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74 (iv) after estimating q 5 and L, T was varied to give a least squares fit to the flow data; (v) t was assumed to be the reciprocal of the satur- ation flow of the arm from which the main circulating flow emerges. Method (iv) was described as the most consistent, with the disadvantage that for certain flow conditions it did not give satisfactory results; however Armitage and McDonald preferred to use method (v) as can be seen from equation 4.6 where the denominator of the right-hand side is the expression for the saturation flow. The other two parameters, q 5 and L, were estimated together by the method of least squares. Taking the simplest case of a single lane of traffic entering a roundabout, two straight lines were fitted to a plot of the number of entries (y) during each gap against the length, (x), of the gap. The line for x ^ L was y = 0, while for x ^ L, it was y = q*(x_L). This is illustrated by Fig. 4.6 for a 2-lane entry where the model is fitted to some sample data and compared with the conventional gap-acceptance step function model which uses parameters cL and 3. The model uses both accepted and rejected gaps. However it should be noted that all rejected gaps less than L have a zero contribution to the least squares value. Also all accepted gaps less than L have a constant contrib- ution since the line for x L cannot change slope being defined as y 0. Therefore those points have no influence on the slope of the line for x > L which determines q 5 . As L decreases more rejected gaps are contributing to the sum of the squares of differences, but it is not possible to know in

75 advance which rejected gaps shculd or should not be abstracted from the data. This results in a considerable number of rejected gaps which although abstracted from the data, are not utilized finally. It should be noted that the rejected gaps will be numerous and proportionally the majority of all the gaps, especially at high circulating flows. Therefore this method is very inefficient in the use of data which have to be manually abstracted. It should be noted that Fig. 4.6 refers to a 2-lane entry of a roundabout. The slope indicated by q 5 on the figure is in fact half the value of the actual slope. This is necessary in order to estimate the saturation flow per lane. Also, it should be noted that no rejected gaps less than L were included on the diagram. It is of interest to examine the relationship between the parameters q 5 and L, used by Armitage and McDonald, and the parameters critical gap, a, and move-up time, , as used in the present study. As can be seen from Fig. 4.6, the move-up time, , is the reciprocal of the saturation flow, and the critical gap, a, is related to L and q 5 as is shown in eq. 4.7 a = = 1 1 (eq. 4.7) (eq. 4.8) These two relationships allow the reinterpretation of the data given in Armitage and McDonald (1977) into the conventional parameters. These are included in Table 4.1.

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A COMPUTER SIMULATION STUDY OF THE

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11 SUMMARY This thesis reports on a

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iv TABLE OF CONTENTS Page No Acknow

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2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9

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viii LIST OF TABLES 3.1 Observed Fl

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1.1 Roundabout Design 1 Intersectio

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3 a modified formula was introduced

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CHAPTER 2 LITERATURE REVIEW: CAPACI

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(Wardrop, 1957). The investigation

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9 They looked also at ways of impro

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11 small-island layouts were design

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13 operating under no clearly defin

- Page 26 and 27: where a: the critical gap (sec), NQ
- Page 28 and 29: where = Q e cx e -1 17 the maximum
- Page 30 and 31: 19 The research carried out at TRRL
- Page 32 and 33: take account of local operating con
- Page 34 and 35: 23 These types are illustrated in f
- Page 36 and 37: 25 exceeded by a considerable margi
- Page 38 and 39: 27 queues at the end and beginning
- Page 40 and 41: 29 TYPICAL CONVENTIONAL ROUNDABOUT
- Page 43 and 44: EXAMPLE OF GRADE SEPARATED JUNCTION
- Page 45 and 46: EXAMPLES OF MINI-ROUNDABOUT LAYOUTS
- Page 47 and 48: "- C) 0 '.-. ) LU 0 S.- 0 C) ( j 0
- Page 49 and 50: 38 CHAPTER 3 COLLECTION 0F DATA
- Page 51 and 52: 40 Sheffield. It was observed that,
- Page 53 and 54: 42 using a SONY AV342OCE portable m
- Page 55 and 56: 44 Ecciesall Road. However, this di
- Page 57 and 58: 46 TABLE 3.2 Day Entry Total flow F
- Page 59 and 60: \\ Ec.esa11 Road \"\\/i? LLjji 1lTh
- Page 61 and 62: \\\\\ ' \\\\ r * ' \\\_\ ' ' \\% .'
- Page 63 and 64: 61 CHAPTER 4 GAP ACCEPTANCE CHARACT
- Page 65 and 66: 63 this field. The conventions used
- Page 67 and 68: 65 have been developed that use mor
- Page 69 and 70: 67 of drivers who accept such gaps,
- Page 71 and 72: 69 consistently accept all gaps gre
- Page 73 and 74: 71 a merging platoon. Although they
- Page 75: 73 They related the gap-acceptance
- Page 79 and 80: 77 proposed by Bennett (1971), Horm
- Page 81 and 82: larger than the respective ones for
- Page 83 and 84: 81 The direct linear relationship i
- Page 85 and 86: 83 mean squared errors or variances
- Page 87 and 88: 85 produce reasonable predictions,
- Page 89 and 90: 87 the rejected gaps. The results o
- Page 91 and 92: 89 exclusion of top values decrease
- Page 93 and 94: 91 definition of gap size as depend
- Page 95 and 96: 93 4.5.8 The Effect of Assuming the
- Page 97 and 98: 95 demonstrated on Fig. 4.8 and Fig
- Page 99 and 100: 97 When the model was validated by
- Page 101 and 102: 99 4.8.2.2 The Negative Exponential
- Page 103 and 104: 101 0: the proportion of restrained
- Page 105 and 106: 103 coefficient of the regression s
- Page 107 and 108: 105 From the point of view of which
- Page 109 and 110: 107 TABLE 4.1 (continued) No.1 Loca
- Page 111 and 112: Cl U) a) a) 0 I )1) H U) 0 U) a) '-
- Page 113 and 114: 1 2 3 4 56789 10 2.95 2.94 2.68 2.9
- Page 115 and 116: Ci) (ii) 0. 113 TABLE 4.7 mean st.d
- Page 117 and 118: 1 2 345678 9 0 2.42 2.44 2.50 2.63
- Page 119 and 120: 1 2 3 4 5 6 7 8 9 10 2.61 2.93 2.68
- Page 121 and 122: (i) (ii) a 119 TABLE 4.13 mean st.d
- Page 123 and 124: oup 121 TABLE 4.16 no.of entries on
- Page 125 and 126: 1 2 3 4 5 67 8 9 10 11 12 13 14 15
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1 2 3 4 5 6 7 8 9 10 125 TABLE 4.21

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4i -1 0 '-I- U-I a) .li.IC 127 E- .

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129 TABLE 4.26 Time interval- (sec)

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No. of passing vehicles 0. 1 2 3 4

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ci) 4) x4-4 ..-..' .,-4 CDV) U H N

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250 200 50 I00 50 135 o i 6 7 8 9 1

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tag ..engfñLf Weaving Width •3/

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0 0 1, 0 C- 4.5 4. 0 3. 5 3. 0 2.5

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3. 5 3. 0 2.5 0 0 2. 0 1.5 141 1.5

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U, II 114 U z isa 114 Ii. z 0 U) (/

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145 CHAPTER 5 THE SIMULATION PROGRA

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147 following a uniform (rectangula

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149 Let F(t) = r, the random fracti

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151 5. Entering or alternatively up

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153 (b) Three initial numbers for t

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155 vehicles are not of such length

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U U, a Ia- LO 0.9 0.8 07 0.5 - 0.4.

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159 CHAPTER 6 RESULTS AND COMMENTS

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161 equivalent to the capacity of a

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163 parameters. It was found that a

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165 least 50% straight ahead traffi

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167 left-turning vehicles, is not u

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169 exhibit a minimum average delay

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171 not operating at or near capaci

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Input 500 1000 1500 2000 2500 3000

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4000 3500 3000 L 2500 N -c > ..2000

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177 1. Ashworth and Laurence (1977)

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(0 C -J Lj_ o L 0 -a 3 z > 4.0 3. 5

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C.. -C N-c > 1000 980 960 940 920 9

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0 1 U- uJ 540 520 500 480 183 0. 0

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N > 0 -J IL > C- C ILl 0 200 160 16

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C) Co 6 4 >2 -J a m C.. 0 > -I 8 18

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C, Co >\ CD 0 CD CD S 15 10 189 % S

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C) •1 > 0 L. > 10 5 191 ST 101 =

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U (0 >.' -J C, (I > -J 20 10 193 %

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' -J a m C.. > 10 5 195 Qi = 500 ve

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0 CD CD Ii >\ CD CD CD CD C.. CD >

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0 (U (U (U Cj (U (U > -J (U 20 10 0

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0 I. >' Oi C.. > -J 0 '-0 30 20 10

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0 60 40 IT 203 cx = 2.50 sec 500 =

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C) (0 60 40 20 205 02 = 3.50 sec c.

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t!) 60 40 >20 207 Beta 01 = 1000 ve

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0 0 60 40 120 209 Beta Q1 = 3000 ve

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.0 60 40 11 1.5 211 Alpha Q1 = 1000

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C) Co 60 40 20 213 ALpha Q1 = 3000

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215 A computer simulation model has

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217 hou1d. Therefore any change in

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219 Ashworth, R. and M.Z.H. Mattar,

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221 Kirnber, R.M. and E.M. Hollis,

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223 Wagner, F.A., 1966. "An Evaluat

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7 0 4 225 0 4 20 24 F re A. 1 Qb.er

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4-. C'- -7 227 0 4 12 20 24 -. z ec

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DOUBLE PRECISION R INTEGER*4 I A =

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231 GPNO(i13) = GPNO(K3)+1 NOG GPNO

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43 121(SX,A1) 12 IF (A1.GE.AP) AX =

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235 DELY(H2,M3) T3(i12,N3)-121(112,

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82 2 237 sui entries of lane tar

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108 106 CONTINUE 109 CONTINUE DO 10

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CAP CAP+CA(N3) 125 CONTINUE 00 128

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ci) 0 ci) a) '-I 0 a) 0 4-1 in 4-1

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I-i a) 0 ci) a) $4 a) L;l 4-I 0 -'-