4 Phases Analysis of the Demand

8/12/2019 4 Phases Analysis of the Demand

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Politecnico di Milano Faculty of Civil, Environmental and Territorial Engineering Laboratory of Transport and Mobility

Design department

Lesson contents

- Zoning

- Trip demand model systems

- Generation

- Distribution

- Modal split

- Choice of the route

4-phases Analysis of the Demand


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Design department

Zoning

division of the territory - plan area: area of project interventions

- on the transport systems - offer- on the system of activities - demand

- study area: external area, sensitive to interventions

- OD zones: division of plan and study areas- discretization of the territory- aggregation of data diffused in a limited number of units

- aggregation of the multiplicity of Origin and Destination places of each journey- dimensioning of the OD matrix- dependence on data acquisition- dependence on the organization of surveys

4-phases Analysis of the Demand Zoning


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Design department

Zoning

division of the territory (continued) - OD centroids: fictitious nodes of the graph

- correspondence centroid OD zone- representative point of all the significant elements of a zone

- connection with an adequate point on the graph by means of a connecting arc- barycentric point of connection



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Design department

Definition of zoningCriteria (continued)

- number / dimensions of zones: compromise between- precision and detail of the analysis- representation of intrazonal flows- calculation time

- data acquisition- preexisting administrative divisions

- to be respected by zones



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Design department

Lesson contents

- Zoning

- Trip demand model systems

- Generation

- Distribution

- Modal split



f f


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Design department

Factorization into phases

Distributionp [d/osh ]

Generation or frequency of journeysp [x/osh ]

Choice of the means of transportp [m/odsh ]

Choice of the routep [k/odshm ]

Number of users in a zone on [o ]

OD for way, reason, time band and routed od [s,h,m,k ]

Socio-economic characteristics SECharacteristics of the service level T

4-phases Analysis of the Demand Trip demand m odel sys tems

P li i di Mil F l f Ci il E i l d T i i l E i i L b f T d M bili


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Design department

Factorization into phases

TSETSETSETSE ,/,/,/,/ oshdmk poshd m poshd posh x xpon s,h,m,k d iii x

iiiod

DEMAND

average valueof journeys

of the category i over a reference

period h with

choice dimensionso , d , s , m , k

numberof people

of category i in the

zone oforigin o

GENERATION

fraction of peopleof the category i

in omaking

x journeysfor the reason s

in the time band h

Result:

margins of the OD matrix

DISTRIBUTION

fraction of peopleof the category i who moving fromo

for the reason s in the time band h

have a destination d

Result :

totalOD matrix

MODAL SPLIT

fraction of usersof the category i

who movingbetween o and dfor the reason s

in the time band h use the means m

Result :

modalOD matrices

CHOICE OF THEROUTE

fraction of usersof the category i

who movingbetween o and d for the reason s

in the time band h using the way m

follow the route k

Result:

flows of link

(ASSIGNMENT)


P lit i di Mil F lt f Ci il E i t l d T it i l E i i L b t f T t d M bilit


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Design department

Random utility models for partial shares

description of the procedure of choice for the two-dimension case:Choice of destination d and mode m(o, s, h, i omitted)

example:

Two possible representation with different structures of random utility models:

1. Multinomial Logit2. Hierarchical Logit


dmd md dm V V U /

d md md m

d d

C T V

SHOPS V

/3/2/

1

Politecnico di Milano Fac lt of Ci il En ironmental and Territorial Engineering Laborator of Transport and Mobilit


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Design department

1.representation with multinomial logit

distribution of random residues dmbased on a Gumbel (WG) variable having null average and parameter :

Factorialization of p[dm] in p[m/d] and p[d]:


' '/' /)(/)(

'/''

/

d d m

V V

V V

d md

d md

ee

=dm p

mmV V =V V V V =d m p dmd mdmd mdmd md dmd md 'Pr Pr ]/[ '/'/'/'/

'

/

/

/'

/

/

m

V

V

d m

d m

ee

=d m p

Politecnico di Milano Faculty of Civil Environmental and Territorial Engineering Laboratory of Transport and Mobility


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Design department

1.representation with multinomial logit

stability with respect to maximization

max of i.i.d. WG with parameter = i.i.d. WG with parameter and average:


E U d

= E V d + max m' V m'/ d + dm '( ) = V d + q ln eV m'/ d /qm' = V d + q Y d

'/''max dmd mmd d V V U

d d d d Y V U '

)/(

)/(

''

d

Y V

Y V

d d

d d

ee

=d p



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Design department

2.representation with hierarchical logit

Elementary alternatives (dm) grouped by destination Group I d contains alternatives related to destination d (d,m)

residues dm based on a Gumbel (WG) variable having null average and parameter d

Factorialization of p[dm] in p[m/d] and p[d]:


'

/

/

/'

/

/

m

V

V

md m

md m

ee

=d m p

U dm

= V dm

+ dm

= V d

+ V m/d

+ d

+ tm/d

)()6/(, 22' md d dmdm Var Cov

p d [ ] = e(V d / d )+ d Y d

e(V d ' / d )+ d Y d 'd ' d

md =


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Design department

Generation

emission or trip frequency models:estimate the mean number of trips d io[sh ] undertaken in the period h for thepurpose s by the users belonging to category i with origin in zone o

= number of user in zone o belonging to category i= mean number of trips undertaken by the generic user

in the period h , for the purpose s and with origin in zone o

total journeys generated (or attracted ) by each origin (destination) zone

its possible to define margins of the total OD matrix

4-phases Analysis of the Demand Generation

][][][ oshmon shd iiio

][oni

][oshm i



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Design department

habitual or systematic journeys (home-work or home school) : mobility choice thatcant be modified with each journey

use of descriptive models (statistics, regressions)

not systematic journeys (home-shopping or entertainment): choice of journey thatcan be modified with each journey

use of behavioural models (random utility: logit)

Composition of journeys with respect to a zone


GEN

INT

OUT

INATT



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y , g g y p y

Design department

Generation-determining elements

- strong dependence: on the system of activities- residential settlements- production settlements- services

- strong dependence: on users characteristics - age, income, etc.

- average dependence: on the transport system- overall infrastructures or transport services- accessibility




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y , g g y p y

Design department

Descriptive formulationIndex per category

direct estimate of the average no. of journeys mi[osh ] category of users

NO explanatory variables

Example: type of trips, type of user

- Home-Work, industry: 1,024- Home-Work, services: 1,084- Home-School, primary: 0,84- Home-School, Italian middle: 0,87- Home-School, secondary: 0,86- Home-Shopping, non-durable goods: 0,25- Home-Shopping, durable goods : 0,11- Home-Services: 0,16- Home-Entertainment: 0,27



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Descriptive formulation

Explanatory variables

- generated journeys- resident population- age, sex, income (availability to pay)

- active population- type and density of houses- number of cars, number of driving licenses

- attracted journeys- local units per category- employees per category- number of shops, branches, banks, public offices, etc.- hospital beds- type and dimensions of schools and universities- type and dimensions of gyms, cinemas, etc.




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21Design department

Behavioural formulationPartial aliquot part individual journey for the category i

part of individuals of the category iwho, being in o,

make a number x ofjourneysfor the reason s

in the time band hx = 0,1,2 or more


TSE , x/osh p xoshm i x

i



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Behavioural formulationHyp: limited

reference period h

only one probable journey

Binomial Logit - 2 alternatives: journey YES (x=1) journey NO (x=0)


p i 1 / osh[ ] = eV 1/ osh

i / x

eV 0/ oshi / x + eV 1/ osh

i / x



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Behavioural formulationIp: wide reference period h

more than one probable journeys

Multinomial Logit - n alternatives:

probability to make x journeys=

probability to choose between 1, 2, , n alternatives


n j

V

V i

xi

osh j

xi

osh x

e

e =osh x p

..0/

/

/

/

/


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NOTRIP SOF SOS V ACC WOM INC AGE OCC CARV

NOTRIP

TRIP

987

654321

Example of generation model

CAR = disponibility of car

OCC = occupied (0 = no, 1 =yes)AGE = age class (0 if > 35, 1 if


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Lesson contents

- Zoning- Trip demand model systems

- Generation

- Distribution

- Modal split





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Components of modelling and their relationsOffer Demand

zoning

connection of centroids

impedances between centroidsdistribution

total demand flows

modal service levelsmodal split

modal demand flows

arc costschoice of the route

routes used

arc flowsassignment

traffic flows assigned networkarc costs charged

recalculation of link flows

4-phases Analysis of the Demand Dis t r ibu t ion

INT OUT

IN TRA

Centroidi esterni

Centroidi interniallarea di Piano

Archi connettori

Archi reali

Nodi reali

Confine o cordonedellarea di Piano

Centroidi esterni


Archi connettori

Archi reali

Nodi reali




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Distribution

journeys exchanges by each couple of OD zones elements of the total OD matrix

demand flows or indefinite route flows


Partial aliquot part individual journeyfor the category i

part of users of the category iwho moving fromo

for the reason sin the time band h

have a destination d

oshd p i /



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Distribution-determining elements

- strong dependence: on the system of activities- location of residential and production settlements and services on the territory

- strong dependence: on users characteristics - job, level of education, propensity to travel, income

- strong dependence: on the transport system- distance between OD zones




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Explanatory variablesTerritorial characteristics SE

attractiveness of the zone of destination Ad

- number of employees, school members, shops, etc.- shadow variables specific of some zones (example: city centre)

to carry out the activity s

Characteristics of the offer T

general cost of the journey C od

- distance (crow-fly distance or average distance of the several modal routes)- time on foot

- time on board- monetary cost




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Descriptive formulationGravitational model

formal analogy with Newton's law of universal gravitation


)()(

)()(

)()(

)(][][][

ceC C f

bC C f

aeC f

C f shd shd shd

od

od

C od od

od od

C od

od d ood

d d = d od o (1)

d o = d od (2)d



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Descriptive formulationGravitational model

to satisfy only one condition (1) or (2)

simply constrained gravity model


d od [sh ] = d o [sh ] p[d / osh ]

p[d / osh ] = d d [sh ] f (C od )

d d '[sh ] f (C od ' )d '



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The most used behavioural formulationComplete notation


'

/

/

/'

/

/d

V

V i

ioshd

ioshd

e

e =oshd p

Systematic utility

linear combination based on theparameters k

of the characteristics of the possibledestinations d

in relation to the zone of origin o

j jd jd X V


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Behavioural formulation

Hypothesis 1:choice of the whole zone of destination d

Ad = variable of attractiveness of zone dCod = disutility of going from o to d

Hypothesis 2:not treated here


'

'2'1

21

/d

C A

C A

od d

od d

e

e =oshd p



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37Design department

Lesson contents


- Generation

- Distribution

- Modal split




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39Design department

Modal split

demand share per means of transport modal OD matrices

Modal split-determining elements

- no dependence: on the system of activities- strong dependence: on users characteristics

- age, income, social condition , job, - possession of a car, of a driving license- personal propensity to a certain means

- strong dependence: on the transport system- characteristics of the service levels of each means- journey time, waiting time at stops and in a queue, time to look for a car park- fare (monetary costs)- fuel, toll, parking cost- routes on foot

- crowding, risk, comfort, etc.

4-phases Analysis of the Demand Modal spl i t



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General formulationPartial aliquot part individual journey for the category i

part of individuals of the category i

who moving from o to d for the reason s in the time band h use the means m


TSE ,m/oshd p i



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The most applied formulations

behaviouralEquivalent alternatives

Multinomial Logit

Different levels of correlationbetween perceived utilities

of different groups of means(individual and collective means and/or services of the same means)

Hierarchical Logit



h l f h d


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Behavioural formulationAlternatives utility functions

Systematic utility

linear combination based on the parameters j of the characteristics of the means m


j jm jm X V


4 h A l i f h d


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Behavioural formulationVariable inclusive of the characteristics of the choice of the route

service level on the lower choice dimension

characteristics of the several routes availablefor the several means of transport present in the OD relations

logsum satisfaction variable

overall general cost: perceived average utility of the characteristics of ALL alternative routes k availableto reach the several destinations from the several origins

with a given means of transport


' /'

explnk mk m

V =Y


4 h A l i f h D d


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Example of hierarchical logit model of mode and parking choice



4 h A l i f h D d


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Behavioural formulation Example



4 h A l i f h D d d l l


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4 h A l i f th D d


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Lesson contents


- Generation

- Distribution

- Modal split




4 h A l i f th D d Ch i f h


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Components of modelling and their relationsOffer Demand

zoning connection of centroids

impedances between centroidsdistribution

total demand flows

modal service levelsmodal split

modal demand flows

arc costsChoice of the route

routes used

arc flowsAssignment

traffic flows - assigned networkarc costs charged

recalculation of link flows

4-phases Analysis of the Demand Choice of the route

INT OUT

IN TRA

Centroidi esterni


Archi connettori

Archi reali

Nodi reali


Centroidi esterni


Archi connettori

Archi reali

Nodi reali



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4 phases Analysis of the Demand Ch i fth t


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50Design department

Input data

- graph of the network- geometrical and functional characteristics of links

Operating method

- drawing of the graph of the network

with the characteristics of linksin particular: cost functions - application of optimization algorithms

to find a route (or routes)at a minimum general cost

- contextual implementation of assignment



4 phases Analysis of the Demand Choiceofthero te


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Route at a minimum cost


Minimum routeof all possible routes

connecting the centroids h and k Origin hc entroid

Destination k centroid

Connecting link

Connecting link


4 phases Analysis of the Demand Choiceoftheroute


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General formulationPartial aliquot part individual journey for the category i

part of users of the category i

who moving from the zone o to the zone dfor a reason sin the time band husing the means mfollow the route k


TS E ,oshdmk p i /




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53Design department

The most applied formulations

behaviouralElementary mechanisms of choice

general cost of links

general cost of routes

characteristics of the offer T related to the service level offered

by links (and nodes/intersections) of the single modal networks





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Behaviours of the choice of the routePreventive choice

totally made before the journey- road network ( continuous service)- low frequency and high quality collective services

Adaptive/preventive choice (mixed)

1 phase: choice preliminary to the journey2 phase: adaptations during the journey

- congested road network- high frequency and low quality collective services

Model specification- definition of choice alternatives- definition of the set of choices admissible- definition of the model of choice among alternatives





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Behaviours of the choice of the routeModel specification

- definition of choice alternatives- choice among several routes (sequences of links and nodes)

- definition of the set of choices admissiblevery high number of routes necessary to limit the paths to evaluate- theoretical approach probability to belong to K

odm

- exhaustive approach all admissible k - selective approach definition of admissible routes heuristic rules, criteria

- definition of the model of choice among alternatives- definition of the characteristics of V k - definition of the distribution law of k

functional form of the probability of choice: logit, probit, C- logit,



4-phases Analysis of the Demand Choiceoftheroute


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Behaviours of the choice of the routeSelective approach

- topological criterion- admissible route each link implies getting far from the origin

( Zo,i is the minimum cost to reach i from o )

- cost comparison criterion- admissible route general cost not higher than a share ( ) of the minimum cost

- progressive criterion- the first n routes of minimum general cost are admissible

- multi-characteristic criterion- the minimum routes based on several components of the general cost are admissible

ex.: time, length, toll, motorway distance,

- behavioural criterion- the routes free from non realistic behaviours are admissible

ex.: repeated entry into and exit from the same motorway,

- distinguishing criterion- the routes that differ for at least a share of their general cost are admissible


k K od if Z o,i < Z o, j (i,j) k

min1 if g g K k k od




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Behaviours of the choice of the routeEnumeration of the routes

- explicit enumeration- all possible routes that connect the several od couples are identified- operation that is not feasible on very wide, complex and thick networks - operation that is theoretically required by some methods of choice of the route- operation necessary in the selective approach

- implicit enumeration- among all the possible routes only one limited set is identified- the limited set is defined by applying some admissibility criteria- operation used in the exhaustive approach to limit its complexity- some algorithms allow to use the implicit enumeration



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59Design department

Continuous service systems

If each path attribute z nk is the sum of the corresponding link variables r nl

path cost gk will be purely additive :

= incidence matrix links/routes, lk

= (0 ,1)cl = average perceived cost of the link l

Non additive costs (presence of shadow variables, non linear laws , ):

4 phases Analysis of the Demand Choice of the route

n nk nk z g

crrg TTT

n n nnnn ADD

l l lk l n nl nlk n l nl lk n ADDk cr r g

l nl lk nk r z

NAk

ADDk k g g V




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60Design department

Continuous service systemsFunctional forms of the probabilities of choice

Hyp.: Var k 0

deterministic utility

model of choice all or nothing (AoN)

- p[k/odsm ] = 1 if g k < g h h k h , k K odm = 0 otherwise

for computational reasons are often applyed with implicitpath enumeration to very congested network


k k k C V U




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61Design department


Hyp.: Distribution k based on Gumbel i.i.d. r.v. with

Multinomial Logit

Problem: routes of K odm with common branches

Cov kh 0 NO i.i.d. residues

inapplicability of the multinomial Logit


od m

h

k

K h

g

g

e

e =osdmk p

/

/

/




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Hyp.: Distribution k based on the Multivariate Normal (MVN) r.v.

probit

- variance: Var [ k ] = z k

- co-variance: Cov ( k h) = z hk z k = attribute of path cost (like distance)

z hk = attribute of path cost only for links belonging to both paths ( h and k)

possibility to evaluate the routes with common branches Problem: difficolty to calculate

numerical methods (Monte Carlo)

4 phases Analysis of the Demand


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66Design department

Continuous service systemsMultinomial Logit model of choice of the route with common branches

ExampleModel of choice of the route for heavy vehicles in extra-urban areas

- TT = journey time [ h] - M c = monetary cost [ L 10 -3]

- ML = distance covered on a motorway [ km] - MinT = dummy variable for the minimum time route ( 0/1 ) - MaxM = dummy variable for the route with the maximum distance on a motorway ( 0/1 ) - HVP = dummy variable for the minimum time route for perishable or high value goods ( 0/1 ) - CF k = overlapping factor of the route - VOT = value of time[ L/h ]

p y

TT[h]

M c[L/1000]

M L[km]

MinT0/1

MaxM0/1

HVP0/1 CF k

VOT[L/h]

2Lratio

-4,525 -0,033 0,013 -0,9524 137.121 0,176 -2440

-3,110 -0,031 0,012 1,785 -0,8390 100.323 0,250 -2222

-5,440 -0,036 0,012 2,292 2,585 -1,2960 151.111 0,306 -2055

-3,650 -0,030 0,009 3,370 3,702 3,788 -1,2050 121.667 0,450 -1650

k c j CF HVP MaxM MinT ML M TT V 7654321




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67Design department

Continuous service systemsMultinomial Logit model of choice of the route

ExampleModel of choice of the route in urban areas

- PTT = journey time on sections of the primary network [ h] - STT = journey time on sections of the secondary network [ h] - L = total length of the route [ km] - HVP = dummy variable of choice of the route on a motorway ( 0/1 ) - NST = number of intersections with traffic lights - NLT = number of left turns

p y

HDV NLT NSI LSTT PTT V j 654321

PTT

[h]

STT

[L/1000]

L

[km]

NSI NLT HVP

0/1

2 %ri ght Lr atio

-16,462 -61,257 -9,601 -0,209 -2,296 3,158 0,403 0,532 884.344


4-phases Analysis of the Demand Bybl iography


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Some images and numerical examples

in these slides are taken from:Ennio Cascetta, Transportation systems analysis models and

applications, second edition, Springer, 2009

Italian version:Ennio Cascetta, Modelli per i sistemi di trasporto- teoria e

applicazioni, UTET Universit De Agostini Scuola SpA, 2006

p y y g y

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4 Phases Analysis of the Demand