Work Journey Rescheduling – Model Development Analysis.

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Published paper

Mongtomery, F.O. and May, A.D. (1983)

Work Journey Rescheduling – Model

Development Analysis.

Institute of Transport Studies, University of Leeds,

Working Paper 167

Working Paper167

-May

1983

WORK JOURNEY RESCHEDULING ' MODEL DEVELOPMENT AND

m e s I s

F. 0. Montgomery and A. D. M a y

. . . . . . ~ . .

F. 0 . Montgomery and A. D. May (1983) Work journey rescheduling: model development and a n a l y s i s . Leeds: University of Leeds, I l l s t . Transp. Stud., WP 167 (unpublished

1.

Using Wakefield a s a case study, a method

was

developed of t e s t i n g t h e e f f e c t s on t r a f f i c of s e v e r a l d i f f e r e n t work journey rescheduling s t r a t e g i e s . The method c o n s i s t e d

e s s e n t i a l l y of assigning a s e r i e s of s i x 0-D matrices t o t h e Wakefield network, each matrix r e p r e s e n t i n g t h e t r i p s f o r consecutive 1 5 minute periods over t h e morning peak. The s i x m a t r i c e s were obtained by f i r s t l y disaggregating t h e la hr peak matrix by purpose ( i n t o home-based work,

commercial v e h i c l e , and o t h e r t r i p s ) and t h e n disaggregating each of t h e s e t h r e e m a t r i c e s by time. This temporal

disaggregation was based, f o r t h e home based work t r i p s , on employee a r r i v a l p r o f i l e s by zone, and f o r t h e CV and other t r i p s on cordon crossing p r o f i l e s . The d i f f e r e n t s t r a t e g i e s were modelled by making adjustments t o t h e parameters of t h e employee a r r i v a l p r o f i l e s .

CONTENTS

Abstract

1. INTRODUCTION

1.1 Background

1 . 2 The study approach 1 . 3 The study a r e a

1 . 4

Model o u t l i n e 1 . 5 Report o u t l i n e

2. EMPLOYEE ARRIVAL PROFILES

2 . 1 Introduction 2.2 Data

2.3 Need f o r a model 2.4 Form of t h e model 2.5 C a l i b r a t i o n

2.6 R e s u l t s of c a l i b r a t i o n 2.7 C l a s s i f i c a t i o n of curves

2.8 Extension t o firms not surveyed i n Stage 2

3. MATRIX DISAGGmGATION

3.1 Introduction

3.2 0-D d a t a a v a i l a b l e

3.3 Zoning, network and cordons

3.4 Modifying t h e initial 0-D matrices 3.5 Required form of d a t a

3.6

Outline of proposed method

3.7 Disaggregating t h e t o t a l 0-D matrix by purpose 3.8 Temporally disaggregating t h e

HBW

p r i v a t e matrix

3.9 Temporally d i saggregating t h e "other" p r i v a t e v e h i c l e matrix

3.10 Temporally disaggregating t h e CV matrix

4.

SATURN MODIFICATIONS AND APPLICATION

4 . 1

Introduction 4.2 SATURNQ

5. CfiIBRATION, VALIDATION AND STRATEGY FORMULATION

5 . 1

Recapitulation 5.2 C a l i b r a t i o n Runs 5.3 Validat ion

5.4

S t r a t e g y Formulation

6.

CONCLUSIONS ON OUTSTANDING MODELLING ISSUES

7.

REFERENCES

APPENDICES

A. Summary of SIC Orders

B. Requirements of a Model t o Test t h e Response t o Work Journey Rescheduling P o l i c i e s

Figure 1: Zoning System f o r Wakefield

2: General form of cumulative a r r i v a l d a t a

3:

Typical a r r i v a l p a t t e r n of f i r m w i t h f l e x i b l e work hours

4:

Typical a r r i v a l p a t t e r n of f i r m w i t h fixed s t a r t time

5:

Unusual a r r i v a l p a t t e r n of firm 96 due t o use of works bus

6:

D i s t r i b u t i o n of 8 with SIC

7:

D i s t r i b u t i o n of s t a t e d average a r r i v a l times ( A l l Modes) by SIC

8: Scattergraph showing d i s t r i b u t i o n of

a

and

8

by f i r m f o r a r r i v a l s b y a l l modes

9: Scattergraph showing d i s t r i b u t i o n of a and

8

by firm f o r a r r i v a l s by c a r

1 0 : Production of 1980 updated peak period 0-D matrices

11: Relationskip of cordons t o zoning system 12: Resultant p a r t s of t h e 0-D matrix

13:

Relationship of cordon flows t o p a r t s of t h e matrix ( P r i v a t e v e h i c l e t r i p s )

1 4 :

Production of p r o f i l e f o r a p p l i c a t i o n t o "OTHXR" p r i v a t e v e h i c l e matrix

15: Measured Journey Times

-

Barnsley Rd approach t o Chantry Bridge

16:

Measured Journey Time

-

Doncaster Rd approach t o Chantry Bridge

Table 1: R e s u l t s of f i t t i n g LOGIT curves t o f i r m s ' a r r i v a l p r o f i l e s

2: R e s u l t s of f i t t i n g LOGIT curves t o f i r m s ' a r r i v a l p r o f i l e s

-

s p l i t according t o employee's a b i l i t y t o v a r y hours o r not

3: Summary of UPDATE Runs

4:

1975 and 1980 0-D Matrices (7.45-9.15 am] by purpose 5: 0-D T r i p T o t a l s f o r 1980 Base S t r a t e g y by Time

rfil

Purposes1

6:

Comparison of Modelled v e r s u s Observed Flows f o r

Calibration R u n s

7:

Numbers of Firms (and c a r d r i v e r employees) a f f e c t e d

1. INTRODUCTION

1.1 Background

This paper p r e s e n t s t h e a n a l y s i s method adopted f o r a study c a r r i e d out f o r t h e Department of !Cransport, t h e o b j e c t i v e s of which were

( 1 ) To study t h e p r e s e n t p a t t e r n and d i s t r i b u t i o n of journeys t o and from work i n Wakefield, and t h e c o n s t r a i n t s imposed by employers, unions, domestic conditions, and

( 2 ) To study t h e p o t e n t i a l r o i e of i n c e n t i v e s i n encouraging change on journey timing, and t h e p o s s i b l e c o s t s and b e n e f i t s which would a r i s e .

The morning and evening peak i n t r a f f i c l e v e l s i n urban a r e a s give r i s e t o s e v e r a l problems. High l e v e l s of car use cause congestion and l e a d t o increased delays and u n r e l i a b i l i t y t o c a r , bus and commercial v e h i c l e u s e r s , and increased c o s t s t o t h e i r operators. They a l s o encourage use of environmentally s e n s i t i v e r o u t e s t o avoid congestion.

High l e v e l s of bus and r a i l use i n c r e a s e t h e l e v e l of discomfort on public t r a n s p o r t and t h e chance t h a t waiting times

w i l l

i n c r e a s e because buses or t r a i n s a r e f u l l . Peak demands determine t h e l e v e l a t which t r a n s p o r t capacity i s provided; new roads t o a l l e v i a t e congestion w i l l

o f t e n only be f u l l y used during t h e peak periods; equally a l a r g e proportion of urban public t r a n s p o r t v e h i c l e s and s t a f f a r e required s o l e l y f o r t h e peak and a r e i d l e a t other times.

The spreading of morning and evening peak t r a v e l demands i s f r e q u e n t l y advocated a s a means of a l l e v i a t i n g t h e s e problems and a s an a l t e r n a t i v e t o l e s s p a l a t a b l e congestion reducing measures such a s road c o n s t r u c t i o n o r r e s t r a i n t . The most obvious w a ~ i n which t h i s can be achieved i s by removing, o r modifying t h e requirement on i n d i v i d u a l s t o t r a v e l a t p a r t i c u l a r times. Since work journeys predominate i n t h e peaks t h e emphasis has been on employees' hours, which have been modified by t h e i n t r o d u c t i o n of b o t h staggered and f l e x i b l e working hours. There h a s a l s o been some i n t e r e s t i n modification of school and shop opening hours t o

1978)) can a l l be expected t o have some e f f e c t . So, a s i n d i c a t e d by experience i n York, can a reduction i n highway c a p a c i t y , s i n c e it

i n e v i t a b l y causes more congestion i n t h e peak t h a n a t o t h e r times (Dawson,

1979 )

.

While spreading of peak demand can have obvious b e n e f i t s , it i s not

without i t s drawbacks. Increased demand immediately o u t s i d e t h e peak may add t o delays and t r a v e l c o s t s then, and may c o n f l i c t with o t h e r t r a v e l requirements. It may a l s o c o n f l i c t with t r a n s p o r t o p e r a t o r s ' need f o r

some spare off peak capacity f o r such a c t i v i t i e s a s road and v e h i c l e maintenance. Choice of mode may a l s o change; peak period bus u s e r s could conceivably be a t t r a c t e d t o c a r use outside t h e peak because d r i v i n g

conditions were e a s i e r o r c a r s more r e a d i l y a v a i l a b l e and c a r sharing could perhaps be made more d i f f i c u l t i f p o t e n t i a l s h a r e r s 1 working hours change.

Perhaps t h e g r e a t e s t drawback, however, i s t h e l a c k of information on t h e s c a l e of e f f e c t s of d i f f e r e n t s t r a t e g i e s f o r spreading t h e peak, without which it i s d i f f i c u l t t o p r e d i c t t h e e f f e c t s of t r a n s p o r t a u t h o r i t i e s 1

a c t i o n s o r , equally importantJy, t o know how t r a n s p o r t demands w i l l change

if employers introduce f l e x i b l e working hours t o an i n c r e a s i n g extent.

Some information i s a v a i l a b l e on t h e changes r e s u l t i n g from t h e i n t r o d u c t i o n of staggered working hours ( S e l i n g e r , 1 9 7 6 ) , f l e x i b l e working hours

(Safavian and McLean, 1975, Department of Transport, 1977). a r e a l i c e n s i n g (Watson, 1978) and c a p a c i t y reductions ( ~ a w s o n , 1979) but t h i s information

i s o f t e n incomplete and more importantly, t h e r e i s no information on t h e causal process by which t r a v e l l e r s s e l e c t any p a r t i c u l a r changed time t o t r a v e l .

The current p r o j e c t was designed t o c a s t more l i g h t on t h i s i s s u e by i d e n t i f y i n g t h e f a c t o r s influencing time of t r a v e l ( i n terms of c o n s t r a i n t s a t workplace and home, and c o s t s of t r a v e l ) estimating t h e changes i n time of t r a v e l which would be made if t h e s e c o n s t r a i n t s or c o s t s were modified, and p r e d i c t i n g t h e e f f e c t s on t h e t r a n s p o r t system of such changes.

1.2 The study approach

Early work on t h e d e v e l o p e n t of t h e form of model necessary t o cover t h e behavioural a s p e c t s of t h e o b j e c t i v e s ( a s o u t l i n e d i n Appendixg )

Rather than attempt t o simulate t h e response of firms and t h e i r

employees t o d i f f e r e n t types of work journey rescheduling s t r a t e g y , t h e study makes t h e simplifying assumption t h a t employees' responses t o

d i f f e r e n t s t r a t e g i e s w i l l be s i m i l a r i n s i m i l a r t y p e s of f i r m , and uses t h e p a t t e r n s of response t o e x i s t i n g arrangements i n Wakefield (May e t a1 1981) t o estimate t h e s e responses. It then considers s i x s t r a t e g i e s

( i ) a base s t r a t e g y r e p r e s e n t i n g c u r r e n t conditions

( i i ) a 'backwards looking' s t r a t e g y i n which all firms work f i x e d hours, t o t e s t t h e e f f e c t s of t h e l e v e l of rescheduling which has already occurred

( i i i ) a ' r e a l i s t i c f l e x i b l e hours' s t r a t e g y i n which h a l f t h e firms f o r whom f l e x i b l e o r i n t e r n a l staggered hours a r e f e a s i b l e , b u t which a r e c u r r e n t l y on f i x e d hours, reschedule t h e i r a c t i v i t i e s

( i v ) a ' r e a l i s t i c e x t e r n a l staggering' s t r a t e g y i n which h a l f t h e firms on f i x e d hours who a r e unable t o introduce f l e x i b l e hours, but have s t a r t times near t h e peak, have t h e i r s t a r t times rescheduled

(v) a ' r e a l i s t i c rescheduling' s t r a t e g y representing a combination of

(iii) and ( i v )

( v i ) a 'maximum e f f e c t ' s t r a t e g y i n which a l l firms i n ( i i i ) and ( i v ) reschedule t h e i r operations.

The e f f e c t s on t r a f f i c p a t t e r n s a r e then modelled i n d e t a i l t o provide four

d i f f e r e n t l e v e l s of response of t h e hi&way system. The question of which l e v e l of response i s most l i k e l y i s not answered, but t h e r e s u l t s serve t o i n d i c a t e t h e importance t o be placed on obtaining a c l e a r e r understanding of t h e behavioural processes which would determine t h e response.

1.3

The study a r e a

It was decided t o base t h e study on Wakefield, which has been i d e n t i f i e d a s l i k e l y t o b e n e f i t from peak spreading (Wytconsult, 1976). It was f u r t h e r decided t o concentrate on morning peak period work t r i p s by p r i v a t e c a r , because

1 ) o r i g i n d e s t i n a t i o n d a t a was a v a i l a b l e f o r t h e study a r e a f o r t h e a.m. peak period only

2) work t r i p s predominate i n t h e a.m. peak and appear t o be more amenable

t o spreading t h a n education t r i p s (Wytconsult, 1977)

1 . 4

Model o u t l i n e

Perhaps t h e e a s i e s t way t o understand t h e model i s t o consider t h e process i n reverse. The required f i n a l output (flows on l i n k s , journey times, o v e r a l l network performance measures) i s produced by means of a

modified version of SATURN ( &TUF~NQ) which i s an assignment-simulation. model designed f o r t e s t i n g t h e e f f e c t s of t r a f f i c management schemes on urban networks. The b a s i c i n p u t s t o t h e modified v e r s i o n of SATURN a r e t h e network coding, and a s e t of o r i g i n - d e s t i n a t i o n matrices one f o r each of s i x q u a r t e r hour periods covering t h e

1 2

hour morning peak.

These matrices a r e not simply s c a l e d down versions of t h e t o t a l peak period matrix, because t h e d i s t r i b u t i o n of t r i p purposes changes over t h e peak. Rather t h e y were produced by f i r s t l y disaggregating t h e t o t a l peak period matrix i n t o purpose groups, and then f a c t o r i n g each purpose-matrix i n t o i t s quarter-hour components. The f a c t o r s f o r work t r i p s were obtained by c a l i b r a t i n g curves ( o r p r o f i l e s ) t o t h e a r r i v a l p a t t e r n s of employees, and f o r o t h e r groups of t r i p s by using a combination of t h e s e work t r i p f a c t o r s , and f a c t o r s obtained from cordon counts.

1 . 5 Report o u t l i n e

Chapter 2 d e s c r i b e s i n d e t a i l how t h e a r r i v a l p r o f i l e s of employees were obtained and Chapter 3 describes how t h e s e and o t h e r p r o f i l e s were used t o a i s a g g r e g a t e t h e 0-D matrices. Subsequent chapters then describe t h e modification and a p p l i c a t i o n of SATURN, t h e c a l i b r a t i o n and v a l i d a t i o n of i t s output.

*

2. EMPLOYEE ARRIVAL PROFILES

2 . 1 Introduction

This chapter d e s c r i b e s t h e process by which t h e d i s t r i b u t i o n s of

employee a r r i v a l times were obtained f o r d i f f e r e n t t y p e s of firm with d i f f e r e n t t y p e s of work schedules. These ' a r r i v a l p r o f i l e s 1 were used t o disaggregate t h e peak period t r i p matrix f o r t h e 'base1 s t r a t e g y and were assumed t o be t r a n s f e r a b l e t o s i m i l a r types of firm when t h e y were r e q u i r e d ,

i n any of t h e o t h e r s t r a t e g i e s , t o change t h e i r work schedules. Thus t h e a r r i v a l p r o f i l e f o r a f i r m i n Standard I n d u s t r i a l C l a s s i f i c a t i o n (SIC) 27

which t r a n s f e r r e d t o f l e x i b l e hours i n t h e ' r e a l i s t i c rescheduling' s t r a t e g y was assumed t o be t h e average p r o f i l e of t h o s e SIC 27 firms

-.

2.2

_-

Data

WP

150 (Report of surveys) gives full d e t a i l s of t h e r e l e v a n t surveys.

B r i e f l y , questionnaire surveys were c a r r i e d out among employers ( s t a g e 1)

and employees (Stage 2 ) over a range of firms i n t h e c e n t r a l and intermediate a r e a s of Wakefield. The primary aim was t o o b t a i n a s much information as

possible about t h e a r r i v a l p a t t e r n s of firms i n t h e c e n t r a l a r e a (Zones 1-11

& 1 6 ) (Fig. 1

.

However poor response among some employment c a t e g o r i e s l e d us t o survey some intermediate a r e a firms a s a proxy f o r t h e i r c e n t r a l

a r e a counterparts.

Stage 1 d a t a c o n s i s t s of d e t a i l s of t h e f i r m s ' l o c a t i o n , SIC group, and t h e number of persons working i n t h e firm, c l a s s i f i e d by type of work hours ( f i x e d , f l e x i b l e , r o t a t i n g s h i f t s o r staggered h o u r s ) . The s t a r t and f i n i s h times of each s h i f t a r e a l s o g i v e n (ranges i n t h e c a s e of f l e x i b l e hours).

Stage 2 data, which i s a v a i l a b l e f o r only a proportion of t h e Stage 1

firms, c o n s i s t s of d e t a i l s of t h e employee's journey t o work, including modes used, journey times, times of a r r i v a l over a week, and whether t h e respondent i s a b l e t o vary h i s / h e r a r r i v a l time from day t o day.

The main input t o t h e modelling process described h e r e consisted of t a b u l a t i o n s of t h e Stage 2 d a t a using SPSS. Tabulations were produced of t h e number of respondents a r r i v i n g by f i r m by 5-minute period (within t h e range 7.00 a.m.

-

10.15 a.m. ). The t a b u l a t i o n s were run f o r those a b l e t o vary t h e i r work hours from day t o day, and ( s e p a r a t e l y ) f o r t h o s e not a b l e t o do so; and f o r t h o s e a r r i v i n g a s c a r d r i v e r a s well a s a l l modes.

2.3 Need f o r a model

Even if d a t a had been a v a i l a b l e on t h e arrival times of a l l employees

i n a l l firms, it would s t i l l have been u s e f u l t o construct a model r a t h e r than use t h e a c t u a l d a t a a s input f o r t h e following reasons:

1) Reported a r r i v a l times a r e o f t e n c l u s t e r e d around e a s i l y remembered times such a s 8.30, 8.45 e t c . , giving t h e i l l u s i o n of l i t t l e peaks within t h e main peak. A s u i t a b l e model f i t t e d t o t h e d a t a smooths

out t h e s e peaks.

2 ) The use of an a n a l y t i c a l function i n t h e model enables t h e a r r i v a l p a t t e r n s t o be represented much more s u c c i n c t l y

-

by 2 parameters

r a t h e r than one per time s l i c e .

<. .

NOT TO SCALE

K E Y :

-.-

Central Area boundary

_@

_{Barnsley Road}

----

Intermediate Area boundary

-

M a i n roads

@

Doncaster Road

.

.

.

.

.

.

.

.

.

Railways

- .

@

Westgate

examine and a l t e r i n d i v i d u a l firms' p a t t e r n s when t e s t i n g s t r a t e g i e s .

Data i s a v a i l a b l e f o r only a proportion of firms however, so t h a t t h e

model must a l s o be used t o estimate t h e a r r i v a l p a t t e r n s of t h o s e firms f o r which no d a t a i s a v a i l a b l e . This process e n t a i l e d examining t h e parameters of t h e fixed a r r i v a l p a t t e r n s t o s e e whether and how t h e y were r e l a t e d t o p o t e n t i a l c l a s s i f i c a t o r y v a r i a b l e s such a s S I C . The r e s u l t s of t h i s process a r e described l a t e r .

2.4 Form of t h e model

F i r s t l y , r a t h e r t h a n model t h e a c t u a l numbers a r r i v i n g i n each time period, it was decided t o model t h e cumulative p a t t e r n , i . e . t h e proportion

a r r i v e d by a given time, expressed a s a percentage of t h e t o t a l a r r i v a l s i n t h e period modelled (7.00

-

10.15 a.m. ), See Fig. 2.

The modelling process then r e s o l v e s i t s e l f i n t o a c u r v e - f i t t i n g e x e r c i s e . That i s , t h e form of curve t o be used i s decided simply on t h e b a s i s of how w e l l it f i t s t h e d a t a and conforms t o t h e c o n s t r a i n t s p r e s e n t l y

s e t o u t , and i s not based on any behavioural assumptions. There i s indeed scope f o r f u t u r e r e s e a r c h t o develop such a behavioural model.

There i s only one c o n s t r a i n t on t h e f i t t e d curve, and t h a t i s t h a t

it must be non-decreasing ( i . e . it i s impossible f o r l e s s people t o have a r r i v e d a t time t

+

1 t h a n a t time t ) .

Various forms of curve were attempted including polynomials, cubic s p l i n e s and l o g i t , and t h e l a t t e r was chosen because 1) it was t h e only one c o n s i s t e n t l y t o s a t i s f y t h e forementioned c o n s t r a i n t ; 2 ) it i s defined by

only two parameters a s opposed t o

4

o r

5

f o r t h e o t h e r forms; 3 ) t h e function i s e a s i l y c a l c u l a b l e by computer.

(Note t h a t t h e cumulative normal curve could have been used and would s a t i s f y 1 and 2 above, but i s not so e a s i l y c a l c u l a b l e ).

The form of t h e function chosen i s t h u s

where x = time i n minutes a f t e r midnight y = estimated

%

a r r i v e d b y t i m e x e = base of n a t u r a l l o g s

a , 8

a r e parameters t o be c a l i b r a t e d . - .

2.5 C a l i b r a t i o n

The parameters a &

6

were determined f o r each s e t of d a t a p o i n t s a s follows :

eqn ( 1 ) becomes

Taking l o g s ; -B(x-a)

=

l n ( ( 1 0 0

-

y ) / y )

O r : l n ( (100

-

y ) / y ) = -Bx + Ba

. . .

.

..

( 2 )

Eqn ( 2 ) i s a l i n e a r equation with a b s c i s s a = x and o r d i n a t e =

l n ( (100-Y

)/Y).

Thus t h e b e s t s t r a i g h t l i n e f i t t e d through t h e transformed d a t a p o i n t s has slope = -6 and i n t e r c e p t

=

Ba.

(note t h a t only t h o s e values .of y g r e a t e r than 0 and l e s s than 100 a r e used i n t h e c a l i b r a t i o n . )

The advantage of t h i s method of c a l i b r a t i o n i s i t s s i m p l i c i t y and

robustness. However it s u f f e r s from t h e disadvantages t h a t 1 ) a goodness of f i t s t a t i s t i c

i s

a v a i l a b l e only f o r t h e transformed d a t a , and cannot be t r a n s f e r r e d t o t h e o r i g i n a l d a t a ; 2 ) d a t a p o i n t s close t o y = 0 o r y = 100 tend t o e x e r t a s t r o n g e r influence than t h e y should on t h e r e s u l t .

2.6 Results of c a l i b r a t i o n

A program was w r i t t e n t o c a r r y out t h e c a l i b r a t i o n f o r each d a t a set

and a l s o t o p l o t t h e d a t a and t h e f i t t e d curve. Examples of t h e output a r e shown i n Figs. 3 and

4.

It w i l l be seen t h a t t h e form of t h e d a t a c o n s i s t s of a f l a t s e c t i o n (during which t h e r e a r e no a r r i v a l s ) followed by a curved

s e c t i o n ( r e p r e s e n t i n g t h e a r r i v a l s ) , followed by another f l a t s e c t i o n (during which t h e r e a r e no f u r t h e r a r r i v a l s ) . The program automatically

f i t s a l o g i t curve t o t h o s e p o i n t s where ( 0 < y < l o o ) , and g i v e s a s output t h e c a l i b r a t e d range and c o e f f i c i e n t s of t h e curve.

Examination of t h e g r a p h i c a l output f o r each d a t a s e t g r e a t l y aided t h e decision whether t o accept or r e j e c t t h e f i t t e d curve a s being

Legend

:

survey d a t a

f i t t e d l i n e

420 440

460

4 8 0

500

520

5 4 0

560

580

600

Period ending (mins a f t e r midnight)

Legend

:

survey d a t a

' f i t t e d line

Legend

:

survey d a t a

f i t t e d line

420 4 4 0

4 6 0

4 8 0

500

520

5 4 0

560

580

600

Period ending (mins a f t e r midnight)

The problem of how t o r e p r e s e n t t h i s type of a r r i v a l p a t t e r n i s worthy of f u r t h e r i n v e s t i g a t i o n , but a s i n t h i s study we a r e concerned primarily with a r r i v a l s by c a r t h e problem need not concern us f u r t h e r .

Tables 1 and 2 t h e n , show t h e r e s u l t s of c a l i b r a t i n g t h e curves. Table 1 shows t h e r e s u l t s f o r each firm, both f o r c a r a r r i v a l s and f o r all

modes. Table 2 r e f e r s t o t h o s e firms where t h e proportion of employees

a b l e t o vary t h e i r work hours i s not close t o 0 o r 1. Table 2a shows f o r t h e s e firms, t h e r e s u l t s of c a l i b r a t i n g curves a g a i n s t only t h e a r r i v a l times of t h o s e employees who can vary t h e i r hours. Table 2b shows t h e r e s u l t s f o r employees who cannot vary t h e i r hours.

2.7

C l a s s i f i c a t i o n of curves

2.7.1 I n c l a s s i f y i n g t h e curves i n t o t y p e s , t h e r e a r e two a t t r i b u t e s t o be considered, corresponding t o t h e two parameters

B

& a . The f i r s t a t t r i b u t e i s t h e maximum slope of t h e curve, which i s determined by B and i s i n v e r s e l y

proportional t o t h e standard d e v i a t i o n of t h e a r r i v a l time d a t a . The second a t t r i b u t e i s t h e p o s i t i o n of t h e curve on t h e time a x i s , which i s determined by a and i s d i r e c t l y r e l a t e d t o t h e mean of t h e a r r i v a l times.

2.7.2 C l a s s i f i c a t i o n by SIC It had been thought from t h e s t a r t t h a t t h e r e would be some c o r r e l a t i o n between t h e type of t h e curve and t h e SIC of t h e

firm, and t h i s was t h e r e f o r e t h e f i r s t r e l a t i o n s h i p t o be examined.

Fig.

6

t h e n , shows t h e d i s t r i b u t i o n of B with SIC, f o r a l l mddes and f o r c a r s only. It i s obvious from t h i s t h a t t h e v a r i a t i o n within SIC'S i s a s much a s or g r e a t e r t h a n t h e v a r i a t i o n between them, i . e . t h e r e is no d e t e c t a b l e r e l a t i o n s h i p between SIC and 8.

The next s t a g e was t o look a t t h e c o r r e l a t i o n between SIC and a.

I n f a c t r a t h e r than a we examined t h e mean a r r i v a l time, determined from Stage 1 surveys f o r firms on f i x e d o r staggered hours, o r Stage 2 surveys f o r those on f l e x i b l e hours. (The reason f o r ex-ningmean a r r i v a l times r a t h e r than a was t o i n c r e a s e t h e amount of d a t a f o r comparison

-

a & B parameters were only obtainable f o r t h o s e d a t a s e t s where s u f f i c i e n t Stage 2 responses had been obtained t o c a l i b r a t e a curve).

Fig.

7

t h e r e f o r e shows t h e r e l a t i o n s h i p between SIC and mean a r r i v a l time, and f r o m t h i s it can be seen t h a t t h e r e i s i n f a c t a degree of

-

1 4

-

TABLE

1.

Results of f i t t i n g LOGIT curves t o f i r m s ' a r r i v a l p r o f i l e s NB. Curve formula i s y = 1 0 0 / ( 1

+

e

-@(x-"));

,

= tirne

TABLE 2.

Results of f i t t i n g LOGIT curves t o f i r m s ' a r r i v a l p r o f i l e s

-

s p l i t according t o employee's a b i l i t y t o vary hours o r not

NB Curve formula i s y = 100j(l

+

e

Stated average starting time (mins

1

-.

-.

.-.

.-.

C-.

27

Key: Average s t a r t time of firm on staggered hours

A Stated s f a r t time

-

fixed hours

-.+.--Range and average s t a r t time for f l e x i b l e hours

42 0

440

460

480

500

520

540

560

580

S I C

Fig. 7

Distribution of stated average arrival times ( a l l modes)

by

SIC

I I CI I I I

Hence, although t h e r e i s no evidence of a r e l a t i o n s h i p between SIC and

6 ( t h e shape of t h e curve) t h e r e does appear t o be a correspondence with t h e mean a r r i v a l time (hence a , t h e p o s i t i o n of t h e curve).

2.7.3 C l a s s i f i c a t i o n by s t a t e d work hour type It was t h e r e f o r e s t i l l

necessary t o f i n d a c l a s s i f i c a t o r y v a r i a b l e f o r 6, and t h i s was found i n t h e "type of work hours" a s s t a t e d by t h e firms i n t h e Stage 1 surveys. Work hours types included Fixed hours, F l e x i b l e hours, and Staggered hours

( t h e l a t t e r including r o t a t i n g s h i f t s , a category occurring i n only

5

firms). Fig. 8 i s a s c a t t e r g r a p h showing t h e c a l i b r a t e d a & 6 f o r each firm ( a l l modes). The symbols denote t h e dominant work hour t y p e i n each firm. (Note t h a t f o r those firms where no one t y p e i s dominant, i . e . t h o s e l i s t e d on Table 2 , t h e r e s u l t s f o r both types a r e

Fig. 9 shows t h e same b u t f o r c a r a r r i v a l s only.

It can be seen t h a t i n both graphs t h e points f a l l i n t o two groups, with f i x e d hour firms tending t o have 6 values i n a higher range than e i t h e r

f l e x i b l e o r staggered work hours firms.

Thus f o r a l l modes ( F i g . 8 ) t h e 6 value f o r f l e x i b l e / s t a g g e r e d hours firms l i e s between 1. 0.05 and 0.10 whereas t h e value f o r f i x e d hour firms

i s between 0.10 and 0.15. S i m i l a r l y f o r car a r r i v a l s , f l e x i b l e / s t a g g e r e d hours firms have a 6 from % 0.05 t o 0.09, with f i x e d hours ranging from

1. 0.08 t o 0.16.

The r e l a t i o n s h i p between s t a t e d work hours and a i s not s o d i s t i n c t , but t h e r e does appear t o be a tendency f o r t h e average s t a r t time of employees

on f l e x i b l e hours t o be e a r l i e r t h a n t h o s e on staggered, and f o r t h e l a t t e r t o be e a r l i e r than t h o s e on f i x e d hours. This i s a f u r t h e r t o p i c which would b e n e f i t from f u r t h e r study.

Hence it would appear t h a t t h e type of work hours, a s s t a t e d by t h e firms i n t h e Stage 1 surveys, can be used t o c l a s s i f y t h e 6 values.

2.7.4 Difference between c a r a r r i v a l s and all modes Referring back t o Table 1, an examination of t h e a parameter firm by firm shows t h a t i n 8 cases

a i s lower f o r ' c a r s only' than f o r ' a l l modes', and i n

6

cases it i s higher.

Key

:

A

Fixed hours

0

Flexible

Staggered

0.15

0.10

'P

0.05

0 -

45

-

Key

:

A

Fixed

hours

0

Flexible

0

Staggered

-

-

I I I I I I I I I I 1

0

46 0

47 0

480

490

500

510

520

530

540

550

560

a

This being t h e case, it becomes j u s t i f i a b l e t o u t i l i s e t h e p a t t e r n s f o r 'all modes' i n t h e model where i n s u f f i c i e n t d a t a had r e s u l t e d i n u n r e l i a b l e o r non-existent ' c a r s only' p a t t e r n s .

2.8 Extension t o firms not surveyed i n Stage 2

The purpose of c l a s s i f y i n g t h e curves a s described above i s of course s o t h a t reasonable estimates can be made of t h e a r r i v a l p a t t e r n s of t h o s e firms not surveyed. For t h o s e firms which have been surveyed i n Stage 2 ,

and f o r which p r o f i l e s a r e t h e r e f o r e a v a i l a b l e , t h e parameters c a l i b r a t e d f o r ' c a r s only' were used where a v a i l a b l e , otherwise t h o s e f o r ' a l l modes'

were used.

For t h o s e firms not surveyed i n Stage 2 , t h e following procedures-

were adopted.

1) Firms surveyed i n Stage 1

For t h e s e firms d e t a i l s of t h e work hourswereknown, and a could t h e r e f o r e be determined by r e f e r e n c e t o t h e s t a t e d average a r r i v a l time. The p o s s i b l e range of

0

f o r each firm was determined on t h e b a s i s of t h e s t a t e d work hours t y p e , and w i t h i n t h a t range t h e

a c t u a l choice of 8 was taken randomly from t h e observed

d i s t r i b u t i o n of 8 ' s .

2 ) Firms not surveyed i n Stage 1, within t h e c e n t r a l a r e a

The SIC'S of t h e s e firms i s known, and t h i s was t h e r e f o r e used t o determine t h e p o s s i b l e range of a. Again t h e a c t u a l choice was. made randomly from t h e observed d i s t r i b u t i o n of a w i t h i n t h e range.

The choice of

0

f o r firms i n t h i s group i s more of a problem a s t h e i r work hour types a r e not known. The procedure a d o p t e d w e s t o go through t h e l i s t examining each f i r m i n d i v i d u a l l y , and f i r s t l y a l l o c a t e a

work hour t y p e t o each f i r m f o r which t h e choice i s f a i r l y s t r a i g h t - forward (e.g. f i x e d hours f o r small shops, schools, f l e x i b l e / s t a g g e r e d hours f o r l o c a l government o f f i c e s ) ; and then t o a l l o c a t e t h e remainder by randomly sampling t h e observed d i s t r i b u t i o n of work hour t y p e s .

(This ensures t h a t t h e f i n a l estimated d i s t r i b u t i o n of work hour types among firms i s approximately t h e same a s t h a t surveyed.)

3) Firms not surveyed i n Stage 1, intermediate a r e a

It i s not necessary t o have individual p r o f i l e s f o r firms i n t h e

intermediate a r e a , a s t h e t e s t s t r a t e g i e s a f f e c t only c e n t r a l a r e a firms. It i s s u f f i c i e n t t h e r e f o r e t o have only one o v e r a l l p r o f i l e f o r t h e whole intermediate a r e a , and i n t h e absence of contrary information i t w a s assumed t h a t t h e o v e r a l l a r r i v a l p r o f i l e s of t h e c e n t r a l and intermediate a r e a s a r e s i m i l a r . Thus t h e o v e r a l l a r r i v a l p r o f i l e f o r t h e c e n t r a l a r e a a s obtained i n 1 & 2 above

was applied t o t h e intermediate a r e a a s a whole.

3.

MATRIX DISAGGREGATION

3.1 I n t r o d u c t i o n

This chapter d e s c r i b e s t h e methods by which t h e morning peak o r i g i n d e s t i n a t i o n matrices obtained from t h e WYTCONSULT Surveys of 1975 were

updated and disaggregated by purpose and by time. The process i s summarised

i n Fig. 1 0 .

3.2 0-D d a t a a v a i l a b l e

The b a s i c source of o r i g i n - d e s t i n a t i o n d a t a i s t h e WYTCONSULT surveys

of 1975. 0-D matrices were produced f o r Wakefield by c a l i b r a t i n g a g r a v i t y model a g a i n s t t r i p s observed a t roadside interview s t a t i o n s , on a cordon

drawn round t h e former Wakefield CB area. These matrices a r e f o r t h e morning peak period (7.45

-

9.15 a.m. ) i n 1975, disaggregated by purpose

(HEW, HBO, NHB, EDUC, HGV & LGV) on a 129 zone zoning system.

3.3 Zoning, network and cordons

3.3.1- The 129 zone system used i n WYTCONSULT i s t o o f i n e i n t h e outer zones f o r our purposes, a s we only r e q u i r e t o know by which r o u t e s t r a f f i c approaches t h e c e n t r a l a r e a . For t h i s reason, a 32 "zone" system was used, c o n s i s t i n g of 21 WYTCONSULT zones covering t h e c e n t r a l a r e a of ~

Wakefield, and 11 " r o u t e zones" by which all e x t e r n a l t r a f f i c e n t e r s t h e network. It should be noted t h a t t h e s e "route zones" a r e not simply aggregations of WYTCONSULT zones, but r a t h e r t h e t r i p s to/frorn them were obtained by a cordon i s o l a t i o n procedure, i . e . by running an assignment on t h e 129 zone system and recording t h o s e t r i p s passing through each "route

zone".

Thus a 32 x 32 zone 0-D_,matrix was obtained i n which only t h o s e

Roadside i n t e r v i e w surveys on

1. cordon surrounding Wakefield CB

(w.Y.T.s. 1975) d

W.Y.T.S. O'-D Matrix 1975 3. _7.45

_-

_{9.15, 129 zones}

I

Link i s o l a t i o n

-

assignment t o I3l.Y.T.S. - network

Other

C V

*

mw

0-D Matrix 1975

9.15, 32 zones

P

Growth f a c t o r s 75

-

8 3

Veh.

-

P.C.U. f a c t o r s

I

Other

CV

+

m\r

c

I

0-D Matrix, 1975 f a c t o r e d t o 80

1

1

2

,

0 "

1

7 . 4 5 - 9 . 1 5 , 32 zones Counts on

+

o u t e r cordon

I

T o t a l 0-D N a t r i x

1

I

7.

1975 f a c t o r e d t o 80

7.45

-

9.15, 32 zones

1

I

I

F u r n e s s 4

f

Counts on v a r i o u s

1

network l i n k s . (1 h r Furnessed 0-D Matrix 1980 f a c t o r e d t o 12 h r s ) 7.45

-

9.15, 32 zones

C o r r e c t Row/col. t o t a l s

I

I

.I#

Updated 0-D Matrix 1980

7.45

-

9.15, 32 zones

%

HBW e t c by element

c

I

, , :: Otlher

I C V

V HBW

had simply been aggregations of t h e o r i g i n a l zones, t h e n t r i p s from say 10 miles n o r t h of Wakefield t o say

5

miles south, would have been included and hence assigned t o t h e SATURN network, whereas i n f a c t t h e y would most probably avoid t h e Wakefield a r e a a l t o g e t h e r by using t h e M l . )

3.3.2 Network The network used f o r t h i s study i s based on, but d i f f e r e n t from, t h e WYTCONSULZ network. It covers t h e c e n t r a l a r e a of Wakefield from Leeds Road/Bradford Road i n t h e North t o Chantry Bridge i n t h e South,

and from Westgate End i n t h e West t o Peterson Road/Jacob's Well Lane i n t h e East. Link l e n g t h s and speeds wire provided by WYCC and t h e network was coded by a postgraduate student i n t h e I n s t i t u t e a s p a r t of h i s M.Sc. d i s s e r t a t i o n p r o j e c t (Yip 1980).

3.3.3 Cordons There a r e two cordons p e r t a i n i n g t o t h i s model a s shown i n Fig. 11. The f i r s t i s t h e o u t e r cordon mentioned i n 3.3.1 above, defined

by t h e l i m i t s of t h e SATURN network which encloses zones 1-21. The second o r i n n e r cordon defines t h e CBD or town c e n t r e of Wakefield, where t h e

bulk of o f f i c e workers a r e employed, and which i s t h e most l i k e l y a r e a

within which Work Journey Rescheduling (WJR) s t r a t e g i e s could be implemented.

I n l o c a t i n g t h e p r e c i s e p o s i t i o n of t h e inner cordon, t h e following points were considered important.

1) As f a r a s p o s s i b l e t r i p s should pass around r a t h e r t h a n through t h i s cordon. This f e a t u r e makes t h e p r o f i l e s obtained from cross-

.

cordon flows more u s e f u l , and was achieved by keeping t h e cordon j u s t i n s i d e t h e main i n n e r r e l i e f roads.

2 ) The number of roads c r o s s i n g t h e cordon should be a s few a s

p o s s i b l e t o reduce d a t a c o l l e c t i o n time and c o s t . There a r e eleven crossing p o i n t s here.

3) The cordon should be c a r - t i g h t , i . e . t h e r e should be no uncounted minor roads, back l a n e s e t c .

4)

The a r e a enclosed by t h e inner cordon should, a s f a r a s p o s s i b l e , contain t h e m a j o r i t y of workplaces amenable t o WJR, and exclude a s f a r a s p o s s i b l e t h o s e workplaces which a r e not so amenable, and a l s o non-workplaces. The chosen cordon t h e r e f o r e excludes t h e

heavy i n d u s t r i a l a r e a south of Ings Road and t h e River Calder (zones 1 9 , 20, 21) and t h e predominantly r e s i d e n t i a l a r e a s t o t h e n o r t h , e a s t and west of t h e c e n t r a l area.

,,J.Y.T.S. C O R D O ~

--

CENTRAL AREA

INTERMEDIATE AREA

EXTERNAL AREAS ROUTE ZONES 22- 32

The following paragraphs describe t h e r e l a t i o n s h i p of each of t h e s e a r e a s t o t h e network and consequently t o t h e survey methods r e q u i r e d t o model t h e e f f e c t t h a t work journeys t o t h e s e a r e a s h a v e o n congestion i n t h e network.

3.3.3.1 Central a r e a Because t h e c e n t r a l a r e a i s s u b j e c t t o WJR s t r a t e g i e s ,

it i s necessary t o model with reasonable accuracy t h e present work journey

a r r i v a l p a t t e r n s i n t h a t a r e a , i n order t o make s e n s i b l e comparisons between base and t e s t conditions. Thus it was attempted t o c a r r y out surveys of every employer i n t h e c e n t r a l a r e a employing more t h a n

1 5

people, t o o b t a i n up- to-date d e t a i l s of t h e number and type of employees, and c u r r e n t work

schedule arrangements. Additionally, a sample of firms was c i r c u l a t e d with

employee q u e s t i o n n a i r e s , i n order t o o b t a i n t h e c u r r e n t modal s p l i t and times of a r r i v d . The information obtained from t h e employee surveys was

expanded by means of t h e employer surveys and o t h e r d a t a t o produce a

histogram o r p r o f i l e of a r r i v a l times by c a r f o r each f i r m . These p r o f i l e s were then added (weighted by t h e number of employees) t o o b t a i n a r r i v a l p r o f i l e s by zone ( s e e Chapter 2 ) .

3.3.3.2 Intermediate a r e a 'Fne intermediate a r e a between t h e two cordons would not be s u b j e c t t o W J R s t r a t e g i e s , but t r a f f i c g e n e r a t e d / a t t r a c t e d t h e r e does have a s t r o n g influence on congestion i n t h e network. Hence it

was thought u s e f u l t o c a r r y out some employer/employee surveys i n t h i s a r e a , but a lower sample f r a c t i o n t h a n i n t h e c e n t r a l a r e a was used.

3.3.3.3 External a r e a Because of t h e extent of t h e e x t e r n a l a r e a , i t s c o n t r i b u t i o n t o network congestion i s l i k e l y t o be much more evenly spread over time t h a n t h e c e n t r a l and intermediate areas. It i s not intended nor indeed would it be p r a c t i c a b l e , t o survey t h e a r r i v a l times of firms i n t h i s a r e a , and i n any case a s w i l l be seen l a t e r t h e p r o f i l e s of t r a f f i c a t t r a c t e d t o e x t e r n a l zones can be obtained f r o m t r a f f i c counts alone.

3.4

Modifying t h e i n i t i a l 0-D matrices

Referring again t o Fig.10, t h e d e r i v a t i o n of t h e i n i t i a l 32 zone

matrix ( ( 4 ) i n ~ i10) ~h a s already been described. . There a r e i n f a c t 3 such matrices, f o r

HBW

p r i v a t e v e h i c l e s , CV's and a l l o t h e r (non-bus ) vehicles. A l l t h e s e matrices of course r e f e r t o 1975 AM peak period flows, and it i s t h e r e f o r e necessary t o modify them t o 1980 flows before they can be used i n t h e model along with 1980 employment surveys, t r a f f i c counts e t c .

-. .

1) The a p p l i c a t i o n of o v e r a l l growth f a c t o r s t o each matrix t o

account f o r o v e r a l l t r a f f i c growth from 1975 t o 1980 and t o

convert from v e h i c l e s t o PCUs

( ( 6 )

Fig. 1 0 ) .

2 ) After adding t h e t h r e e m a t r i c e s t o form a t o t a l PCU matrix, t h e a p p l i c a t i o n of t h e liurness technique t o make t h e row and column t o t a l s f o r t h e r o u t e zones agree with t h e measured 1980 flows on t h o s e r o u t e s ( ( 8 1 Fig. 1 0 ) .

31 The a p p l i c a t i o n of t h e UPDATE program a s s o c i a t e d with SATURN,

which modifies t h e matrix elements within t h e given row and

column t o t a l s so t h a t , when assigned t o t h e network, t h e r e s u l t i n g flows agree w i t h measured l i n k flows ( ( 9 1 Fig. 1 0 ) .

The o u t e r cordon counts applied in ( 2 ) were f o r t h e 1; hour period

7.45

-

9.15 ( i . e . t h e period covered hy t h e 0-D m a t r i x ) . These counts were

aggregations of t h e

5

minute counts conducted i n November 1980.

The counts used in t h e UPDATE process were ohtained mainly from

bTYCC. These counts were c a r r i e d out i n v a r i o u s months and y e a r s , and factored t o 1980 by r e f e r e n c e t o long-term automatic count d a t a . They each

r e f e r t o t h e peak hour, so t h a t before t h e y could he used i n t h e UPDATE program t h e m a t r i c e s had t o he f a c t o r e d down t o 1 hour v a l u e s and suh-

sequently f a c t o r e d back t o a 1; hour matrix using t h e 1980 r a t i o of 1;

hour f l o w / l hour flow a t t h e i n t e r n a l cordon.

The UPDATE. p r o c e s s can be c a r r i e d out a t present o n l y on t h e

0-D matrix, and not on s e l e c t e d purpose sub-matrices. This i s because t h e

process involves running t h e simulation and assignment s t a g e s of SATURN t o determine t h e p a t h s taken from each o r i g i n t o d e s t i n a t i o n , and t h i s i s

obviously dependent on t h e - t r a f f i c using t h e network. Tahle 3 shows

t h e r e s u l t s of t h e updating process i n summary.

3.5 Required form of d a t a

In this study we a r e t e s t i n g t h e e f f e c t of rescheduling work times

in t h e c e n t r a l a r e a of Wakefield, and a r e looking only a t t h e e f f e c t on t h e

1; hour morning peak period. Thus o n l y t h e hatched a r e a s of t h e home-hased- m r k matrix on Fig. 12 ( i . e . t h e journey t o work

_-

in t h e c e n t r a l a r e a l a r e d i r e c t l y a f f e c t e d by t h e t e s t s t r a t e g i e s . Trips i n t h e other p a r t s o f t h e home-based-work matrix, and t h e o t h e r purpose matrices may be i n d i r e c t l y

TABLE

3

SUMMARY OF UPDATE RUNS

Note: shaded cells are potentially affected by W J R

The t r i p s made during t h e a.m. peak t h e r e f o r e f a l l i n t o t w o groups

1. Those which can be d i r e c t l y a l t e r e d by rescheduling s t r a t e g i e s .

2. Those which a r e a f f e c t e d o n l y i n d i r e c t l y .

When disaggregating t h e t o t a l o r i g i n - d e s t i n a t i o n matrix (obtained a s i n

Section 3 . 4 ) i n t o d i s c r e t e time s l i c e s , it i s t h e r e f o r e , necessary t o keep

t h e s e t w o groups separated.

What we r e q u i r e t h e n i s ( 1 ) a s e t of 0-D m a t r i c e s f o r home-based-work

t r i p s t o t h e c e n t r a l a r e a , i n d i s c r e t e time s l i c e s covering t h e morning

peak period; ( t h e s e m a t r i c e s w i l l v a r y f o r d i f f e r e n t s t r a t e g i e s although

t h e t o t a l number of t r i p s f o r each 0-D p a i r a c r o s s a l l time s l i c e s w i l l

remain c o n s t a n t ) ( 2 ) a s e t of 0-D matrices covering a l l o t h e r t r i p s , f o r

t h e same time s l i c e s ( t h e s e m a t r i c e s w i l l remain f i x e d over a l l t e s t s ) .

3.6

Outline of disaggregation method

There a r e two main s t a g e s i n p r e d i c t i n g t h e e f f e c t of t h e s t r a t e g i e s

being t e s t e d . These a r e f i r s t l y , t h e response t o t h e s t r a t e g y and secondly

t h e e f f e c t of t h a t response on t r a f f i c conditions.

I n t h e method described here, t h e response t o a s t r a t e g y i s not p a r t

of t h e model p r e d i c t i o n procedure, but i n s t e a d i s p a r t of t h e input t o

t h e model, In other words, t h e response f o r each workplace ( i n terms of

t h e a r r i v a l p r o f i l e s r e s u l t i n g from p a r t i c u l a r work schedules) i s determined o u t s i d e t h e model, based on surveys of t h e a r r i v a l p r o f i l e s of s i m i l a r f i r m s

on s i m i l a r schedules. The production of t h e s e p r o f i l e s was described i n

some d e t a i l in Chapter 2 , but here we a r e discussing only t h e manner i n

which t h e p r o f i l e s and o t h e r d a t a were used t o temporally disaggregate

t h e t o t a l 0-D matrix.

One o r t w o c a v e a t s should be mentioned with regard t o t h e method

described. F i r s t l y , SATURN does not process groups of v e h i c l e s over l i n k s

i n t h e network i n t h e way t h a t say CONTRAM would do. Rather, a l l t r i p s

in one 0-D time s l i c e a r e assumed t o be loaded on t o t h e network uniformly

during t h a t time s l i c e . Moreover, t h e time s l i c e i n which any t r i p f a l l s

is assumed t o depend on e i t h e r t h e a r r i v a l time a t t h e workplace ( f o r work

t r i p s destined f o r t h e c e n t r a l and intermediate a r e a s ) o r t h e cordon

crossing time otherwise. Hence in t h i s method t h e l e n g t h of t h e time s l i c e s should not be l e s s than t h e average journey time a c r o s s t h e network.

matrices depends on t h e i n n e r cordon being l o c a t e d such t h a t t h e majority of "throughtt t r i p s pass around it r a t h e r than through it.

Section

3.4

described how t h e updated t o t a l 0-D matrix ( ( 9 ) of Fig. 1 0 ) was obtained. The r e s t of t h i s s e c t i o n describes i n a u t l i n e t h e r e s t of t h e method from t h a t s t a g e . The following four s e c t i o n s w i l l then d e s c r i b e

each s t a g e i n more d e t a i l .

Referring again t o Fig.10, t h e next s t a g e i s t o disaggregate t h e

t o t a l matrix

( 9 )

i n t o t h r e e matrices by purpose. It i s necessary t o separate t h e HEiW matrix because we wish t o disaggregate it i n d i f f e r e n t

ways f o r d i f f e r e n t t e s t s . It i s not s t r i c t l y necessary t o separate t h e commercial v e h i c l e matrix, but f a i l u r e t o do so i s l i k e l y t o l e a d t o

l o s s of accuracy, due t o t h e d i f f e r e n t shape of t h e t r i p - t i m e p r o f i l e of CVs compared t o o t h e r t r a f f i c .

Having obtained t h e s e 0-D matrices f o r t h e peak period, t h e next

s t a g e i s t o disaggregate them i n t o time s l i c e s of 1 5 minutes. F i r s t l y , home based work t r i p s with d e s t i n a t i o n s i n t h e c e n t r a l o r intermediate a r e a s

a r e disaggregated by a p p l i c a t i o n of t r i p - t i m e p r o f i l e s obtained from f i r m s t surveys, by d e s t i n a t i o n zone. Secondly t h e commercial v e h i c l e t r i p matrix i s disaggregated by a p p l i c a t i o n t o t h e matrix a s a whole of t r i p - t i m e p r o f i l e s obtained from cordon counts of CVs. (Note t h a t CVs a r e t h e only

11

purpose" group, capable of being s e p a r a t e l y i d e n t i f i e d from cordon c o ~ y l t s . ) Thirdly t h e remaining p a r t s of t h e 0-D matrix ( i . e .

HBW

t r i p s with e x t e r n a l d e s t i n a t i o n s , o t h e r home-based, non-home based and education trips), a r e t r e a t e d a s one, and disaggregated by means of a combination of cordon count p r o f i l e s and f i r m s ' surveys.

3.7 Disapuregatinu t h e t o t a l 0-D matrix by purpose

To c a r r y out t h i s process, it i s assumed t h a t t h e purpose s p l i t f o r each 0-D p a i r i s t h e same i n 1980 a s it was i n 1975.

i . e . t h a t T . .

80

T . .

75

where p denotes purpose.

-u.F! = 3

T . . 80

75

L J T i j

Hence t o o b t a i n t h e 1980 m a t r i x f o r purpose p we simply f a c t o r each element

This process maintains t h e same t o t a l number of t r i p s i n each 0-D p a i r , hence t h e UPDATE previously c a r r i e d out i s not i n v a l i d a t e d . It would not of course be a b l e t o d e a l properly with cases where major l a n d use changes have a l t e r e d t h e purpose s p l i t between zonal p a i r s . Table

4

shows t h e o v e r a l l

r e s u l t s of t h i s process, with t h e 1975 purpose s p l i t s f o r comparison.

-

3.8 Temporally d i s s g r e g a t i n ~ t h e HBW p r i v a t e matrix

Fig. 1 3 shows i n t a b u l a r form t h e 9 p a r t s o f t h e KBW p r i v a t e v e h i c l e

matrix and t h e nine p a r t s of t h e "other" p r i v a t e v e h i c l e matrix (CVs not included). This s e c t i o n describes t h e procedure used f o r disaggregating t h e f i r s t s i x p a r t s of t h e HBW matrix, i . e . t h o s e with d e s t i n a t i o n i n t h e c e n t r a l o r intermediate a r e a s .

A s already mentioned, t h e s t r a t e g i e s t o be t e s t e d applied only t o firms i n t h e c e n t r a l a r e a , and t h e r e f o r e it was not necessary t o have a r r i v a l p r o f i l e s ?or i n d i v i d u a l firms i n a r e a s o u t s i d e t h e c e n t r e . For HBW t r i p s t o intermediate a r e a d e s t i n a t i o n s t h e r e f o r e , one a r r i v a l p r o f i l e was e s t a b l i s h e d f o r t h e whole a r e a , t h i s being t h e same a s t h e aggregate p r o f i l e f o r a l l c e n t r a l a r e a firms.

Once p r o f i l e s had been obtained or estimated a s described i n Chapter

2 , they were added t o g e t h e r on a zonal b a s i s , weighted by t h e number of employees i n each f i r m a r r i v i n g by c a r . Then, by assuming t h a t t h e p r o f i l e s of firms employing l e s s than 1 5 (which i n 1976 accounted f o r

25%

of t o t a l

employees i n t h e c e n t r a l a r e a ,

6%

intermediate) a r e not s u b s t a n t i a l l y d i f f e r e n t from t h o s e employing more, t h e s e zonal a r r i v a l p r o f i l e s were applied t o t h o s e p a r t s of t h e HBW matrix with d e s t i n a t i o n s i n t h e c e n t r a l and intermediate areas. The zonal a r r i v a l p r o f i l e s were a p p l i e d by

d e s t i n a t i o n zone, by applying a f a c t o r H t o each element i n t h e column _t where

t+L+A t

j r ( t )tit

TABLE

4

1975 and 1980

0-D

Matrices (7.45-9.15

am) by

Purpose

PURPOSE

CV

HBW

OTHER

TOTAL

1975

%

1 8

5 3

29

100

1980

UP DATE

%

19

51

30

100

TRIPS

3151

8301

4942

Fig. 1 3 Relationship of cordon flows

t o p a r t s of t h e matrix ( p r i v a t e veh.

t r b )

1 2

3

4

5

6

7 8

w

X _{Trips i n t e r c e p t e d i n f u l l by t h e given cordon.}

A t = l e n g t h of time s l i c e

n = no of time s l i c e s over t h e period of t h e t o t a l 0-D matrix

f ( t ) = t h e a r r i v a l p r o f i l e function

L = time l a g

The time l a g L i s t o account f o r t h e d i f f e r e n c e between t h e time a t which v e h i c l e s t r a v e r s e t h e cordon, and t h e ( l a t e r ) time a t which t h e

occupants of t h o s e v e h i c l e s a r r i v e a t work. It i s an average f i g u r e , obtained from surveyed network times as

5

minutes.

3.9

Temporally disaggregating t h e "other" p r i v a t e v e h i c l e matrix

This s e c t i o n d e a l s with t h e method f o r dealing with t h e remaining t h r e e p a r t s of t h e HBW matrix ( t r i p s with e x t e r n a l d e s t i n a t i o n s ) and a l l o t h e r p r i v a t e v e h i c l e t r i p s combined. Fig. 1 3 , c o l .

4,

shows t h e p a r t s which have t o be disaggregated and c o l . 2 shows t h e number of t r i p s i n each p a r t (only those t r i p s which t r a v e r s e p a r t of t h e SATURN network a r e

included). Cols.

5

t o

8

show t h e p a r t s of t h e matrix which a r e i n t e r c e p t e d by each of t h e two cordons, i n each d i r e c t i o n . It can be seen t h a t t h e

outer cordon outbound ( c o l .

8 )

i n t e r c e p t s a l l t h e remaining p o r t i o n of t h e HBW matrix, t h e equivalent p a r t s of t h e "other" matrix, and nothing e l s e . Hence p r o f i l e s obtained from outbound flows a t t h e o u t e r cordon can be

applied d i r e c t l y t o t h e sum of t h e s e s i x p a r t s ( i . e . a l l t r i p s with e x t e r n a l d e s t i n a t i o n s ) .

To avoid problems caused by r o u t e choice, t h e cordon flows were added t o produce one p r o f i l e , which was applied t o t h e sum of t h e s i x p a r t s

uniformly ( i . e . one f a c t o r per time s l i c e ) .

Note t h a t a s we a r e not using t h e cordon flows i n terms of a b s o l u t e numbers, b u t r a t h e r a r e looking a t t h e r e l a t i v e flows a t d i f f e r e n t times i n t h e peak period, it i s not necessary t o have a completely " c a r - t i g h t "

cordon, i . e . no harm w i l l be caused by leakages through minor uncounted roads. (This i s not so f o r t h e i n n e r cordon a s w i l l be shown l a t e r . )

There t h e r e f o r e remain t o be disaggregated, t h o s e p a r t s of t h e "other" matrix with c e n t r a l and intermediate a r e a d e s t i n a t i o n s . As can be seen, no cordon matches t h e s e flows p a r t i c u l a r l y w e l l , ( a p e r f e c t match being where t h e flows t o be s p l i t a r e counted, and no o t h e r flows a r e counted.) However it i s p o s s i b l e because of t h e l o c a t i o n of t h e i n n e r cordon ( i n s i d e t h e inner r e l i e f roads) and t h e r e l a t i v e number of t r i p s i n each p a r t of t h e matrix, t o use t h e i n n e r cordon inbound flows i n conjunction with p a r t s of

-

36

-

Fig.

1 4

Production of p r o f i l e f o r a p p l i c a t i o n t o "OTHER" p r i v a t e veh.matrix.

No vehs.

No vehs.

I-'HBW & E-C HBW

(from firm's surveys)

3.

time

%

of

peak p e r i o d

4.

Non-wgrk t r i p s time