14th Behavior Modeling in Transportation Networks, UTSat. 26 September. Early bird session.

A context-dependent scheduling model
considering measurement errors
in pedestrian network

Yuki Oyama* and Eiji Hato
* Ph.D. Candidate / The University of Tokyooyama@bin.t.u-tokyo.ac.jp

Behavior in Networks Studies Unit	Table of Contents
1. Introduction :*Part 1	– City Center Sojourn of pedestrians

2. Behavior Model :– Pedestrian dynamic scheduling model– Context-dependent energy

3. Measurement Model :– Probe Person data with GPS technologies– Detection of pedestrian activity pathsPart 2	

4. Case study :– Model Estimation and Results

5. Conclusions

Part 3	Time use pattern in pedestrian network
Development
around station

Large scale buildings
No. of visitors 	

1Urbanrenovations

Small scale projects
Frequency / Duration /…	

How people spent their time in these districts?	

Target | City Center Sojourn2• City Center Sojourn refers to pedestrian scheduling behavior incity centers, which includes a sequence of moving (travel) andstaying (activity) decisions.	

Time	Exit	Sojourntime	Entry	Space	(About 1 km square)	

Target | Pedestrian scheduling

3

Activities can be generated (walking) context-dependently	•••

Spatial attributes (stumbling on an attractive shop,… )Activity history (finding next shop for goods she wants, …)
Social interaction (a friend says he wants to drop in a café,…) …

Pattern is not alternative but
result of dynamic schedulingprocesse.g.; Habib (2011)	

Activities (staying) do notalways decided to conduct
before travels (moving)Review | Scheduling models
1. Markov chain	

4

2. Time allocation	

Lerman (1979),
Borgers and Timmermans (1986)	

3. Utility maximization	
Bowman and Ben-Akiva (2001),
Recker (1995)

Bhat et al. (2005),
Fukuyama and Hato (2013)	

TimeTime

T : Time budget

t=2
t=1

t2

t2

t=3

ABt1

CBAt1

CABCSpaceSpaceSpaceK

pt (i, j)∑t = TkmaxU

k=1◯ ordered	

× random ordered	◯ ordered	× separated	△ semi-separated	◯ linked	× independent	

× independent	

◯ context-dependent	( but only at the time )	

( pre-trip )	

( pre-trip )	

Model | Dynamic scheduling model
Activity = Time allocation behavior to a certain ’space’	-Staying : duration time choice in a certain ’node’ 	n ∈ STimeNodeSpace-

Moving : duration time choice in a certain ’link’ l ∈ STimeLinkSpace

5Model | Dynamic scheduling model

5

Activity = Time allocation behavior to a certain ’space’	-

Moving : duration time choice in a certain ’link’ l ∈ S
Staying : duration time choice in a certain ’node’ 	n ∈ S

TimeDynamic scheduling model in space
1. Activity generation model
tl5

Continue or Finish activities ?
*‘Continue’ means moving next space*‘Finish’ means moving out of districttn5

FinishContinuelink1

tl1

tl2
link2

link3tl3What this decision is based on?

tl4
node5

2. Time allocation model
Duration time choice in the space

link5

link4

Spacemax uk (tk )Model | Activity generation model6

Is it enough with only time constraints ?	
350

∑t

300

kk=1

250

tour ID•K•

ID: 220 (67.3%)

200

Non-mandatory tour (shopping,eating, recreational, other activities
are included).
Sojourn time (cumulative duration)is continuously distributed.

150

100

•50

0484.3min(max.)

050

100

150

200

250

300

350

400

450

500

We cannot explain the sojourntime differences among tours by
only time constraint.

Sojourn time of tour (min.)

We have to consider: 	

Psychological (personal) concept as resource 	Model | Activity generation model

7

Psychological mechanisms in behavior modeling	- Need	 （Maslow, 1943; Arentze and Timmermans, 2004; Nijland et al., 2013)	
- Satisfaction	
（Pattabhiraman et al., 2013)	
- Satiation	 （MacAlister, 1982; Bhat et al., 2005)	
need- For a particular activity- Monotonicity	

utility0undu(t) =need = f (t)0dayt0time‘Energy’ : personal resource for engaging in activities.	
••All of activities in a tour have ‘energy’ in common.
Energy decreases by engaging activities, and can increase based on context.

Model | Activity generation model8

Step1: Initialization
n=0
Remaining energy stock :Remaining energy :E (n) = E

E (n+1) = Ei,d − Ec(n) + Eg(n+1)

Step2: Conducting an activityt (n)Activity duration choice :ec (t (n) )Calculating energy consumption :E

Update of stock :(n)= E(n)ec (t (n) )Energy consumption :nEContext-dependent energy gain (or loss) :eg (c(n) )E(n)g= ∑∑γ ki I ki + ∑δnj snj
k=1 i

E (n) = E (n) + eg (c(n) )Step6: Finish district sojourn(2)n

Step4: Update of stock

No= ∑ ec (t (k ), x (k ) )Energy gain (or loss) :Step3: Preparation for next activity

E (n) > 0(n)ck=1n := n + 1

Step5:(1)Yes

I nisnjj: Activity history variables: Spatial attributes variables(3)Model | Pedestrian scheduling model

9

Activity generation model	
(1)'

E (n) = Ei,d − Ec(n−1) + Eg(n) + ε

ε ：random error term (i.i.d. gumbel distribution)
If energy is greater than zero, the sojourn will be continued, otherwise finished.

Pr(continue) = Pr(E (n) > 0)Time allocation model	 (Habib, 2011)	
*k=1: next activity, k=2: composite activities
21exp (ψ k zk + ε 'k ) (tkαk −1)
k=1 α ks.t., t1 + t2 = T

max U(tk ) = ∑α k ：satiation parameter ( < 1)zk ：vector of variables

ε 'k ：random error term (i.i.d. gumbel distribution)(4)(5)

ψ k ：vector of weights

Model | Pedestrian scheduling model
Joint probability :10Habib(2011)*

Pr(continue ∩ Time = tk )−2$ J (ε ) − ρ J (ε ' ) '" 1− α1 1− α 2 % 1" −(V '2 −V '1 ) % )" −(V '2 −V '1 ) %,dck )=$+' ⋅ exp $' ⋅ +1+ exp $'. ×Φ &&)#& *#&T − tk & σσσ
1− ρ 2# tk%(where,V 'k = ψ k zk + (α k −1)ln (tk )(6)J(ε ) : the inverse of CDF of standard normal distribution (Lee, 1983)

MLE (Maximum Likelihood Estimates)" nδic %L = ∏ $∏ ( Pri (continue ∩ Time = tk )) '&i=1 # k=1
I*Khandker M. Nurul Habib (2011). A random utility maximization (RUM) based dynamic activity scheduling model:
Application in weekend activity scheduling, Transportation, Vol.38, pp.123-151.

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Part 2 : Data processing*

1. Introduction :– City Center Sojourn of pedestrians

2. Modeling :– Pedestrian dynamic scheduling model– Context-dependent energy

3. Measurement Model :– Probe Person data with GPS technologies– Detection of pedestrian activity paths

4. Case study :– Model Estimation and Results

5. Conclusions

Part 2	

Data | Probe Person survey
Methods :11GPS (automatic) m̂ = ( x̂, tˆ)Latitude / Longitude (a coordinate)
Timestamp (at the interval of 5~30 s)••+ Web diary a = (x, t −, t + )Trip purpose
Transportation mode
+ personal information••

Personal day-to-day data
Measurements :m̂1:J d = (m̂1,..., m̂ j d ,..., m̂J d )Reported activity episodes :a1:Rd = (a1,..., ar d ,..., aRd )iiwhere,iiii

i : an individual, d : a day

Data | Probe Person survey
Reported path ():m̂ = ( x̂, tˆ)

12Timetm̂38 = m̂J diar = (x, t −, t + )There can be dropped (nonreported) staying activity.
• Measurements have notconnected with ‘space’ yet.
(and it has measurement error)

m̂30
m̂20

•

We need tom̂19

ar
1

m̂11

m̂10
m̂2
m̂1

x1r

1. Label measurements (‘moving’ or ‘staying’)
2. Connect measurements with ‘space’ (node / link)xSpaceData | Detection of activity paths

13

Step1: Classification of moving or staying
Step1-1: Comparison travel timemin(ttk,k+1 ttk,k+1) > Tmin

NoLabelingm̂k,k+1
1:J: ‘move’minttk,k+1= d(xk , xk+1 ) / vw

Yes

Step1-2: i = 1tˆi+1 tˆi > Tmin andd( x̂i , x̂i+1 ) / (tˆi+1 tˆi ) < vmin

No
Step1-3: j = i~ptˆi tˆp > Tmin andd( x̂ j [i,p], g) < ri =: i+1NoLabeling−ttk,k+1 = tk+1
− tk+ : Reported travel time

Yes Labeling(8): Shortest path travel timem̂ ik,k+1 : ‘stay’

p =: p+1
Yes Labelingk,k+1m̂ i:p: ‘stay’k,k+1

Centroid of m̂i:ppp1gi:p =(∑ x̂ jlat , ∑ x̂ jlon )p − i +1 j=i
j=i

(9)

m̂ ik,k+1 : ‘move’

Noi=JYesk =: k+1*Tmin = 180s, vw = 1.4m / s, r = 50m

Data | Detection of activity paths

14

Step1: Classification of moving or staying
TimeTimettm̂38 = m̂J da1eim̂30m̂20m̂11m̂10x1r×m̂30m̂19a1rm̂11m̂2
m̂1im̂20m̂19a1rm̂38 = m̂J dm̂10xSpacem̂ = ( x̂, tˆ, 'move')m̂2
m̂1×x1r

xSpacem̂ = ( x̂, tˆ, 'stay')

Next: Connect activities with ‘space’ (move - link / stay - node)Data | Detection of activity paths

15

Step2: Estimation of activity space for ‘stay’ data
Step2-1: Candidate set generation
Universal set:

U N = {n : n ∈ S}

Space frequency score from day-to-day data:i,dfni = ∑∑δk,n,di,dδk,ni,dfn = ∑∑∑δk,nkid(10)k: 1 if individual i stay n for activity k on day d, otherwise 0.

Importance Sampling using MCMC method
Adoption rate of i :ri = Pi / Pj = exp(Vin ) / exp(Vjn ), Vin = ∑ βnj X nj + w1 fni + w2 fnj

Finally we get a subset:

CiN ⊂ U N

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Data | Detection of activity paths

16

Step2: Estimation of activity space for ‘stay’ data
Step2-2: Probability calculation
Prior probability:e.g.; Danalet et al. (2014)

Pi (n) = exp(Vin ) / ∑ exp(Vim )Measurement probability:(12)m∈CiN

P(m̂ p:q | n) = P( x̂ p:q | xn ) = Π qj=p P( x̂ j | xn )2%"(x̂−x)1
P( x̂ j | xn ) =exp $$ − j 2n ''2σ2πσ#&(13)* We assume that measurement error is only localization σProbability of space n for ‘stay’ measurement setm̂ p:q :P(n | m̂ p:q ) = a ⋅ P(m̂ p:q | n)⋅ Pi (n)(14)

Data | Detection of activity paths

17

Detected activity path:
Step2: Estimation of ‘stay’ spaceTimeTimem̂ = ( x̂, tˆ, 'stay')−a6+

a = (n, t , t )tl5

a5 tn5Space

Step3: Estimation of ‘move’ space(Map-matching)m̂ = ( x̂, tˆ, 'move')a = (l, t −, t + )

a2

a1

tl1

link1

link2

a3
tl2
link3

a4 tl

tl3

4

node5

link5

link4

Space

Activity sequence with space

a1:M d = (a1,..., amd ,..., aM d )

Lon.

i

Lat.

ii

Part 3 : Case study in Matsuyama city*

1. Introduction :– City Center Sojourn of pedestrians

2. Behavior Model :– Pedestrian dynamic scheduling model– Context-dependent energy

3. Measurement Model :– Probe Person data with GPS technologies– Detection of pedestrian activity paths

4. Case study :– Model Estimation and Results

5. Conclusions

Part 3	Case study | City center of Matsuyama

18

Matsuyama city :Data	RussiaChina••
Matsuyama city••

D.P.R. Korea

Korea

Tokyo

Ehime, JapanN

200km

Ehime prefecture, Shikoku
regionPopulation: 516,637(December 1, 2010)
Area: 428.86 sq. km
Density: 1,204.68/sq. km

Case study | City center of Matsuyama
City center of Matsuyama :••19

Matsuyama
castle2 department stores / 2 malls
Various retails andrestaurants are locatedaround the streets.

Prefectural office

ParkMuseumDepartment
store

LibraryTram
City hallMallStationŏġ

Department
store

YokoMall

gaw

ara

line

Ishite riverĲııŮġ

About 1.5 km square

Case study | PP survey in Matsuyama

20

Data collection :Survey

Weeks

No. of monitors

Data (trip)

CityCenterPP2007 2007/02/19~2007/03/22

484

7,810

PP survey 2007A

2007/10/29~2008/01/21

12508

17,697

PP survey 2007B

2007/10/29~2008/01/21

12205

14,706

Bike sharing PP

2009/02/21~2009/03/07

215668Elderly PP 20102010/11/18~2011/01/31

1230

1.380

42842

42,261

Total

Period-> 1582 sojourn tours (non-mandatory) were observed

Estimation | Variables of Energy
E (n+1) = Ei,d − Ec(n) + Eg(n+1)

Remaining energy
Initial stock of energy- Female dummy (sex)- Car inflow dummy (mode)- Dist. between Entry point and Main
(Location of entry point)

Ei,d = ∑α k xkkn

Energy consumption

E= ∑ ec (t (k ), x (k ) )(n)ck=1s
By staying : ecs = (βtime+- Shopping purpose dummy- How many times∑ β x )⋅ ts sk kkmmm

By moving: ec = (βtime + β speed s +∑ β x )⋅ tm mk kk

Energy gain (or loss)- Sidewalk width- Shooing street dummy- Cumulative number of activities- Previous trip purpose

Eg(n) = ∑γ ki I ki + ∑δnj snji21j- Dist. from EP or Main facilities- Shopping street dummy

Estimation | Results
ραcαmαsα1α2α4α5β1β2β3β4β5β6β7γ1γ1γ2γ4γ5γ4γ5Variable
Parameter
Correlation
0.048
Satiation Parameter of composite
0.594
Satiation Parameter of moving-3.196
Satiation Parameter of staying-0.176Discrete choiceConstant
5.354
Female dummy-0.170Log(EP-Main dist.(km) + 1)
0.164
Car inflow dummy
0.632
Basic parameter of time (min.)-0.004
A Number of trips
0.002
Shopping dummy-0.003
Basic parameter of time (min.)-0.264
Walking speed (m/s)-0.063
Sidewalk width (m)0.070
Shopping street dummy-0.240
Cumulative stay activities-0.986Cumulative move activities
0.638
Cumulative shopping stays
0.246
Previous activity : eating
0.364
Previous activity : Main
-1.957Dist. from EP-0.040Dist. from Main
-0.23022t-value
0.90
12.98 **
-93.23 **-8.92 **
26.03 **
-1.52
11.07 **
5.06 **-6.75 **
6.74 **-2.60 **
-7.15 **
-8.49 **
6.42 **-3.72 **
-17.65 **10.78 **
3.67 **
1.82-14.24 **-2.60 **
-14.52 **Variable

βmc
βtime1βtime2βtime3βtime4βtime5
βtime6βtime7βtime8βms
βtime9βtime10βtime11βtime12βtime13βtime14
βtime15

Continuous choice (move)
Constant
Elapsed time (min./10)
Cumulative stay activities
Cumulative move activities
Link length (m)No. of lanes
Sidewalk width (m)Shopping street
Street trees
Continuous choice (stay)Constant
Elapsed time (min./10)
Cumulative stays
Cumulative moves
Public facilities
Department store
Shopping street
No. of retails
Observations
Initial Likelihood
Final Likelihood
Rho square (adj.)

Parametert-value-1.0540.006-0.004-0.0060.024
0.104-0.067
0.665-0.057-5.17 **
2.55 **-0.16-1.13
21.56 **
2.98 **-2.49 **
2.99 **
-0.56

2.368
-0.004-0.175-0.0420.113-0.564-0.606-0.02910.89 **
-0.86
-4.87 **
-4.45 **
0.99
-4.78 **
-3.86 **
-2.48 **
7247
-24949.15-18855.90
0.243

Conclusions•

To capture context-dependent activity generation andscheduling process in pedestrian behavior,•

we incorporated “energy” into the scheduling model anddescribed a sequential time-allocation behavior tospaces.
•And using PP data, we detected activity paths with space.

•As a result, it was clarified that the energy consumption and gain
process are dependent on some behavioral and spatial

context variables.

23

Thank you for your attentions!!
Questions?	

Contact: oyama@bin.t.u-tokyo.ac.jp 	
or oymyk.dom@gmail.com