)

2. Time Loss is reduced from One Phase duration to Zero.

3. Time saved (One Phase duration) when invested in travel improves

average speed.

4. Fuel Loss due to idling for a duration of One Phase is reduced.—

results in Fuel efficiency.

5. Vehicular exhaust (for one phase duration) of vehicles of two

directions is saved. Pollution due to idling at Traffic Signals is

eliminated.

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118

The Results of revised Pedestrian Crossing Graph are as follows:

Before After Inference

--------- ----------- ------------------------

Scope for Accidents/Jam

1. No. of Conflict Points 4 Zero Reduced

Time and Fuel Loss :

2. a Time Loss 1 Phase Nil. Time saved

b Fuel Wastage (idling) 1 Phase Nil. Fuel Saved.

Time saved and fuel saved when invested in travel improves Average

Speed and results in Fuel Efficiency.

Exposure To Vehicular Pollution.

3. a Intensity 2 direction nil Reduced

b Duration 1 Phase nil Reduced.

Exposure to Vehicular Pollution of two direction Vehicles for one Phase

duration is Reduced. Pedestrian will cross the road without any risk of

accident. Vehicles donot have to stop at the signals.

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119

Section C : Data Base Management System Approach to Assess Pedestrian Load

Overview of Data Base Management System Concepts:

A Data Base is a collection of inter related data stored in a controlled

fashion for use of multiple purposes by multiple users. A Data Base

Management System is a collection of programs useful for collection and

maintaining data and process them to give required information, speedily,

accurately and reliably. Specific feature of Database approach are:

a. Sharability : Data can be used by multiple Application Programmers.

b. Availability : The data stored will be made available to any

application programmer

Each application does not require collection and storing data

required for processing a query . This facility saves time of the

programmer.

c. Data Independence: The programmer is not concerned where and

how the data is stored, Actual and Physical storage devise and area,

Who collected and how it is stored.

d. Evolvability : The system can support unanticipated requests and

process it and provides information.

e. Data Integrity : High accuracy and consistency and validation

facilities are integral part of DBMS. Mostly, it operates on live data

collection and storage facility, thereby, highest reliability, validity is

assured.

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120

Data Sharing facility:

Data Sharing by all functionaries is possible. Both Horizontal and

Vertical functionaries are supported by the system. Similarly, data can be

shared from differing locations. Thereby, timely data and information are

accessable. Different functionaries of the organsiation will have access to

the system.

An analysis of trip of vehicular and Public Transport users, reveals

that each one will cross the road twice in a trip. Thereby, the number

people who cross the road is twice to that of number of commuters.

In view of the finding that increased individual and Public Transport

will result in increased number of commuters crossing the road. Thereby,

increased facilities are needed for permitting crossing the road. The Traffic

Management Personnel, need an effective Data-Base Management system,

to assess the pedestrian taking/leaving public transport and make sufficient

arrangement for faster crossing the road.

For this purpose, we propose a System, which accepts input of the

passenger as soon as he takes the road, note their destination; arrive at the

time they reach the destination and inform the Traffic Managers, the time

and strength so that they can supervise the road crossing as. The

consolidated report of passengers reaching each destination can be prepared

and concerned officials at the destinations are provided with the

information. So that proper arrangement for last-mile connectivity and safe

crossing the road can be supervised. Thereby, congestion due to pedestrian

and inconvenience to vehicular traffic can be minimized.

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121

The Pedestrian Load Predicting System works as follows:

As soon as passenger takes the bus and ticket is issued, his

destination (bus-stop) and time of reaching the destination is worked out.

As passengers from several direction reach the destination point, from

various routes, the number of people reaching that particular destination,

according to time of reaching is arrived and provided to the supervisors at

all destination points (live). This report is the consolidation of arrival of

buses from different directions. So that arrangements can be made for

crossing the road for taking last mile connecting (reaching work place or

home). Thereby, Pedestrian safety is ensured and their time can be saved.

Similarly, a Help Centre may be constituted which can receive SMS

from Public Transport User, mentioning time of reaching Bus Stop,

destination to which he is planning to reach. The consolidated, processed

information can be generated from all sources, so that the load of

passengers according to time, will be available, and the fleets can be

scheduled and customer needs served. This results in improved capacity

underutilization and improved profits.

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122

The system can also be used to monitor capacity utilization, fuel

efficiency, staff Demand/supply, Bus shortage, Average Speed monitoring,

driver’s efficiency, Demand assessment on festival and examination

seasons, Accident rate Drivers’ efficiency. Profitability of Routes, For

Assessment of demand on festival days, examination dates, feasibility of

routes.

The approaches need more detailed examination, which can be

undertaken after applying the Models suggested in the Thesis. We

recommend the same for future study.