Calculation of parameters estimation on combined ... - Springer Link

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Calculation of Parameters Estimation on Combined Model of Destination, Mode, Route and Time Period Choice in EMME/2 Macro By Moon NAMGUNG* and D. E. Boyce**

At~traet

P ~ estimation o f combined nxxiels is a different p r o b l e m as a practitioners o f transportation. The transportation engineers w h o w a n t to use the c o m b i n e d m o d e l have to understand the procedure o f estirrmting p a r m ~ t e r s and its rrmthermtieal t h e o r y in detail. H o w e v e r , available software is not user fiiendly. This paper is carried out the parameter eslimation o f the m o d e l w h i c h combines the origin- 0.1, t h e n ;,7" = ~(Z~/Z~ ~

Table 1. Matrix Description

where, n means the n ~ o f iterations for estimation o f parameters. This scheme results in smaller adjustmeat in the vicinity o f the desired ratio (0.1). The procedures is repeated until the ratio is app r o x i n ~ t e l y 1.0.

l:l~n~d m m~n~p" mC'lmlll~

mC'maw~

~-vnhm~ ~

mom~of-whk:le ~

12~1r o f m~o

t~ mn~ ~ m am~ ~

~ u

Table 2. List of Tables used during the Implementatmon of Estimation Procedure ~

~

Sum oe Aura ntr~ Sum of Trmsit lxil~ Stma of Ax~o ~ 1 T n m ~ t l r i ~ ~

m~"mu~.df'

~ m of r ~ x m ~ Stma o f ~

Cnlculetio~

or T r ~ for A~o ana~ o~ T~il~ f ~ Tnm~t dlmi~ 71 of At~o ~'l of Atao

~~du~t~m~

7X ~ f T r m a t

I~dict~! ~ l u ~ m m ~ o r 71 o f T r m ~ ~v~lt~t~m f ~ 72 of Amo P r ~ U c t ~ v ~ l u c m m f o r 77 o f Auto Observ~ v a ] u e t m n f ~ P r e d i m ~ v a h t e m m for ~ v a ~ t m n fer Ptedi~dvaluetetmf~

72 72 73 73

of of of of

ll~'l~ll21n"

~"so,plja"

mrplj,kp"~pij,k3"

ms-~jt-

((rEd"~._.~"+radf"~'y~smo~'r,o~am)"

~"t~la"

both ~rk~l Ol~n~l wl~tctmf~r l~r~tic~wlt~mm~o~

~ in IIIlS"W**

"

((mcr'~"~mf'aom'*)*m~'piib~')4~"u~pija" ma'i~tt"

(r~*(=d~"~jtn,p'-~pUe,:s')An~'~j*" Cmf"aen" ~,~o,o")~"~,:~a.m" ~lL~B2a

n

'r,'~"sol~a"

Transit Trmait Au*o Auto

(m.er ~veiueterm f~- 74 of Tnmsit Pledicu~ value term for 74 of Tnmsi~

Vet. 2, N o 3 / S e p t e m b e r 1998

-',."m83t" ,,.-"xlq3g3L" ,r,',~"nlpl~4"

- 227 -

B y Moon NAMGUNG and D. E. Boyce

have to be calculated b y e a c h iteration because they depend o n the link flows.

005.

o001

The mC'pijhkp", mf'r jhks", mf'pijtkp"

OIL'S

+

],,o,, I....

and m f ' p i j t k s " m a y be obtained f r o m the combined model calculalion. Table 2 shows the matrixces used in the procedure o f ~ estimatiorL In the combined model the function o f link costs based on the link flows is usecL The function is saved in file d411.in in the E M M E / 2 data bank. Note that because It considers the p a m n ~ t e r s o f 1 and 2 for auto, the term o f function should be changed b y n e w ixtrar~ters per iteration.

.,4ooi

,i

OO3

a

4L

:

|

$

9 $

O 01 9

o 6

2

I

}

LO l l

L2 l ) 1 4 1 5 1 6

l ? 1 1 1 9 2t}

Fig, 3-a. Convergence for In-Vehicle Travel Time for Auto Parameter O0] -

0

0O09

~9 O001

~ 0007 1

4. Calculations and Results The calculations o f tmrma~ters cstin~tion were carried b y using the dam o f Chicago Regional area, surveyed in 1990. Data are adapted to the 317 sketch-zones systen~ Since the nxxiel considers two

+j

r" o

Jr

-O(]OO6

0 ~ ' 1 ', .

2

.

3

.

4

.

.

$

.

6

.

.

?

I l l ' ilium+ n n~?ln'+

.

;~

I rl

.

,

t

-00O07

$ 9 1011121]14151617111920

Fig. 3-b. Convergence for Auto Fare Parameter,

periods, first w e h a v e to f i n d the v a l u e o f 0 l&l - - - -

that produces on the desired ratio o f total trip between the peak and shoulder t i n ~ periods. The value is calculated as:

D O01a

0 l~tJ ~OOt6

P,~ = observed proportation in p e a k

i: i

J~ t.+J

~ P , ~ = observed proportation in shoul

'i" "nl" k

In order to calculate, the nxxlel was nan with a value o f zero for. Then, the valtm o f proportion should be the same, i. e. 0.5, for the peak and shoulder perioct After that, the n e w value is set b y changhag it a little until it satisfy above conditions. Atkzr adjusting the value, we Wied to estimate the parameters. Figure (3-a-c) shows the convergence procedure o f ~ estimation and relative c h ~ g e for auto per each iteration. The relative change o f 1, g a - l - ~ and 2, ga-2-a, for auto approaches zero. The relative change o f 3, ga-3-a, for auto

2 l

4

•

•

"/ I

t

0111102 10 LI 12 13 14 111 16 | ? 15 19 ~ll

Fig. 3-c. Convergence for Out-of-Vehicle Travel Time Parameter for Auto.

converged ~ 10 iterations to about 0.0. The convergence procedure o f parameters estimation and relative change for transit is depicted in Figure (4-a-d). In figure (4-a-d), ga-l-t, ga-2-t, ga-3-t and ga-4 correspond with 1, 2, 3 and 4 o f transit, respectively. T h e parameters, except for 3 o f transit, converged to about

228

KSC~ Journal o f Civil Engineering

Cafculation of Parameters Estimatlon on Combined Model of Destination, Mode, Route

"

"

ZJ IJI

IlJ2 Ills

i

t,II

t

(I,II~

|

U

.4 ,.M/~ 1

$

$

4

$

1

7

9

~pq4

|

F~g. 4-a. Convergence for In-Vehicle Travel Time Parameter for Transit ...................................................................

I.,N~

I

11 ll~ll I L I I I I 4 U I ~ I ' ~ I I I I I . ~ I I ~

9 l,/~t 7

ILINI'$$

1= ]:=

'. . . . . . .

_ __~..,

1

4

1

1

T 9 !

11 | |

12 I1 | l

I t 1~ 17 |$ 1~

Fig. 5-a. Convergence of the Ratio of Estimated and Observed Parameters for Auto.

II,III

- ~

2

25-

lllPJ$

2 I

II

l#~

r liamt,i, I~lr iI~,I-I

1,5 1'

0,01 9

#,~tl

l

$

$

9 $

6

I

I

~ lI111JlSl~l.Sl@I~II]~I 9 N

05

Fig. 4-b. Convergence for Transit Fare Parameter.

9&

. 1

(Jl7 '

8,0M

. . . . . . . CIMml~ . . . . . . . . fwr g,b-IL~JL~ 411 ' . . . . . . ~. . . . . . .[ . .~. r. . . . .~. . .m

w.ul~lt.l$&lj

i "[ *S

1:2

1=

....

.

.

1 I

.

1::1 .77. i-r .

.

.

~ 9 9 $

.

~" |

.

.

.

~t M I l l L~ l ~ 1 4 1 J

.

.

-Ikl[~

li:ltIUl.911

IJ 1

?l .| -lJ

!

$

9 5

9 7

I

]1 l e l l l s D l 4 l s l ~ l f l l l t ~

Fig. 4-d. Convergence for in-Vehicle Travel Time for T r a n s i t Bias

0.0 after 5 iterations. However, 3 parameters for transit converged after 11 item-

V o L 2, N o . 3 / S c p t ~ x ~ b e r 1998

. 3

.

. 4

. J

. $

.

. 7

. $

,, 9

10 | 1

l!

,,,,,-,~,

,

13

14 l s

.

. 16

. 17

.

. 1]1 19

Fig. 5-b. Convergence for the Ratio of Est.mated and Observed Parameters for Transit.

.

F|g. 4-c. Convergence for Out-of-Vehicle Travel Time Parameter for Transit.

1

. 2

tioI1S.

Figure (5-a-b) r c p m s ~ t s the ratio o f estimated and observexi values for each ~ter. The ratio should be converged to 1.0. As the figures, both o f them arc converged about 1.0. In this study, the ratios for each parameters got b e t w e e n 0. 9 9 8 9 to 1.001 at 20 iterations. Figure 6 shows tim value o f objective function and relative change values for peak and shoulder ~ periods. The value o f objective funelion in the figure were taken f r o m the final iteration values o f Eavns' algorithro_ The values o f objective function for peak and ~ o d d e r am virtually minimized ~ 11 immtions. Another evaluate the reasonableness o f estimates is to l o o k at the impliexl values o f fin~. This is done by calculating the ratio o f n u r a ~ c a l values o f the cost co-

- 229 -

B y Moon NAMGUNG a~d D. E. Boyce

can b e c o n d u c t e d successfully in E M M F J 2. It seems that a reasonable n u m b e r traffic f o r the m o d e l parametem to adjust. F o r e a c h adjustment o f the model paranaeter values the Evans solution algorithm for the m o d e i needs to b e iterated f o r at least 20 iterations.

I~G~0

! t

j

84

i

le,Ak.~r.~..i--~.~,

4.

-i- . b -i

o

M

5. Conclusions 2

+

4

$

7

6

~1 I # I1 12 13 14 1~ 1~ 17 l 9 1~

9

Fig, 6. Convergence of Objective Function per Iteration by Time Period.

6

~

4

z

•

, 2

]

4

5

. 6

~

:'-

.

.

.

.

~

-'" ~

-

~

r

. . . . . . . . . . . . . ?

9

~1 | 0

ll

12

L~ t 4

I1

i 16 I~I 1 9 IP

21~

Fig T. Implied Measurements of Estimates per Iteration.

efficients f o r time and cost/fare. T h e implied values are calculated as: Value o f In-Vehicle travel time = (r,./r~=)*0.6 Value o f O u t - o f - V e h i c l e travel time = (r~/n=)*0.6

In this p a p e r w e h a v e s h o w n that param e t e r estimation o f c o m b i n e d r r o d e l s o f destination, m o d e and route choice for t w o t h ~ periods c a n b e c o n d u c t e d successfully and e c o n o m i c a l l y using E M M E / 2 system_ I n d e e d the results o f thi.~ s t u d y are consistent with other research depen d e d o n research code. T h e parameters estimation is calculated b y lots o f iterations o n estimation procedure for getting accm~te pammetem. T h e relative changes f o r auto and transit are c o n v e r g e d to about 0.0 on 10 iterations. This results m e a n that the estimation proc e d u r e d e v e l o p e d in this study is reasonalble. W e w o u l d like to encourage practitioners and users o f the Elk4MFJ2 system as well as users o f c o m b i n e d rr~dels to in~ p l e m e n t this estimation p r o c e d u r e in their professional practice.

Acknowledgments

T h e y represent the travelers' implied perceptions o f trade o f f b e t w e e n time and r r o n e y . T h e rate m a y v a r y with the socio -economic status o f the travelers and also with the circurr~tances o f the trips. Figure 7 shows the c o n v e r g e n c e o f implied values. T h e implied value o f out-of-vehicle travel time f o r auto was the highest, next was o u t o f vehicle o f transit. T h e implied value o f in-vehicle travel time was the lowest at the final iterations. As the a b o v e results show the estimation o f parma~ters o f c o m b i n e d rru~els

This p a p e r was supported b y T h e University o f Illinois at Chicago and partially T h e W o ~ z w a n g University in 1998.

References 1. Abrahamsson, T. and L. Ltmdqvist, Formulation and esamatton o f combined network equihbr~'um models with applica~on to Stockholm, Transportation science, in press, 1997. 2. Boyce D. E., M~ Tafine~m and Y. Zhang, Scenario Analysis for the Chicago Region vath a Sketch Plarming ]Vlodcl o f OrigirbDcslanafion~

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K S C E Journal o f Ciwl Engineering

Calculation o f Parameters Esnmat~on on Combined Model o f Dest~a~'on, Mode, Route ...

Niode m,d Rout~ Choice, F / h a / R e p o r t s to the lllinois Depewtment o f Transportation, Spring-

field,IL, USA, 1992. 3, Boycc. D. E., and Y. Z h a r ~ Parameter Est/hum'on f o r Alternative Funcffonal Forms o f Combined Model o f Ot~n-Dez~nat~on, Mode and Route CYloice: ~ s o n s for the Chicago Region, a paper prepared at the 4Ist North Amm-ican Meetings RSAI, Ontario, ~ pp. 1 7 - 2 0 October, 1994. 4. Eh43,IFd2 User's Manual, Software Release 8, INR.O Conmaitants, Inc. 1Vlontaeal, quebec, Canada, 1994. 5. Evm~s, S. P., EX-rivation and Analysis o f Some Niodcl for Combining Trip IMstribufion and

Vol. 2, No. 3 I September 1998

- 9.31 -

Assir#m'~t, Transportation Research 10, pp. 37-57, 1976. 6, L E. Hicks, NL M~ Atxi~l-Aal, Mam'mun L/ke/ihood Eatlmation f o r Combined Travel Choice Model Pamameers, a paper to be publication at the TRB, I998. 7. Metaxat0~ Boyce D. E. et al, Implerremlang Combinetl Model o f OrigirvI:~..smmtion and Route Choice in EMME]2 System, Transportation Research Record 1493, pp. 57-63, 1995. 8. 3:. Zhang, Parameter Estimation f o r Combined Models o f Urban Travel Choices Consi.rtozt with E4ndlibriura Travel Costs, Phi). Thesis o f the university o f Illir~is at Chicago, 1995