Urban Change and Spatial Interaction

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NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

URBAN CHANGE AND SPATIAL INTERACTION

P i o t r K o r c e l l i

November 1980 WP-80-161

P a p e r p r e s e n t e d a t t h e Workshop o n U r b a n S y s t e m s M o d e l i n g , M o s c o w , S e p t e m b e r 3 0 - O c t o b e r 3 , 1980

W o r k i n g P a p e r s a r e i n t e r i m r e p o r t s o n w o r k o f t h e I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s a n d h a v e r e c e i v e d o n l y l i m i t e d r e v i e w . V i e w s o r o p i n i o n s e x p r e s s e d h e r e i n d o n o t n e c e s s a r i l y r e p r e - s e n t t h o s e o f t h e I n s t i t u t e o r o f i t s N a t i o n a l Member O r g a n i z a t i o n s .

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS A-2361 L a x e n b u r g , A u s t r i a

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FOREWORD

D e c l i n i n g r a t e s o f n a t i o n a l p o p u l a t i o n g r o w t h , c o n t i n u i n g d i f f e r e n t i a l l e v e l s o f r e g i o n a l economic a c t i v i t y , and s h i f t s i n t h e m i g r a t i o n p a t t e r n s o f p e o p l e a n d j o b s a r e c h a r a c t e r i s t i c e m p i r i c a l a s p e c t s o f many d e v e l o p e d c o u n t r i e s . I n some r e g i o n s t h e y h a v e combined t o b r i n g a b o u t r e l a t i v e ( a n d i n some c a s e s a b s o l u t e ) p o p u l a t i o n d e c l i n e o f h i g h l y u r b a n i z e d a r e a s ; i n o t h e r s t h e y h a v e b r o u g h t a b o u t r a p i d m e t r o p o l i t a n g r o w t h .

The o b j e c t i v e o f t h e Urban Change Task i n I I A S A ' s Human

S e t t l e m e n t s and S e r v i c e s A r e a i s t o b r i n g t o g e t h e r a n d s y n t h e s i z e a v a i l a b l e e m p i r i c a l and t h e o r e t i c a l i n f o r m a t i o n o n t h e p r i n c i p a l d e t e r m i n a n t s and c o n s e q u e n c e s o f s u c h u r b a n g r o w t h a n d d e c l i n e .

I n t h i s p a p e r , P i o t r K o r c e l l i d e a l s w i t h i n t e r r e l a t i o n s h i p s between u r b a n form, s p a t i a l i n t e r a c t i o n , and t h e i n t e r - u r b a n p a t t e r n s o f p o p u l a t i o n and employment c h a n g e . S e v e r a l c o n d i -

t i o n s a r e i d e n t i f i e d f o r t h e improvement o f t h e p l a n n i n g r e l e v a n c y o f u r b a n m o d e l s .

A l i s t o f p u b l i c a t i o n s i n t h e Urban Change S e r i e s a p p e a r s a t t h e end o f t h i s p a p e r .

A n d r e i R o g e r s Chairman

Human S e t t l e m e n t s and S e r v i c e s A r e a

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ABSTRACT

Changing i n t r a - u r b a n s t r u c t u r e and s p a t i a l i n t e r a c t i o n p a t t e r n s r e p r e s e n t a m a j o r a s p e c t o f r e c e n t u r b a n t r e n d s . A framework i s o u t l i n e d i n t h i s p a p e r f o r t h e s t u d y o f i n t e r - a c t i o n p a t t e r n s o v e r t i m e by t a k i n g i n t o a c c o u n t c h a n g i n g u r b a n f o r m s . The p a p e r a l s o a t t e m p t s t o t r a c e t h e i m p a c t o f i n t e r - a c t i o n c o s t s o n t h e o v e r a l l l e v e l o f p o p u l a t i o n a n d employment c h a n g e i n a c i t y . S e v e r a l c o n d i t i o n s a r e d i s c u s s e d f o r t h e d e v e l o p m e n t o f dynamic u r b a n models. T h e s e c o n d i t i o n s r e f e r t o p o p u l a t i o n c o m p o s i t i o n , l a n d - u s e c o n v e r s i o n , r e s i d e n t i a l r e l o c a t i o n , a n d t h e e v o l u t i o n o f t h e c h a n g i n g f u n c t i o n o f d i s t a n c e i n u r b a n a r e a s .

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CONTENTS

1 . FACTORS O F URBAN CHANGE,l 2 . A MODELING FRAMEWORK, 5

3 . PROBLEMS O F IMPLEMENTATION, 1 0 3 . 1 ~ o p u l a t i o n D y n a m i c s , 1 1 3 . 2 L a n d - U s e C o n v e r s i o n , 1 3

3 . 3 R e s i d e n t i a l R e l o c a t i o n and J o u r n e y t o Work, 1 5 3 . 4 E v o l u t i o n of D i s t a n c e F u n c t i o n s , 1 8

3 . 5 E v a l u a t i o n , 2 2 4 . CONCLUSIONS, 2 4 REFERENCES, 2 5

PAPERS I N THE URBAN CHANGE S E R I E S , 2 9

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URBAN CHANGE AND SPATIAL I N T E R A C T I O N

1 . FACTORS OF URBAN CHANGE

While d i s p u t e s c o n c e r n i n g c o n c e p t u a l d e f i c i e n c i e s and v i r t u e s o f u r b a n m o d e l s w i l l s o o n a c q u i r e a d e c a d e - l o n g t r a d i - t i o n (see G o l d n e r 1971; Lee 1973; S a y e r 1976; B a t t y 1 9 7 9 ) , t h e n e e d f o r f u r t h e r d e v e l o p m e n t o f s u c h m o d e l s becomes e v e r g r e a t e r . The demand i s s t r e n g t h e n e d i n view o f r e c e n t t r e n d s o f p o p u l a - t i o n d e c l i n e e n c o u n t e r e d i n some o f t h e l a r g e u r b a n a g g l o m e r a - t i o n s o f h i g h l y u r b a n i z e d c o u n t r i e s and o f t h e c o n t i n u i n g popu- l a t i o n c o n c e n t r a t i o n i n t h e p r i m a t e c i t i e s o f many l e s s - d e v e l o p e d c o u n t r i e s . A s a c o n s e q u e n c e o f t h e s e t r e n d s , p l a n n e r s a r e now f a c i n g t h e n e c e s s i t y o f r e f o r m u l a t i n g s e t t l e m e n t p o l i c i e s

c a r r i e d o u t a t t h e n a t i o n a l a n d u r b a n l e v e l s , s i n c e t h e p r e s e n t - d a y p o l i c i e s h a v e e i t h e r s u p p o r t e d t r e n d s n o l o n g e r deemed

f a v o r a b l e ( a s h a s b e e n t h e c a s e f o r many E u r o p e a n c o u n t r i e s t h a t promoted l a r g e c i t y - g r o w t h l i m i t a t i o n m e a s u r e s ) , o r h a v e f a i l e d t o p r o d u c e more b a l a n c e d s e t t l e m e n t p a t t e r n s ( a g o a l

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a s p i r e d t o by a number o f T h i r d World c o u n t r i e s i n t h e i r s p a t i a l p o l i c i e s ) .

E x i s t i n g u r b a n p o l i c y - o r i e n t e d m o d e l s , s u c h a s s p a t i a l i n t e r a c t i o n m o d e l s , h o w e v e r , r e p r e s e n t a l i m i t e d a i d i n s u c h e n d e a v o r s . I n p a r t i c u l a r , t h e s e m o d e l s s a y l i t t l e i f a n y t h i n g a b o u t how and why economic a c t i v i t i e s o r i g i n a t e w i t h i n , o r m i g r a t e t o o r o u t o f a g i v e n u r b a n a r e a , a n d w h a t t h e l i k e l y c o n s e q u e n c e s s u c h moves may h a v e on o t h e r u r b a n a r e a s . F o r e x a m p l e , t h e a l l o c a t i o n o f p u b l i c f a c i l i t i e s w i t h r e s p e c t t o p o p u l a t i o n d i s t r i b u t i o n ( d i s a g g r e g a t e d by a g e , e d u c a t i o n , income, e t c . ) p r e s e n t s i n i t s e l f a p r o b l e m o f c o n s i d e r a b l e p l a n n i n g i n t e r e s t . T h i s p r o b l e m , h o w e v e r , s t i l l r e m a i n s t o b e t r a n s l a t e d i n t o a g g r e g a t e p e r f o r m a n c e m e a s u r e s i f q u e s t i o n s c o n c e r n i n g t h e a t t r a c t i n g a n d d i s c o u r a g i n g mechanisms w i t h r e s p e c t t o i n - a n d o u t f l o w s o f p o p u l a t i o n a n d f a c i l i t i e s a r e t o b e c o n s i d e r e d .

I f s u c h b a s i c q u e s t i o n s c a n n o t b e t r e a t e d w i t h i n t h e a v a i l - a b l e s p a t i a l i n t e r a c t i o n m o d e l i n g f r a m e w o r k s , why s h o u l d t h e e x p a n s i o n o f t h e s e m o d e l s b e e m p h a s i z e d ? I t i s b e c a u s e t h e i n t e r n a l f u n c t i o n i n g o f u r b a n a r e a s r e p r e s e r : t s o n e o f t h e s u b - s t a n t i a l f a c e t s a s w e l l a s d e t e r m i n a n t s o f u r b a n c h a n g e , b o t h i n t h e c a s e o f c o n t r a c t i o n a n d o f r a p i d g r o w t h . I n h i s d i s c u s - s i o n o f " m e t r o p o l i t a n m a t u r i t y " Leven ( 1 9 7 8 ) i d e n t i f i e d t h r e e g r o u p s o f f a c t o r s u n d e r l y i n g r e c e n t u r b a n t r e n d s i n h i y h l y u r b a n i z e d c o u n t r i e s . T h e s e f a c t o r s i n c l u d e : ( a ) c h a n g i n g i n t e r s e c t o r a l p r o p o r t i o n s a n d l o c a t i o n a l r e q u i r e m e n t s w i t h i n i n d i v i d u a l economic s e c t o r s , a s w e l l a s e v o l v i n g s p a t i a l p a t - t e r n s o f g e n e r a t i o n a n d d i f f u s i o n o f t e c h n i c a l a n d o r g a n i z a t i o n a l i n n o v a t i o n s , ( b ) d e m o g r a p h i c and r n o b i l j t y transitions c h a r a c -

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t e r i z e d by d e c l i n i n g r a t e s o f n a t u r a l p o p u l a t i o n g r o w t h and r e p l a c e m e n t o f r u r a l - u r b a n m i g r a t i o n s by i n t e r - u r b a n f l o w s , a n d

( c ) s p a t i a l p o l i c i e s , b o t h e x p l i c i t a n d i m p l i c i t , w h i c h i n f l u e n c e t h e s h i f t s i n t h e d i s t r i b u t i o n o f p o p u l a t i o n a n d economic

a c t i v i t y a t t h e i n t e r - u r b a n a n d i n t r a - u r b a n s c a l e . T h u s , o u t - m i g r a t i o n from some l a r g e u r b a n a g g l o m e r a t i o n s i s s e e n a s b e i n g d e t e r m i n e d , among o t h e r f a c t o r s , by f e a t u r e s o f i n t e r n a l o r g a n i z a - t i o n i n t h e s e a r e a s w h i c h make them l e s s a t t r a c t i v e compared t o o t h e r ( f o r e x a m p l e , s m a l l e r ) c i t i e s . Once t h e o u t m i g r a t i o n p a t - t e r n b e g i n s t o p r e v a i l , i t may i n t u r n b r i n g a b o u t new r o u n d s o f s p a t i a l a d j u s t m e n t s w i t h i n u r b a n a r e a s c o n d u c i v e t o f u r t h e r i n c r e a s e d p o p u l a t i o n o u t f l o w .

I n t h e c a s e o f r a p i d u r b a n g r o w t h , t h e i n t e r e s t i n s p a t i a l i n t e r a c t i o n p a t t e r n s l i e s n o t s o much i n t h e i r p e r c e i v e d i m p a c t o n o v e r a l l r a t e s o f p o p u l a t i o n e x p a n s i o n ( s i n c e t h e s e p r i m a r i l y r e l y o n t h e d e m o g r a p h i c momentum a n d t h e c o n t i n u i n g d o m i n a n c e o f s c a l e e c o n o m i e s ) . , a s on q u e s t i o n s o f s o c i a l a n d e n g i n e e r i n g s y s t e m s management. The m a j o r c i t i e s i n many l e s s - d e v e l o p e d c o u n t r i e s a r e now a p p r o a c h i n g t h e s i z e o f t h e l a r g e s t c i t i e s o f t h e h i g h l y u r b a n i z e d c o u n t r i e s ; a t l e a s t two o f them (Mexico C i t y and SSo P a u l o ) h a v e r e a c h e d t h e t e n m i l l i o n p o p u l a t i o n mark. I t i s s a f e t o p r e d i c t t h a t o v e r t h e n e x t s e v e r a l d e c a d e s t h e s e u r b a n a r e a s w i l l c o n t i n u e t o e x p a n d beyond t h e s i z e s o f a r e x p e r i e n c e d e l s e w h e r e . C o n s e q u e n t l y , e x i s t i n g r u l e s con- c e r n i n g t h e i n t e g r a t i o n o f t r a n s p o r t a t i o n s y s t e m s , work t r i p s , a n d f a c i l i t y l o c a t i o n p a t t e r n s w i t h i n u r b a n a r e a s may b e

r e n d e r e d i n a p p l i c a b l e u n d e r s u c h q r o w t h c o n d i t i o n s .

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Hence, t h e r e l e v a n c e o f s p a t i a l i n t e r a c t i o n s t u d i e s f o r t h e u n d e r s t a n d i n g o f u r b a n growth and c o n t r a c t i o n may be j u s t i - f i e d n o t s o much by t h e m e r i t s o f t h e a v a i l a b l e s p a t i a l i n t e r - a c t i o n m o d e l s , a s by t h e r o l e p l a y e d by p o p u l a t i o n f l o w s and

l a n d - u s e i n t e r d e p e n d e n c e i n t h e p r o c e s s e s u n d e r c o n s i d e r a t i o n . The development o f submodels which would a l l o w o n e t o t r a c e a d j u s t - ments o f u r b a n s p a t i a l s t r u c t u r e t o c h a n g i n g i n t e r s e c t o r a l p r o p o r t i o n s , t e c h n o l o g i c a l c h a n g e , and h o u s e h o l d - s i z e and c o m p o s i t i o n , s e e m o f p a r t i c u l a r r e l e v a n c e i n t h i s c o n t e x t .

S p a t i a l a d j u s t m e n t s o c c u r r i n g w i t h i n u r b a n a r e a s may b e e x p r e s s e d i n a number o f metrics, s u c h a s p o p u l a t i o n and employment

d i s t r i b u t i o n , d e g r e e o f i n t e r n a l s p e c i a l i z a t i o n ( h o m o g e n e i t y ) a n d i n t e n s i t y o f i n t e r a c t i o n s among c i t y s u b a r e a s . I n a

t e m p o r a l framework s u c h m e t r i c s may d e f i n e i n d i v i d u a l s t a g e s o f t h e t r a n s f o r m a t i o n o f u r b a n r e g i o n s , s u c h a s t h e c i t y - h i n t e r l a n d

( t h e c o n c e n t r a t i o n p h a s e ) , m e t r o p o l i t a n dominance ( t h e s p e c i a l - i z a t i o n p h a s e ) a n d u r b a n f i e l d ( t h e d i s p e r s i o n p h a s e ) ( K o r c e l l i 1 9 8 0 ) . Each s t a t e o f t h i s s e q u e n c e i s c h a r a c t e r i z e d by s p e c i f i c p a t t e r n s o f i n t e r a c t i o n and f u t u r e p a t t e r n s c a n , i n f a c t , b e p r e d i c t e d w i t h t h e h e l p o f t h e t r a j e c t o r y d e s c r i b e d , u s i n g more s p e c i f i c a l t e r n a t i v e a s s u m p t i o n s c o n c e r n i n g e c o n o m i c , t e c h n o l o g - i c a l , and s o c i a l c h a n g e , a s w e l l a s s p a t i a l p o l i c y . *

*The i m p a c t o f o n e s u c h p o l i c y , n a m e l y , t r a n s p o r t a t i o n p r i c i n g , h a s b e e n modeled r e c e n t l y by Cordey-Hayes and V a r a p r a s a d

( 1 9 8 0 ) who u s e d somewhat s i m i l a r a s s u m p t i o n s c o n c e r n i n g a l t e r n a t i v e p a t t e r n s o f p o p u l a t i o n c o n c e n t r a t i o n and decon- c e n t r a t i o n w i t h i n a n u r b a n r e g i o n .

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2. A N O D E L I N G FRllKEWORK

The f o r e g o i n g d i s c u s s i o n s s u g g e s t t h r e e s e t s o f i n t e r - r e l a t i o n s o n w h i c h f u t u r e u r b a n models may f o c u s . One o f t h e s e p e r t a i n s t o l o c a t i o n t r e n d s o f what i s now u s u a l l y c o n s i d e r e d a s e x o g e n o u s s e c t o r employment. A n o t h e r a r e a o f i n t e r e s t r e l a t e s t o t h e i m p a c t o f p o p u l a t i o n t r e n d s o n t h e i n t e r n a l s t r u c t u r e o f u r b a n a r e a s . The t h i r d domain may b e d e f i n e d a s t h e i n t e r d e p e n d e n c e b e t w e e n i n t r a - u r b a n s t r u c t u r e a n d t h e s t r u c t u r e o f s e t t l e m e n t s y s t e m s o n a n a t i o n a l a n d r e g i o n a l s c a l e .

Some o f t h e s e i n t e r r e l a t i o n s a r e shown i n F i g u r e 1 . The scheme a t t e m p t s t o a c c o u n t f o r t h e c h a n g i n g n a t u r e o f s p a t i a l i n t e r a c t i o n - - i t s d e p e n d e n c e on s o c i o - e c o n o m i c c o n d i t i o n s - - a s w e l l a s t o i l l u s t r a t e p o s s i b l e f e e d b a c k r e l a t i o n s b e t w e e n t h e e n d o g e n o u s a n d e x o g e n o u s s e c t o r s i n s p a t i a l i n t e r a c t i o n m o d e l s . The r u l i n g p a r a d i g m i n s u c h m o d e l s i s t h e g e n e r a t i o n o f t r i p d i s t r i b u t i o n s o n t h e b a s i s o f t h e knowledge o f l o c a t i o n o f t r i p o r i g i n s and d e s t i n a t i o n s o r t h e g e n e r a t i o n o f r e s i d e n t i a l , work- p l a c e , a n d s e r v i c e l o c a t i o n s w h i l e u s i n g t h e i n f o r m a t i o n p e r -

t a i n i n g t o t r a v e l c o s t and a t t r a c t i v e n e s s o f i n d i v i d u a l z o n e s f o r t r i p o r i g i n s and d e s t i n a t i o n s . To b e a b l e t o r e p r o d u c e p a s t and p r e d i c t f u t u r e i n t e r a c t i o n p a t t e r n s , h o w e v e r , i t i s n e c e s - s a r y t o i n t r o d u c e r u l e s t h a t w i l l a l l o w f o r t h o s e m e a s u r e s t o v a r y s y s t e m a t i c a l l y o v e r t i m e .

G e n e r a l r u l e s o f t h i s t y p e a r e c o ~ t a i n e d w i t h i n t h e e x i s t i n g t h e o r y o f u r b a n g r o w t h a n d s t r u c t u r e , n o t a b l y i n t h e c o n c e p t o f u r b a n t r a n s i t i o n . A c c o r d i n g t o t h a t c o n c e p t t h e d i s t r i b u t i o n

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F i g u r e 1 . S p a t i a l i n t e r a c t i o n a n d t h e c h a n g i n g u r b a n s t r u c t u r e .

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POPULATION EMPLOYMENT

CHANGE QUALITY OF L I F E

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URBAN FORMS: LAND USE AND D E N S I T Y PATTERNS URBAN

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. I N T E R A C T I O N STAGE 1: CONCENTRATED STAGE

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DECONCENTRATED STAGE 3 : D I S P E R S E D

R E S I D E N T I A L

PATTERNS

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TECHNOLOGY SOC I A L ENVIRONMENT

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and density of residences, as well as spatial employment patterns within an urban region, evolve in a predictable manner, while being shaped ~.ainly by two factors, i.e., the changing

transportation cost and the increase of urban size. Following Klaassen and Paelinck (1979), urban transition may be portrayed as a sequence of six phases (see Figure 2). Phase One of this sequence refers to a situation when advantages of spatial concentration are still predominant and growth occurs in the urban core at the expense of the surrounding territory (conventionally called the ring) which becomes increasingly depopulated. This latter trend is reversed in Phase Two when the growing population size of an urban area causes its territorial expansion.

Phase Three marks the increasing competition among land uses within the core, resulting in the transfer of some jobs to the ring. By the end of this phase, which may be identified as the spillover stage, the growth of an urban area in terms of population size is entirely due to the expansion of its external zone.

Subsequent growth, however, results in agglomeration disadvantages (Phase Four), such as a decreasing ease of movement and incom- patibility of land uses, that are strongly felt. This, in turn, results in the transfer of growth to smaller urban areas which at that time may experience Phase Two of their transition. If extended, the sequence leads to negative growth for both an

urban core and the region as a whole (Phase Five) and, ultimately, to the decline of the urban ring as well (Phase Six). New growth impulses, however, typically generated or located at the core

(such as the development of new functions and major infrastructural improvements) nlay prevent the cycle from being completed and rnay

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move the urban area in question back to Phase Two or Three.

Indeed, with respect to contemporary large agglomerations, the

empirical evidence hardly extends beyond Phase Four of the sequence.

While the evolving spatial profile of a large city, in terms of population distribution and the allocation of activities, is seen as a function of its growth over time, a decline in the momentum may not be directly attributable to the emergence of deconcentrated urban forms. Major correlates of metropolitan contraction, as indicated earlier, include a high urbanization level at or close to the saturation point (75-85 percent population urban), declining relative transportation costs, and small overall rates of population change.

The usefulness of the urban transition concept in the present context is that despite its very general nature it offers a logical picture of temporal evolution of locational patterns of residences, jobs, and service functions within a

large urban area--the type of variation which should be accounted for in the modeling of spatial interaction over time. It is

understood that morphological changes attributable to just two variables, i.e., overall transportation costs (a proxy for which can be automobile ownership) and urban size, can only be estimated in gross terms. Demographic factors, inter-sectoral proportions within an urban economy, social environment

and urban policies may be seen as intervening variables, respon- sible for modifications of the general sequence outlined (see the upper-right part of Figure 1). In particular, socio- economic conditions may be considered as filters producing alternative socio-ecological patterns within urban areas. The

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latter in turn should determine the way and detail by which a spatial interaction model needs to be disaggregated (by occupational groups and housing types, for example); they can also provide constraints on residential location. The stability of socio-ecological patterns, measured in terms of residential relocation, indicates directions in which such constraints may evolve.

Evaluation of alternative spatial interaction patterns, established for individual urban areas and time periods, enables one to introduce feedback relations between endogenous and

exogenous sectors of an urban economy. That is, while the allocation of basic employment within the city follows its morphological rules of development, the size of new employment also becomes determined by such variables as the per capita cost of spatial interaction (energy cost) and related quality- of-life indicators. Similarly, alternative socio-ecological patterns can be compared with respect to their efficiency in terms of daily travel within a city.

3.

PROBLEMSOF IMPLEMENTATION

The nature of interdependencies shown in Figure l'puts forth a numter of prerequisites with respect to the structure and speci- fication of individual submodels. These requirements should be presented against the background of available modeling approaches.

However, rather than attempting a comprehensive review of modeling efforts corresponding to each segment in the diagram, it seems justifiable to state 3 priori that the fusion of existing models would not likely result in an orderly overall structure.

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C o n s e q u e n t l y , t h e d i s c u s s i o n c a n b e f o c u s e d o n p o s t u l a t e d l i n k a g e s b e t w e e n t h e models and l e a d t o w a r d s t h e i d e n t i f i c a t i o n o f c o n d i - t i o n s and a s s u m p t i o n s t o b e f o l l o w e d a t e a c h s t a g e o f t h e

m o d e l i n g s e q u e n c e . A s u r r o g a t e l i s t o f s u c h c o n d i t i o n s i n c l u d e s t h e c o n s i d e r a t i o n o f p o p u l a t i o n d y n a m i c s , l a n d - u s e c o n v e r s i o n , s u b s t i t u t i o n among v a r i o u s t y p e s o f s p a t i a l i n t e r a c t i o n ( s u c h a s m i g r a t i o n a n d d a i l y t r a v e l ) , e v o l u t i o n o f d i s t a n c e f u n c t i o n s , and e v a l u a t i o n and i n t e r v e n t i o n p r o c e s s e s . A l t h o u g h r e f e r e n c e w i l l b e made below t o i n d i v i d u a l t y p e s o f models a s p r o p o s e d by a number o f a u t h o r s , t h e e v a l u a t i o n c r i t e r i a a r e r e s t r i c t e d a c c o r d i n g t o t h e s c o p e and p u r p o s e o f t h e scheme p r e s e n t e d i n t h e p r e v i o u s s e c t i o n .

3 . 1 P o p u l a t i o n Dynamics

The i m p a c t o f c h a n g i n g population g r o w t h on u r b a n f o r m s h a s n o t b e e n s t u d i e d so f a r i n a s y s t e m a t i c way. E m p i r i c a l e v i d e n c e f o r t h e h i g h l y u r b a n i z e d c o u n t r i e s s u g g e s t s t h a t a r a p i d e x p a n s i o n o f t h e u r b a n p o p u l a t i o n c a n b e a s s o c i a t e d w i t h t h e d e v e l o p m e n t o f e i t h e r c o n c e n t r a t e d o r d e c o n c e n t r a t e d u r b a n p a t t e r n s , w h i l e d i s p e r s e d u r b a n d e v e l o p m e n t i s t y p i c a l o f

p e r i o d s w i t h d e c l i n i n g r a t e s o f p o p u l a t i o n g r o w t h ( s e e , f o r e x a m p l e , Bourne and K o r c e l l i 1 9 8 0 ) . T h i s g e n e r a l i z a t i o n may a l l o w o n e t o e x t e n d c h e c o n c e p t o f m o b i l i t y t r a n s i t i o n

( Z e l i n s k y 1 9 7 1 ) i n t o t h e domaln o f u r b a n s p a t i a l s t r u c t u r e . I t a l s o p o i n t s o u t t h e c o r r e s p o n d e n c e b e t w e e n t h e d e v e l o p m e n t o f urDan s t r u c t u r e and t h e c h a n g i n g p a t t e r n s and h i e r a r c h y w i t n i n s e t t l e ~ c e n t s y s t e m s a t b o t h a n a t i o n a l a n d r e g i o n a l

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level.* Nevertheless, general empirical observations of this kind allow one to say little about the underlying relationships between population size, its composition, and the location of economic activity.

Interrelations of the latter type have been extensively

treated in the studies of inter-urban migration (see for example:

Alperovich et al. 1975; Cordey-Hayes 1975) which attempt to explain the observed and derive projected population flows on the basis of configurations of labor market characteristics

(employment, unemployment, and vacancy rates) and of demographic characteristics (such as labor formation and participation

rates). What generally has not been answered by these studies is whether the intensity, composition, and spatial patterns of population flows can be translated into the changes of urban hierarchy and evolution of physical forms of urban development.

This type of knowledge is necessary if one attempts to predict

urban spatial interaction patterns over time by taking into account the instability of relations between origins and destinations:

the kind of instability that stems from changing locational factors with respect to households and enterprises. Recent

developments of spatial interaction theory allow one to capture, for example, theeffect of age structure on employment and

*One can note that concentrated urban patterns tend to be assoc- iated with

a

stable .settlement hierarchy at an interregional level;

the emergence of urban regions is accompanied by interregional concentration trends; finally, dispersed urban forms (urban fields) and metropolitan contraction are translated into inter- regional population and settlement deconcentrations. Similarly, the expanding role of circulatory movements which replace a

part of migration movements during the later stages of the mobi-

lity transition is clearly associated with progressive urban

dispersion.

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p o p u l a t i o n a l l o c a t i o n s w i t h i n u r b a n a r e a s ( S c h i n n a r 1 9 7 8 ) , b u t t h e i m p a c t o f s h i f t s i n l o c a t i o n a l r e q u i r e m e n t s w i t h i n i n d i v i d u a l s e c t o r s , i n c l u d i n g t h e h o u s e h o l d s e c t o r , m u s t s t i l l b e a c c o u n t e d f o r .

3 . 2 Land-Use C o n v e r s i o n

A s i s t r u e i n t h e case o f p o p u l a t i o n c h a n q e , t h e e x p l i c i t c o n s i d e r a t i o n o f c o m p a t i b i l i t y a n d c o m p e t i t i o n among l a n d u s e s r e p r e s e n t s a n o t h e r e s s e n t i a l p r e c o n d i t i o n f o r d e v e l o p i n g d y n a m i c m o d e l s o f u r b a n s p a t i a l i n t e r a c t i o n . The u r b a n l a n d - u s e t h e o r y o n w h i c h s u c h c o n s i d e r a t i o n s s h o u l d b e b a s e d i s n o t q u i t e a b l e t o o f f e r r e l e v a n t r u l e s . F o r a n e m p i r i c a l l y m i n d e d r e s e a r c h e r , t h i s t h e o r y , f o r e x a m p l e : ( a ) d i s r e g a r d s i n t e r d e p e n d e n c i e s u r l d e r l y i n g t h e l a n d - u s e s t r u c t u r e , ( b ) f a i l s t o t a k e a c c o u n t

o f l a n d - u s e a d j u s t m e n t a n d s u c c e s s i o n p r o c e s s e s , a n d ( c ) n e g l e c t s l a n d - u s e s u p p l y ( B o u r n e 1 9 7 8 ) . S i m i l a r l y , f o r a g e n e r a l u r b a n t h e o r e t i c i a n , u r b a n l a n d - u s e t h e o r y a n d a p p l i e d u r b a n a n a l y s i s ( a s r e p r e s e n t e d by s p a t i a l i n t e r a c t i o n m o d e l s i n o u r c a s e ) a r e s e e n t o a d v a n c e i n p a r a l l e l r a t h e r t h a n c o n v e r g e i n t h e n e a r f u t u r e ( R i c h a r d s o n 1 9 7 7 , p . 2 4 3 ) .

No m a t t e r how j u s t i f i e d t h e s e s t a t e m e n t s may b e , t h e y u n d e r e s t i m a t e t h e p o t e n t i a l o f e x i s t i n g t h e o r y t o g e n e r a t e

d y n a m i c u r b a n l a n d - u s e p a t t e r n s . One c a n r e f e r h e r e t o p o s s i b l e e x t e n s i o n s b a s e d o n a t t e m p t s t o v a r y t h e s h a p e o f c u r v e s r e p r e - s e n t i n g t h e s p a t i a l s t r u c t u r e o f t r a n s p o r t a t i ~ n c o s t s . ~ o l l o w i n g o b s e r v e d r e g u l a r i t i e s , t h e s p a t i a l v a r i a t i o n s i n a g g r e g a t e

a c c e s s i b i l i t y l e v e l s a n d t h e s h a r e o f t h e i n d i v i d u a l ' s b u d g e t a l l o c a t e d t o c o s t s o f movement may b e allovged t o d i m i n i s h o v e r

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time.

A

decrease in the spatial accessibility gradient results in the flattening of individual bid-rent curves. When the

amenity gradient is kept constant over time (with amenity values rising towards the urban periphery), a flattening of the popula- tion density gradient and a spatial extension of the city occurs.

A

problem to be encountered is the increasing weight of the amenity component in the total value of site rents, since spatial variations of this factor may not follow uniform patterns among cities.

A

decrease of the accessibility gradients favors some sites over others within the city independently of their loca- tion with respect to the city center; this phenomenon is conducive to the emergence of polycentric urban forms (Ullman 1962). As a consequence, the homogeneous character of individual distance- zones, as portrayed by static land-use models, can no longer be retained.

In order to reproduce a land-use transition process within an alternative model, however, it would be necessary to account for such factors as differential inertia and congruency among land uses which explain typical observed land-use sequences.

These sequences include the socio-ecological succession and the redevelopment cycle (see Hoover and Vernon 1959; Schnore 1965;

Davies 1968; Birch 1971). Their inclusion, in turn, suggests

that greater sectoral disaggregation and introduction of time

lags are among the necessary conditions for the development of

temporal models of urban land use.

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3.3 Residential Relocation and Journey to Kcrk

Conventional migration theory.asserts that at an advanced urbanization level the bulk of labor-oriented migrations take place between individual labor market areas, or functional

urban regions, while within such regions the corresponding role is assumed by daily journeys to work (see, for example, Boudeville 1978). An urban modeler (and an urban planner), on the other

hand, tends to view intra-urban migrations as manifestations of a spatial adjustment process of (a) bringinq residences closer to jobs once a better knowledge concerning the local housing market is obtained or once proper housing becomes availzble

and (b) responding t3 the changing location of jobs. Under those assumptions intra-metropolitan migration can be approximated by gravity-type formulas similar to those employed in journey-to- work models.

Empirical data are not quite consistent with the latter approach (see, for example, Simmons 1968; Dzieciuchowicz 1979).

Typically, for a fair majority of intra-metropolitan residential moves the mean time (as well as netric) distance between home and place of work is greater after migration than before. Alter- native interpretations of this phenomenon may be sought, based on the following factors:

(a) Urban deconcentration and the expansion of urban size.

In a growing metropolitan area, new housing, as well as new job opportunities, tend to be situated on the metropolitan fringe, and due to site requirements of individual users, not necessarily In the same city sector. Longer after-migration distances may

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also result from diminishing overall urban densities and from higher inertia on the part of fixed assets in the industrial sectors as compared to the housing stock within urban areas.

(b) The household activity space factor. Residential

relocation may be attributed to daily journey patterns of household members other than the main breadwinner. Also, a change in distance traveled to work may be caused by new entries to, or withdrawals from, the labor market.

(c) Dissociation between spatial allocation of employment and residences. In this case it is postulated that residential relocation within a metropolitan area is attributed to factors other than the place-of-work location. These factors include housing needs (subject to constraints of the housing market), environmental preferences. location of specialized services, as well as such purely push-factors as urban redevelopment. As one author concludes, intra-urban mobility is primarily a manifestation of the process by which families adjust their housing to the needs generated by shifts in family compositibn

that accompany life-cycle changes (Simmons 1968). Proximity to work places, on the other hand, does not represent an inde- pendent factor of residential relocation within a city. Reloca- tion costs and the relative distances must also be considered.

The above interpretations may prove to be complementary rather than mutually exclusive, but they all point to a neces- sity of accounting for intra-urban migration in a dynamic

moaeling of daily journey patterns. Such suggestions are sup- ported by empirical work. Miron (1978), for example, has found

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t h a t r e s i d e n t i a l r e l o c a t i o n from place-of-work a r e a i t o a r e a j d u r i n g t h e t i m e i n t e r v a l t t o t + l had a s i g n i f i c a n t e f f e c t on t h e s u b s e q u e n t l e v e l o f commuting from j b a c k t o i . T h i s e f f e c t was f o u n d t o b e r e m a r k a b l y c o n s t a n t o v e r t i m e a n d i n d e - p e n d e n t o f t h e c h o i c e o f d i s t a n c e v a r i a b l e , i . e . , t i m e - d i s t a n c e o r i n t e r v e n i n g o p p o r t u n i t i e s .

I f l i f e - c y c l e m i g r a t i o n i s f o u n d t o c o r r e s p o n d t o h o u s i n g - d e p e n d e n t m i g r a t i o n a n d t h u s t o r e p r e s e n t t h e m a j o r component o f i n t r a - u r b a n r e s i d e n t i a l r e l o c a t i o n , t h e n t h e m i g r a t i o n d a t a t o b e i n t r o d u c e d t o t h e a t t r a c t i v e n e s s ( m a s s ) t e r m s o f a

s p a t i a l i n t e r a c t i o n model may b e e n d o g e n o u s l y g e n e r a t e d . T h i s would r e q u i r e an a p r i o r i g e n e r a t i o n o f t h e h o u s i n g s t o c k ( i n a way a n a l o g o u s t o p r o c e d u r e s f o l l o w e d by E c h e n i q u e , C r o w t h e r and L i n d s a y 1969) o r , a l t e r n a t i v e l y , an a p p l i c a t i o n o f a c o h o r t - s u r v i v a l framework i n a m u l t i - z o n a l c a s e ( R o g e r s 1975; see a l s o Termote 1980, f o r an e x t e n d e d d i s c u s s i o n o f m i g r a t i o n - c o m m u t i n g i n t e r d e p e n d e n c e i n a d e m o g r a p h i c p e r s p e c t i v e ) .

Such a n a t t e m p t would b e j u s t i f i a b l e i f s y s t e m a t i c v a r i a - t i o n s were i d e n t i f i e d w i t h i n a n u r b a n s p a c e i n t e r m s o f demo- g r a p h i c c h a r a c t e r i s t i c s . I n d e e d , s t u d i e s on f a c t o r a l u r b a n e c o l o g y ( s e e B e r r y 1971, f o r a c o n c i s e r e v i e w ) show t h a t s u c h v a r i a b l e s add up t o a m a j o r s p a t i a l d i m e n s i o n , c o n v e n t i o n a l l y d e f i n e d a s f a m i l y s t a t u s . T h i s a p p e a r s t o b e t r u e u n d e r d i v e r s e s o c i o - e c o n o m i c c o n d i t i o n s , p a r t i c u l a r l y i n p l a n n e d econo,mies where d e m o g r a p h i c c h a r a c t e r i s t i c s t e n d t o b e h i g h l y i n t e r - c o r r e l a t e d w i t h b o t h t h e a g e o f h o u s i n g and i t s l o c a t i o n w i t h r e s p e c t t o t h e c i t y c e n t e r ( J a g i e l s k i 1977)

.

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3 . 4 E v o l u t i o n o f D i s t a n c e F u n c t i o n s

The g r a v i t y a s s u m p t i o n s u s e d i n most u r b a n s p a t i a l i n t e r - a c t i o n m o d e l s h a v e come u n d e r m o u n t i n s c r i t i c i s m ( f o r a

c o m ~ r e h e n s i v e r e v i e w , see Chana-I-Hua and P o r e 1 1 1 9 7 9 ) . T h i s c r i t i c i s v p e r t a i n s t o b o t h t h e t h e o r e t i c a l d e r i v a t i o n s s n d t h e s t r u c t u r a l p r o p e r t i e s o f t h e m o d e l s . The e x p l a n a t i o n o f t h e o c c u r r e n c e and d i s t r i b u t i o n o f f l o w s and t h e i r r e l a t i o n t o t h e o v e r a l l u r b a n f a b r i c h a s n o t p r o g r e s s e d v e r y f a r , and more r e c e n t s t u d i e s ( f o r e x a m p l e , S h e p p a r d 1978; G r i f f i t h and J o n e s

1980) c o n f i r m t h e w e a k n e s s e s e x p o s e d e a r l i e r by C u r r y ( 1 9 7 2 ) , w h i c h i n c l u d e t h e s p a t i a l a u t o c o r r e l a t i o n e f f e c t , i . e , t h e i m p a c t o f t h e a r r a n g e m e n t o f u r b a n l a n d u s e d o n i n t e r a c t i o n p a t t e r n s . Even more b a s i c and s t i l l open q u e s t i o n s a r e t h o s e o f t h e p e r c e p t i o n o f d i s t a n c e a n d d i r e c t i o n o f c a u s a l i t y w i t h

r e s p e c t t o t h e i n t e r d e p e n d e n c e b e t w e e n i n t e r a c t i o n s , a c c e s s i b i l i t y , a n d l a n d u s e . A r e l a t i v e l y s i m p l e b u t p a r t i a l s o l u t i o n o f t h e l a t t e r p r o b l e m i s t o assume t h e e x i s t e n c e o f a f e e d b a c k r e l a t i o n t o b e modeled by a s i m u l t a n e o u s e q u a t i o n s s y s t e ~ ( F o r t h e r i n g h a m a n d Webber 1980)

.

I n a d d i t i o n t o s u c h g e n e r a l p r o b l e m s , t h e r e a r e c e r t a i n c h a r a c t e r i s t i c s o f i n d i v i d u a l a p p r o a c h e s t o t h e m o d e l i n g o f

u r b a n i n t e r a c t i o n p a t t e r n s t h a t a r e u n s u i t a b l e f o r t h e framework u n d e r d i s c u s s i o n . F o r e x a m p l e , a n a n a l y s i s o f t h e s c a l e o f

s e t t l e m e n t s y s t e m s r u l e s o u t t h e a s s u m p t i o n o f t h e f i x e d t o t a l c o s t o f t r a v e l u s e d i n t h e e n t r o p y m a x i m i z a t i o n a p p r o a c h . The c h o i c e o f e l a s t i c , a s o p p o s e d t o i n e l a s t i c t r a v e l demand f u n c - t i o n s ( s e e S h e p p a r d 1980) s h o u l d depend o n e v a l u a t i o n c r i t e r i a o f a g g r e g a t e u r b a n p e r f o r m a n c e .

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Conceptual deficiencies of the gravity approach may prompt one to suggest that the allocation of places of residence and

places of work within an urban region should be modeled separately.

Studies which have followed this track include those by Karlquist (1975) and Wegener (1980). The hypothesis of mutual independence of the spatial processes referred to can be based on the following simple rationale:

(a) With the increasing specialization of skills and occupations, the range of available and acceptable jobs for a given employee becomes smaller rather than broader with

the passage of time. This aspect of place-of-work/place-of-

residence relations was studied extensively in the case of inter- urban migrations (Gleave and Palmer 1975). It generally supports the intervening opportunities notion and suggests the use of hiyhly disaggregate sectoral data.

(b) Due to the inertia factor

,

the formation of new origins and destinations within an urban region is not likely to bring about spatial adjustments which are implied in the gravity- based comparative-statics interaction models, i.e., the reor- ientation of established linkages. This problem was addressed by Wilson (1974) in his two-by-two matrix describing the mover/

stayer behavior with respect to changes of jobs and residences, but few attempts are known which measure the relative magnitude of those mover/stayer groups and the respective determinants of their behavior.

(c) The location of residence is of a multipurpose

character. As suggested in the previous section, the housing needs, environmental characteristics of the site, accessibility to specialized service facilities and alternative activity

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p a t t e r n s o f i n d i v i d u a l h o u s e h o l d members c o u n t e r b a l a n c e t h e s p a t i a l i n t e r d e p e n d e n c e b e t w e e n r e s i d e n t i a l and employment l o c a t i o n s . S t u d i e s on a c t i v i t y s p a c e f o r m a t i o n a n d c h a n g e r e p r e s e n t a n e s t a b l i s h e d f i e l d o f r e s e a r c h ( H a g e r s t r a n d 1970) b u t t h e i r i m p a c t o n u r b a n s p a t i a l i n t e r a c t i o n m o d e l i n g h a s b e e n m a i n l y r e s t r i c t e d t o t h e q u e s t i o n o f m u l t i p u r p o s e t r i p s which 1s o f s e c o n d a r y i m p o r t a n c e i n t h i s c o n t e x t .

( d ) The c h o i c e o f r e s i d e n c e and p l a c e o f work i s s u b j e c t t o a number o f c o n s t r a i n t s . Some o f them h a v e b e e n a l l u d e d t o b e f o r e b u t i t i s u s e f u l a t t h i s p o i n t t o e n u m e r a t e them: ( 1 ) l a n d - u s e s t r u c t u r e , ( 2 ) i n c r e m e n t a l n a t u r e o f u r b a n d e v e l o p m e n t

( i . e . , a g g r e g a t e s u p p l y c o n s t r a i n t s ) , and ( 3 ) s e g m e n t a t i o n o f h o u s i n g and l a b o r m a r k e t s ( s p e c i f i c s u p p l y c o n s t r a i n t s ) .

( e ) Only a p a r t o f e m p l o y e e s p e r c e i v e a s p a t i a l s e p a r a t i o n b e t w e e n home and p l a c e o f work a s a d i s u t i l i t y . T h i s d o e s n o t o n l y i m p l y t h e s a t i s f i c i n g b e h a v i o r , s u g g e s t e d by S h e p p a r d

( 1 9 7 8 ) b u t a l s o t h e p e r c e p t i o n o f c o s t s a n d b e n e f i t s t h a t a r e d i f f e r e n t from t h e o n e s p o s t u l a t e d by s p a t i a l i n t e r a c t i o n

t h e o r y (see I s a r d 1974) and t h a t a r e a l s o d i f f e r e n t f r o m o b s e r v e d b e h a v i o r , which i s i n f l u e n c e d by s p a t i a l c o n f i g u r a t i o n s of

o r i g i n s and d e s t i n a t i o n s ( i . e . , u r b a n f o r m s ) .

A p o s s i b l e r e p r e s e n t a t i o n o f t h e p e r c e p t i o n s l i s t e d a b o v e i s g i v e n i n F i g u r e 3 ( s o l i d l i n e s ) . V e r s i o n s T 1 and T 2 r e f e r t o s u b s e q u e n t p o i n t s i n t i m e . I n b o t h c a s e s t h e c o n c e n t r a t i o n o f d e s t i n a t i o n s i n t h e c i t y c e n t e r a n d t h e e x p o n e n t i a l l y

d e c l i n i n g r e s i d e n t i a l d e n s i t i e s p r o d u c e t h e g i v e n p a t t e r n o f t r i p - l e n g t h d i s t r i b u t i o n , n o t n e c e s s a r i l y c o n g r u e n t w i t h t h e

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UTILITY LEVEL

T R I P DISTRIBUTION

UTILITY LEVEL

DISTANCE

T R I P DISTRIBUTION

O D2 D; D3 ^D; ^D4 DISTANCE

OD

-

the land-use homogeneity constraint 1

OD3

-

^OD2

-

indifference zone OD4

-

time-budget constraint

Figure 3. An alternative representation of the cost of distance function in journeys t o work.

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p e r c e i v e d f r i c t i o n o f d i s t a n c e . A s t h e b u d g e t c o n s t r a i n t on t r a v e l c o s t b e c m e s l e s s p r o n o u n c e d o v e r t i m e a n d t h e f a c t o r o f u n i q u e n e s s o f employment o p p o r t u n i t i e s a n d r e s i d e n t i a l c h a r a c - t e r i s t i c s s o u g h t i n c r e a s e s ( T 2 ) , t h e i n d i f f e r e n c e - d i s t a n c e zone becomes e x t e n d e d , a n d o b s e r v e d l i n k a g e p a t t e r n s a r e decon- c e n t r a t e d . Even when t h e a g g r e g a t e t r i p d i s t r i b u t i o n r e m a i n s s t a b l e , g i v e n t h e s u p p l y a n d demand c o n s t r a i n t s r e f e r r e d t o e a r l i e r , t h e i n d i f f e r e n c e zone may become e x t e n d e d ( D i ) o r c o n t r a c t e d (D;) a s a c o n s e q u e n c e o f a l t e r n a t i v e t r a n s p o r t a t i o n a n d l a n d - u s e p o l i c i e s .

T h u s , o n e c a n c l a i m , t h e employment m a r k e t a n d t h e h o u s i n a m a r k e t c o e x i s t i n s p a c e , a l t h o u g h e a c h i s g o v e r n e d by mechanisms o f i t s own. The d e g r e e o f t h e i r s p a t i a l c o i n c i d e n c e i n f l u e n c e s t h e l e v e l o f a g g r e g a t e u r b a n l i f e q u a l i t y ( a n d t h e a g g r e g a t e u t i l i t y ) w i t h i t s e f f e c t s on d i f f e r e n t i a l p e r f o r m a n c e o f u r b a n

a r e a s i n t e r m s o f p o p u l a t i o n f l o w s a n d s h i f t s i n economic a c t i v i t y .

3 . 5 E v a l u a t i o n

The m e t h o d o l o g y f o r e v a l u a t i n g s p a t i a l i n t e r a c t i o n p a t t e r n s o r i g i n a t e d i n t h e p e r i o d o f r a p i d e x p a n s i o n o f model a p p l i c a - t i o n s i n u r b a n p l a n n i n g . The s t u d y by E c h e n i q u e , G r o w t h e r , a n d L i n d s a y ( 1 9 6 9 ) who p r o p o s e d a s e t o f p e r f o r m a n c e i n d i c a t o r s t o b e u s e d i n t h e c o n s t r u c t i o n o f a l t e r n a t i v e p l a n s f o r t h e d e v e l o p - ment o f N e w Towns i n B r i t a i n , i s p e r h a p s t h e b e s t known e f f o r t

i n t h i s a r e a . The i n d i c a t o r s r e f e r r e d t o t h e e a s e o f s o c i a l i n t e r a c t i o n , a c c e s s i b i l i t y t o employment o p p o r t u n i t i e s , s e r v i c e s and open s p a c e , t h e work p l a c e , s e r v i c e a n d r e s i d e n t i a l c l u s t e r i n g , a s w e l l a s t h e a c t u a l mean d i s t a n c e t r a v e l e d . T h e s e c o n c e p t s

w e r e f u r t h e r d e v e l o p e d by B r e t h a n y ( 1 9 7 4 ) .

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More r e c e n t l y t h e e v a l u a t i o n o f u r b a n s p a t i a l i n t e r a c t i o n h a s become a more p o p u l a r t o p i c a g a i n . Due t o growing e n e r g y c o n c e r n s t h e p e r f o r m a n c e c r i t e r i a h a v e m a i n l y f o c u s e d on e n e r g y e f f i c i e n c y and t r a n s p o r t a t i o n p r i c i n g p o l i c i e s . C o n c l u s i o n s r e a c h e d s o f a r a r e by no means u n i f o r m . I n o n e c a s e i n c r e a s e d e n e r g y - c o s t s c e n a r i o s a r e shown t o p r o d u c e h i g h e r u r b a n d e n s i t i e s

and a d e c r e a s e i n t h e number and a v e r a g e l e n g t h o f work t r i p s ( S h a r p e 1980)

.

A c c o r d i n g t o a n o t h e r s t u d y (Cordey-Hayes a n d

V a r a p r a s a d 1 9 8 0 ) , i n c r e a s e d t r a v e l c o s t s a r e n o t a b l e t o i n f l u e n c e s u b s t a n t i a l l y t h e d e c r e a s e o f commuting f l o w s . These d i f f e r e n c e s r e f l e c t t h e r a n g e o f a s s u m p t i o n s c o n c e r n i n g p r i c e e l a s t i c i t i e s o f t r a v e l a n d , i m p l i c i t l y , a s s u m p t i o n s r e l a t i n g t o t h e a d a p t - a b i l i t y o f e x i s t i n g u r b a n s t o c k s t o c h a n g i n g p r i c e s t r u c t u r e s . N e v e r t h e l e s s , t h e a p p r o a c h e s r e f e r r e d t o c a n b e f u r t h e r d e v e l o p e d . T h e i r e x t e n s i o n t o a n i n t e r - u r b a n s c a l e r e p r e s e n t s a r e l a t i v e l y s t r a i g h t f o r w a r d t a s k .

Some i n s i g h t s i n t o t h e e v a l u a t i o n c r i t e r i a may b e d e r i v e d from t h e c o n c e p t o f an i n d i f f e r e n c e zone (see F i g u r e 3 ) . S i n c e t h e l e n g t h o f t h i s zone i s s e n s i t i v e t o e n e r g y c o s t s , a s u b s t a n t i a l i n c r e a s e i n t r a n s p o r t a t i o n c o s t s would no d o u b t c a u s e i t s con-

t r a c t i o n . What many p o l i c y - i m p a c t s t u d i e s assume, however, i s t h a t s u c h a c h a n g e would a l s o b r i n g a b o u t a n a d j u s t m e n t o f t r i p d i s t r i b u t i o n p a t t e r n s . T h i s may i n d e e d b e a l o n g - t e r m r e s u l t ( p r o v i d e d t h e c o s t i n c r e a s e i s b i g enough t o h a v e a pronounced i m p a c t on t h e b u d g e t e q u a t i o n ) , i n a s h o r t - and m i d d l e - t e r m p e r s p e c t i v e , however, t h e i n c r e a s e o f t o t a l i n t e r - a c t i o n c o s t s and a d e c l i n e o f l i f e - q u a l i t y i n d i c a t o r s a r e i n e v i - t a b l e outcomes a s i s t h e i r i m p a c t on t h e c o r r p a r a t i v e p e r f o r m a n c e

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of cities of various size categories and internal organization patterns.

A

more attractive alternative than the one described above would be to allow an expansion of the indifference zone while restricting the parallel increase of the mean trip length. Such an approach would require both extensive transportation improve- ments and the application of detailed land-use development controls.

Moving over to the settlement systems scale, a differential urban performance in terms of spatial interaction patterns may be seen as a factor contributing to shifts in population and economic activity among urban places. The spatial interaction should of course be measured relative to other factors of

urban change, which include the distribution of economic oppor- tunities, housing, specialized services, and environmental

quality characteristics.

4 .

CONCLUSIONS

It follows from the approach suggested in this paper that an improvement of planning relevancy of urban models is strongly dependent on their ability to incorporate some basic postulates

of urban growth and structure theory. Development costs of the modeling framework outlined may be high, since it not only calls

for the establishment of linkages so far missing but also

requires reformulations of the existing partial models. However, the growing interest in comprehensive and dynamic urban models

(see, for example, Wilson and Macgill

1 9 7 9 ;

Gordon and Ledent

1 9 8 0 )

is founded on their expected role in integrating urban

theory and providing improved tools for urban and settlement

policy.

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