8th sem notes
TRANSCRIPT
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IMPORATNCE OF PUBLIC TRANSPORT
The demand for transport in the cities is linked to the various types of the trips undertaken by the
people. A large section of people make trips to reach their work places, students undertake trips
to reach the schools and colleges, there are trips which are related to recreational purposes,
religious purposes, shopping purposes, entertainment, social etc. As the cities grow in size the
number of trips increases in the city, besides the number of trips the trip length also starts to
increase, therefore there is a need to provide good transport to these people for easy urban
mobility.
The best and the cheapest mode of transportation for the large section of our population in all the
cities is the public transport system, various modes of public in different cities includes metro
rail, buses, auto rickshaws, taxis, rickshaws and local trains. As the income of the families has
started to increase in past two decades the dependence on the bus transport has started to
decrease due to the fact that many people can afford two wheelers and four wheelers now andprefer to make trips in their own vehicles. Liberalization followed with licenses to manufacture
of the different brands, types, etc., made it a buyers market offering innumerable choices to buy
two wheelers, this followed by attractive financing schemes. ven though the usage of public
transport has started to decrease but its importance to the cities can never be neglected. !ublic
transport still remains the cheapest mode of transport and it is safer than most other modes of
transport.
"sage of private vehicles may be possible for smaller families on certain particular occasions but
it is not possible for even small families to use private vehicles all the time so they also have to
make use of public transport. A large section of our society still cannot afford to travel in private
vehicles, so it becomes very important to have an efficient public transport system. !ublictransport is the sole mode of transportation for the school going children and also for a large
section of college students, many companies have assigned buses for catering to the travel
demand of their employees. #arious recreational trips are carried out in buses$ people prefer to
make religious trips in groups so the importance of public transport increases. !ublic transport
plays an important role in running the economy of the city as it caters to the various needs of
different sections of the society so it becomes very important to have an efficient public transport
system.
PROBLEMS ASSOCIATED WITH URBAN TRANSPORT
The problems associated with urban transport are of varying nature, some of them are enlisted
below%
Congestion% There has been a tremendous surge in the number of vehicles in &ndia in the
past two decades, the increase in number of vehicles is due to the increase in the income
of the people, having a vehicle in the family has brought lot of comfort and convenience
to the people but it has created larger problems, even though the number of vehicles has
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increased by large proportions but the road width has not increased by same proportions
which leads to the congestion on the roads. The roads are occupied with vehicles beyond
their capacity which leads to congestion on the roads. The congestion leads to increase in
the travel time of the vehicles which decreases the overall efficiency of the transport
system followed by increase in noise and air pollution.
Growth in nu!er o" #ehi$%es% 'ith the increase in the income of the people there has
been a tremendous growth in the number of vehicles on the road. !eople have started
using two wheelers and four wheelers more fre(uently. The main reason for the increase
in the number of two wheelers are following
Two wheelers are very cheap as compared to other vehicles.
)e(uire very less space for parking
*ave very good maneuverability.
+ecrease the overall travel time, which includes walking time, and waiting time.
&ncrease in comfort and convenience. +ecreases the overall travel time as it avoids
walking and waiting.
*ighly reliable
Travel cost less compared to bus travel.
Liit&tions to ro&' wi'ening% There has been a tremendous growth in the number of
vehicles in past twothree decades but the expansion of the road network has not matchedthe increase in number of vehicles. There have been various factors which prevent the
expansion of roads$ the unplanned construction in the most cities has led to people
constructing various establishments on the land reserved for road expansion. The
situation is worsened by the improper design of roads which doesnt allow for
segregation of vehicles travelling at different speeds. -obility of all the vehicles is thus
limited to the speed of the slowest vehicle on the road. The average speed on the
angalore city during peak hours is /0 to 12 kmph.
De$%ining re%i&n$e on ro&' tr&ns(ort% The most important factor that has led to increase
in the problems of urban transport is that people have started to avoid the public transportsystem$ one of the factors for decreasing dependence on the public transport is the
inefficiency of the public transport and also the higher usage of private vehicles. The
percentage of two wheelers increased from 3.34 in /50/ to 6/.34 in 12//, whereas the
percentage of buses in the total volume on the road has decreased from //./4 to /./4.
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De$%ining us&ge o" non)otori*e' o'es% The usage of non7motorized modes of
transport has reduced drastically in the past decades, people hardly use bicycle for
making trips anymore, and the walking which was a common thing of the past has
literally vanished. The reason for the decrease in non7motorized trips is due to the
increase in risk of walking and riding on the roads, the other reason for decrease in non7
motorized trip is due to the increasing length of the trips.
High %e#e% o" &ir (o%%ution &n' noise (o%%ution% The public transport has brought
people close and made different places in city easily accessible but the urban transport
has led to the high air pollution in cities. The petrol and the diesel cars used in the
cities release a
large amount of pollutants in the atmosphere which has led to degradation in the air
(uality of the cities causing various health problems to the people which are a matter
of concern for the government.
Ro&' &$$i'ents% There has been a tremendous increase in the number of accidents
with the increase in the number of vehicles on the &ndian roads. +ue to the careless
driving of few people the accidents have increased.
In$re&se in $onsu(tion o" (etro%eu (ro'u$ts% 'ith the increasing number of
vehicles the consumption of the petroleum products has increased several folds, &ndia
has to import large amount of petroleum products and a large part of the foreign
exchange is spend on it.
PROBLEMS ASSOCIATED WITH BUS TRANSIT
The bus transit is one of the most common modes of transit in urban areas, it is considered as life
line of the angalore city. Large number of commuters have an easy access to this mode of
transportation, even after having any benefits this mode has few disadvantages also. 8ew of the
problems associated with bus transit are%
Transport inade(uacy i.e not matching with demand.
9entralization% concentrated mainly to centre of the cities.
8ares% due to stage system which makes it costly for shorter distance travel and
economical for longer distance travel.
&nappropriate location
us stops are not scientifically planned and provided.
us fre(uency is low or unevenly distributed.
Longer waiting time at the bus stop
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Lack of information at the bus stop about bus timings, route details, bus number passing
through that stop.
Takes too long to get a seat in the bus
uses are overcrowded
&nade(uate facilities at the bus stops like lack of sheltered stops, lack of seating
arrangements etc.
9ommon entry for exit for commuters% leading to friction and delay to both boarding and
alighting passengers.
The efficiency of bus transit system depends upon the access that passengers have to the bus, bus
stop is the point that provides access to the passengers to board or alight the bus, if the bus stops
are located at the proper places then a higher number of commuters will have easy access to the
buses and therefore the efficiency and occupancy of the buses will increase. :n the other hand ifthe bus stop spacing is improper lot of people will not have an easy access to the bus stop and
therefore affects the efficiency of the transit services. Therefore it becomes necessary to locate
the bus stops at the proper places with an ade(uate spacing between them so as to increase the
transit efficiency.
OB+ECTI,ES OF IDEAL BUS STOP LOCATION
A bus stop should be easily accessible for all the passengers who use the bus, bus stop
layout should be such that the dwell time of the buses at the bus stops is reduced. :ther vehicles like scooters, autos and private vehicles should be prevented from parking
at the bus stops$ the various curb street factors which affect the boarding and alighting
from the buses should be removed.
The bus stop should provide with minimal facilities like shelter, sittings, dust bins etc.
There should be a signage showing the availability of other modes of transport and also
information system about the bus arrivals.
The layout should be such that buses can be parked near to kerbs and passengers can
board and alight from the buses easily. us stops should be connected with footpaths for
easy access.
us stops should not be covered from all the sides as it will prevent the passengers fromseeing the buses coming towards the bus stops.
CONCERNS ASSOCIATED WITH LOCATION OF BUS STOPS
The ma;or concerns associated with location and design of bus tops are as follows%
Per"or&n$e o" Tr&nsit Agen$-% Location of bus stops has a significant effect on the
performance of the transit agency which operates in the city. The location of bus stop determines
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the usage of the transit agency. Travel time of the bus can be divided into four parts, access time
to reach the bus stop, waiting time at the bus stop, on board travel time, time taken to reach the
destination after alighting from the bus. The main goal of the transit agency is to locate the bus
stops in such a way that the total travel time is decreased.
Tr&""i$ "%ow. Location of the bus tops has a significant effect on the traffic flow. 'hen the bus
stops at the bus stop it reduces the capacity of the road, width of the bus is 1.< meters and with
clearance it reduces the road to one lane of width =.0 meters for the time, the bus dwells at the
bus stop one lane of the road is blocked by the bus. *9- 12/2 gives a value of bus blockage
time and it is about /0 seconds for each bus stop. >umber of buses arriving simultaneously at the
bus stop also has an effect on the traffic flow$ dwelling of = buses together at the bus stops
creates a bottle neck and thus blocks all the movement of the traffic.
S&"et-% ?afety refers to being certain that no harm will occur under defined conditions. At a bus
stop the safety should exist between the buses, passengers and other vehicles. 'hile waiting at
the bus stops the passengers should feel safe, the bus stops should be located at such places
which dont cause problems to people while crossing a busy street.Se$urit-% The availability of various amenities at the bus stops like lighting makes passengers
feel safe driving at night, also if the bus stop is located near a residential area or any other land
use people feel safer.
CONCEPT OF BUS STOP OPTIMI/ATION
'hen the spacing between the bus stops is large then the travel time in the buses is less, this is
because buses have to make lesser stops when the spacing is larger. There exists a relation
between the travel time and the bus stop spacing, if the stops are located closer to each other,
then the commuters have to walk lesser distance to reach the bus stops to board the buses but
closer spacing results in larger travel time as buses have to make larger number of stops to cater
to needs of people resulting in loss of time to all bus occupants. Larger spacing between the bus
stops leaves loopholes in the coverage of buses as there exist gaps in the coverage and many
people find it hard to walk larger distances to reach bus stop, when the stops are spaced closer
there occurs an overlap in the coverage and the number of stops increases which increases the
bus travel time.
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EFFECTS OF OPTIMI/ATION OF BUS STOP SPACING
'ith the growth of private vehicles on the roads the overall problems of the cities have
magnified by large proportions, this tremendous growth of vehicles has led to increase in travel
times in the cities due to the delays enroute because of high congestion on road, in angalore
city the average speed during peak hours is about 12 @mph this lead to an tremendous waste of
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time of all the people of the city, it is not easy to reduce the number of private vehicles on roads
but people can be made to shift their mode of transportation which will solve a large portions of
the urban transport problems. 8or people to make a shift from private vehicles towards the public
transport it becomes necessary to make the public transport attractive. 'hen the bus stops are
located at optimal distance the accessibility to the bus stops is easy, people are not reluctant in
walking to the bus stops for catching the bus.
:ptimization process helps in creating a model for urban transport which reduces the
overall travel time of the passengers$ this will help in saving a lot to time of commuters. &n the
optimal spacing model the headway of buses is properly established and this proper headway
between the buses helps to reduce the overcrowding in the buses and helps to prevent the bus
bunching. !eople know about the arrivals of the buses and dont crowd for one bus as next bus is
expected within few minutes.
y optimizing the spacing of bus stops it is possible to reduce the overall travel cost of the
passengers. The operating agencies can make large profits by optimization of bus stop spacing,optimization of bus stops leads to decrease in the fleet size of the transit agency$ it decreases the
dwell times of the buses at the stops therefore reducing the wastage of fuel which is spent during
idling of the buses at the bus stops. Acceleration and deceleration of vehicles for each stop also
increases. These savings can be used to reduce the travel cost of the passengers which is a direct
benefit to the commuters. The overall facilities at the bus stops can be improved which is the
secondary benefit to the commuters.
The effect of spacing between the bus stops has been a critical issue. &f the bus stops are
closely spaced they increase the in bus travel time of the commuters, large spacing of the bus
stops leads to inefficiency in the coverage. The fre(uent stopping of the bus due to close spacingleads to disruption of the traffic flow. +ifferent methods have been used to determine the optimal
spacing of the bus stops. Anthony A. ?aka
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Ta ,d=[PsNs+PcNc+ (Ps+PcPsPc )Nsc+1 ] u (a+d )120ad
'hereTa ,d=time attributedaccelerationdeceleration
PC=probability that a busis stopped by traffic signalat stoplocation;
Ps=probability that a bus makes a stop at regular bus stop location;
PsPc=joint probability of bus stoppingat traffic signalsoverlapping withbus stops $
Ns=number of bus stops considered isolated traffic signals;
Nc=number of signalized traffic intersectionsconsidered isolatedregular bus stops ;
Ns , c
=number of bus stops overlapping with signalized traffic intersections;
N=Ns+Nc+Ns ,ctotal number of potential stopson the bus route
a C normal acceleration rate of the bus
d C normal deceleration rate of the bus
E0u&tion "or 'we%% tie &t !us sto(s%
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The transit agency for the angalore city is -T9 and the agency is currently running in loses
because the income of the agency is falling short of the operating cost. Therefore there arises a
need to identify to identify cost effective measures of sustaining a high system performance.
&t has been found that the operational performance of the transit agencies can be improved
significantly by optimizing the spacing of the bus stops. The highway capacity manual contains
formulas for analyzing the various transit operational parameters$ however these formulas do not
include transit stop spacing as an operational parameter. The spacing of the bus stops clearly or
the number of stops, clearly affects operating speed of the system, the headway, the potential
capacity and the fleet size. 'hen the bus stops are closely spaced and passengers can easily
access these stops, however the problem of having closely spaced bus stops is that there are
fre(uent stops, increased travel times, increased emission rates increased stress on the driver, and
increased disruption on the traffic flow. *owever if the bus tops are spaced at larger spacing the
problem that arises is that the accessibility to the bus stops decreases and the commuters have to
walk more. The basic aim of the transit agency is to maximize the accessibility and minimize
tradeoff. The preferred policy for transit stop spacing is one that attempts to balance the two
issues.
Transit operators decide on the policy, service headway and then determine the fleet size. &t is
hypothesized that it is possible to reduce the re(uired fleet size by optimizing the spacing
between bus stops.
The review into the past research has revealed two categories of work. The first study is related
to minimizing the total travel times and maximization of transit patronage. This approach gives
an insight into the benefits that are derived from the optimization of the bus stop spacing. The
second category of research involves studying the effect of the bus stops on the speed,
acceleration and deceleration of the other vehicles in the interrupted flow.
This pro;ect work is the extension of both the categories of previous research. The optimization
of bus stop spacing can be used for determining the fleet size. y using the bus stop spacing as a
factor to determine the fleet size it is possible to reduce the fleet size which in turn can reduce
the transit operating cost fixed cost of procuring additional buses and operational cost per busB.
?mall spacing between the bus stops leads to increase in the travel time due to fre(uent stoppage
at bus stops. :n the other hand if the spacing between the bus stops is large then the buses can
attain a maximum speed which is the allowable speed limit on the road. *owever there exists a
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bus stop spacing threshold beyond which the operating speed will not increase. 8rom the various
studies conducted throughout the world it has been found that people are not willing to walk
more than 322 meters to reach a bus stop, the studies in &ndia have shown that the optimal
spacing should be about E22 meters. These findings were used as guidelines for determining the
optimal spacing for the pro;ect work.
The following procedure is used to determine the optimal spacing of bus stops
8irst the fleet size for the maximum bus stop spacing was calculated
?econd the assumed bus stop spacing was then reduced gradually until a lower threshold
value that preserves the calculated fleet size.
The actual bus travel time, which is directly related to bus stop spacing, may vary due to various
unstable external factors such as weather, traffic and even bus operators attributes. Therefore in
the actual application of the model the spacing may be increased slightly than the optimalspacing.
The model development process is carried out in two stages$ first the bus travel time that
determines the fleet size re(uirements was computed by dividing the time into four main
components$ acceleration deceleration time$ delay time at stops $ delay time at traffic signals$
and unimpeded travel time involving cruise speed. ?econdly a sensitivity analysis was carried
out by gradually varying the bus stop spacing until the optimal bus top spacing was determined.
METHODOLOG2
The first step in the pro;ect was to determine the bus travel time , the bus travel time is divided
into four components$ acceleration deceleration time, dwell time at bus stops , dwell time at
traffic signals and one way unimpeded travel time.
ACCELERATION AND DECELERATION TIME
+escription$ach bus stop is associated with two activities which affect the total travel time of the bus, the
first is the time spend in decelerating the bus to stop it at the bus stop and the second is the time
spend in accelerating the bus when it starts to leave the bus stop after stopping at the bus stop.The total number of accelerating and decelerating activities along the route is found out and the
total time spends in accelerating and decelerating along the route is calculated.
METHODOLOG2
The acceleration deceleration time was calculated as follows%
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A strip of 02 meter length on the route was selected, the strip was divided into 0 strips of /2
meter length each, the time taken by the bus to traverse a distance of /2 meters was found out by
using a stopwatch, and the speed of the bus was calculated from the formula%
"peed=distance
time
The speed on each strip was calculated using this method, the acceleration and the deceleration
of the buses was found out from the following formula
#2$
2=2a"
Let the displacement from the stop position to cruise speed and the cruise speed to stop position
is denoted by %a and %d respectively. Therefore for cruise speed v we have
%a=#
2
2 a
%d=#
2
2 d
'here a C normal acceleration rate of the bus
d C normal deceleration rate of the bus
Therefore the component of the displacement during which the bus accelerates or decelerates is
given by
%a , d=#2( a+d2 ad)
The total terminal to terminal travel time attributed to acceleration and deceleration of a
bus is determined as under
Travel time attributed to acceleration and deceleration C combined probability of bus
stopping at bus stops and traffic signalsB F dwell time for each stoppage
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-athematically it can be written as
Ta ,d=[PsNs+PcNc+ (Ps+PcPsPc )+1 ][u ( a+d )120ad]
'here
Pc=probability that a bus is stopped by trafficsignal at stop location;
Ps=probability that a bus makes a stop at regular bus stop location;
PsPc=joint probability of bus stoppingat traffic signalsoverlapping withbus stops $
Ns=number of bus stops considered isolated traffic signals;
Nc=number of signalized traffic intersectionsconsidered isolatedregular bus stops ;
Ns , c=number of bus stops overlapping with signalized traffic intersections;
N=Ns+Nc+Ns ,ctotal number of potential stopson the bus route
PROBABILIT2 OF BUS STOPPING AT A BUS STOP$
+escription$
'hile traversing the route the bus has to make stops at the designated stops, the buses may stop
at all the stops or a bus may skip a particular stop. The bus stopping at a bus stop or skipping a
bus stop depends upon the passengers waiting at the bus stops or the passengers who want to
who want to get down at the bus stop. The probability of bus stopping at the bus stop is given by
the formulae
P=1&[e' ]
'= ![( f) (N s+N s , c+1 )]
G is the average demand boarding or alightingB per bus stop for operating headway$
f C E2h or service fre(uency on bus route$
hC operating headway expressed in minutes$ and
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H C hourly demand on bus route
BUS SOP DWELL TIME
+escription$
The dwell time of the bus on each bus stop along the route is found out. This time
includes the time spend in serving all the passengers at the bus stops i.e. the time taken by
passengers to board or alight from the bus at the bus stop and the time taken to open and close
the doors of the bus.
METHODOLOG2.
The time taken by passengers to alight and board the bus is found out along with the
average time it takes to open and close the door of the bus by travelling in the bus along the route
and the average time the bus spends at each bus stop is noted.
-athematically the total dwell time at the bus stops is calculated as% ref
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N=(2Tbus )
h
> is the re(uired fleet sizeh is the headway
REDUCTION IN TRANSIT OPERATION COST B2 OPTIMAL BUS STOP LOCATION
+ue to rising costs and decrease in the subsidies provided by the governments the
transportation funding is becoming very tough, therefore receiving a high level of attention from
transportation departments. The few important issues that need attention include congestion
mitigation, travel time, air (uality improvement and reduction of operating costs.
!ublic transit is considered as being environmental friendly because of the high carrying
capacity. &t has been found that a bus can carry same number of passengers as carried by
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The relation between spacing total cost of access and riding per unit length is parabolic in
nature as shown in figure below. As the spacing between the bus stop increases the total cost
decreases as the bus has to make fewer stops, the total cost goes on decreasing as the stop
distance increases and it reaches a point where the cost is minimum, this spacing gives the
optimal spacing of the bus stops, if the distance is further increases the cost starts to increase as
the bus stops become inaccessible to passengers therefore the number of transit users decreases.
!arameters for setting up of e(uations
s=stop spacing
p=number of passengersdistance
ps=e(pected number of passengers alightingboarding per stop
Assumptions for development of model%
>umber of passengers boarding or alighting at a stop is !oisson distributed$
Travel demand is uniformly distributed over s$
Average access distance Cs4
MODEL DESCRIPTION.
The total cost function is divided into two cost functions%
Access cost
)iding on board and stopping cost
A$$ess $ost.
The access cost is related to the passengers walking distance, the access cost depends upon
the number of people boarding and alighting at the stop, and on the access speed v. the access
cost in terms of length can be written as% ref 0B
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Ca=nl 'a=(ps )( (s4 )( ()a
v)=ps2 )a
4 v
n=average number of passengersboardingalighting per stop=ps
l=average distance=s4
'a=cost per unit distance
v=passenger access speed
)a=averagecost per personfor access
RIDING AND STOPPING COST.
The riding cost of the passengers is determined by the total time spend by passengersriding in the bus and the stopping cost is expressed as the time spend by the passengers at the
various stops. The riding and stopping cost can be formulated as% ref 0B
(1eps)
Cr=N(tr+tl )' r=N ( ( s#+ P r)( ( )r )=Ns)r
#+N )r
N=number of passengerson the vehicle
tr=ridingtime
tl=lost time
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#=vehiclecruise speed
=timeloststopping serve passengers
1eps=probability that bus stops at the bus stop
)r=averagecost per unit time per person
Then the average cost per unit length s is given by% ref 0B
C=( Ca+Cr )
s =[{(ps )a )4 v )r pN}+{(1e
ps)ps }]
*et +=(4 v)r)a)pN
This is a single unit less (uantity
)r)a=value of ridingtime comparedaccess time
pN C number of passengers with origins and destinations that lie within a distance one can
travel by access or walking in lost time D
Then the average cost per unit length becomes
C=[( ps+)+{(1eps )
ps }] )r pN+N )r#
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8rom the above e(uation it is clear that bus stop spacing s is independent of # and IrDp>.
Therefore the bus stop spacing s is solely dependent on J. The idea of optimizing bus stop
spacing with the reduction in the total cost can be formulated as under%
C o=[ps+ + (1eps)
ps ]
The minimized total cost is obtained from the two functionsps+ and
( 1eps )ps
the total
cost reaches a minimum when functions
(1eps )ps
ps
+become e(ual.
The probability of a bus stopping at the bus stop in our case is / as we suppose that buses make a
stop at every bus stop, therefore for our case /7e7psB becomes /. Therefore the e(uation takes the
form
ps
+=
1
ps
+=p2 s2
Therefore - J C ps
ut J C4 v
)r
)apN
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Therefore s +
p
"=(4 vpN
)r
)a)pKiving the values to all the above variables we get ?
ANAL2SIS PART 34 wor5e' e6&(%e &''ition&% 7
!art / of the analysis is associated with helping in reducing the number of buses plying on the
route. The various field values have been used to reduce the fleet size for one hour on the route.
Total distance to be travelled +C 3.1 kilometers C 3122 meters
Acceleration rate of bus a C 2.3 ms1 from field studiesB
+eceleration rate of bus d C 1.0 ms1from field studiesB
>umber of traffic signals >cC 5 from field studiesB
>umber of isolated bus stops >sC 5 from field studiesB
>umber of bus stops at signalized at intersections >scC 1 from field studiesB
Number of buses running per hour = 24 (field studies)
Average occupancy of buses = 1 (field studies)
!ourly passenger trips " = Number of buses running per hour (24) # average occupancy of buses (1)
= 24 # 1= 1224
Average *eadway hM C = minutes average value from field studiesB
D C average service time per passenger C E seconds estimated from field observationsB
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k C average time to open and close the door C < seconds estimated from field observationsB
f = service fre(uency on route C60
h C 12
?peed of the bus on the route C 2kmph C E.5< ms
An&%-sis
Ste( 3.
Average spacing for the existing conditions
%=.N=
$200
%+%+2=
$200
20 =410meters
% is the spacing between the potential stops
!robability that a bus is stopped by traffic signal
Pc=probabillityof bus stoppingat the traffic signal=Cg
C
(1200 )
0 =0&$'
!robability that a bus makes a stop at the regular bus stop location
Ps=1&[e' ]2
'= !
[( f) (N s+N sc+1 )]
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'=1224
[( 60') (2+%+1 )]
G C 0./
Therefore P s=1&[e&1 ]2
!sC probability of bus stopping at the bus stopsC 2.555
Ste( 8% stimation of bus travel time%
!art of travel time attributed to acceleration and deceleration%
Ta ,d=[PsNs+PcNc+ (Ps+PcPsPc )Nsc+1 ][ u (a+d )120ad]C [(0&%%%(%+0&$'( %)+(0&%%%+0&$'&0&%%%( 0&$' )( 2+1 ]
( [6&%4(0&$+2&
120( 0&$( 2& ]Ta ,d=traveltimeattributed accelerationdeceleration C /.E< minutes
+well time at bus stops%
Ts=
[P s (Ns+Ns , c+1 )
][(qs
f)(
60
)+
k
60
]qs=
!Ns+Nsc+1
=1224
12 =102
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[0&%%%( (%+2+1 )] [( 10224)( ( 460 )+( 460 )]Ts=.well time at bus stops=4&$minutes
+well time at traffic signals%
TC=PC(Nc+Ns , c ) [0&0( (Cg )]
60
TC=[0&$'( (%+2 )]( [0&0( 120&060 ]
TC=(6&41' )( (0&$' )
TC=.welltime at traffic signals='& minutes
"nimpeded one way travel time%
T/=(.u)& Ta , d
To=$200
6&%4(60&1&64
To C /3.20 minutes
Total time taken for one way travel%
Tbus=Ta , d+Ts+Tc+To+Tm
Tbus=[P sNs+PcNc+(P s+P cPsPc )+1 ][ u (a+d )120ad]+[P s (Ns+Nsc+1 ) ]
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[( qsf)( 60 )+ k60 ]+[PC (NC+N" ,C)[0&0 (Cg )]
60 ]+[(.u)+Ta , d]+Tm
Tbus=1&64+4&$+'&+1$&0+
C =1.=/ minutes
9alculation of fleet size%
N=2( cycle length
0eadway =
(2Tbus )h
N=2( '2&'1' =22&2=22
Therefore from the analysis it is possible to reduce two buses for one hour on the route.
Sings Due To Re'u$tion in F%eet Si*e.
Assuming that the buses run for a period of /< hours, and then we have
Total number of buses that can be reduced on one route for each hour
14( 2=2$ buses per day
:perating cost of bus per day C )s
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y carrying out the optimization of the routes, it is possible to reduce the fleet size and
the number of bus stops on the route. The spacing of the bus stops has a (uite significant effect
on the efficiency of the public transport systems, by properly spacing the bus stops it is actually
possible to reduce the overall travel time which will lead to savings in time for the passengers
and also help to reduce the operating cost of the agencies. ut the bus stop spacing should be
such that it doesnt discourage the commuters from using the public transport, if the bus stops
have large spacing between them then the commuters may not prefer to walk the long distance in
order to reach the bus stop to catch a bus, on the other hand if the bus stops are located fairly
close to each other the buses have to make fre(uent stops which increases the total ;ourney time.
ased on the study carried out it is possible to change the spacing of the bus stops on the
route without affecting the commuters and bringing it to the standards specified by &ndian road
congress, by using the total cost function it is possible to reduce the number of bus stops on the
route which will help in minimizing the overall costs.
The total cost function is composed of two parts$
Access cost 9a
)iding cost 9r
Access cost can be mathematically written as
Ca=nl'a=(ps )( (s4 )(()av)=p s2
)a4 v
)iding cost can be written as
Cr=N(tr+tl )' r=N ( ( s#+ P r)( ()r )=Ns)r#+N )r(1e
ps )
These two e(uations can be combined to get a final e(uation of the form
C=( Ca+Cr )
s =[{(ps )a )4 v )r pN}+{(1e
ps)ps }]
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&t is possible to introduce a dimensionless (uantity J , where J is e(ual to
+=(4 v )r)a )pN
The final e(uation for the total cost takes the form
C=[(ps+)+{(1eps )
ps }] )r pN+N )r#8rom the above e(uation it is clear that bus stop spacing s is independent of # and I rDp>
.therefore the bus stop spacing s is solely dependent on J.The idea of optimizing bus stop
spacing with the reduction in the total cost can be formulated as under%
Co=[ps+ + (1eps )
ps ]
The final e(uation for the spacing becomes
"=(4 vpN
)r
)a)pThe values for different variables is as under
)r
)a=value of riding time comparedaccess time=6
# C walking speed C /.1 ms
D C time taken to serve each passenger C E seconds field valueB
> C number of people in bus occupancy of bus C 02
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p=density= peopledistance
=6
"=4( 1&2( 6(6(0( 6
6
Therefore ? C
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Total cost saved on the route due to optimization which leads to reduction in fleet size and
number of bus stops is e(ual to
"avings='$00000+10000=2s'%0000 1 '&$ crores