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# PDF (DX094490.pdf) - White Rose Etheses Online

PDF (DX094490.pdf) - White Rose Etheses Online

## 11 small-island layouts

11 small-island layouts were designed in accordance with eq. 2.13. In 1973, results of two research projects were published which showed that Wardrop's formula was no longer satisfactory for the design of roundabouts. Murgatroyd (1973) showed that the predictions of that formula (eq. 2.1) were overestimating capacity or underestimating it if the 80% practical capacity (eq. 2.2) was used. As the proportion of traffic weaving was no longer relevant he suggested that p should have a value of 1.0 in the formula, i.e. all the traffic should be assumed to weave. Ashworth and Field (1973) examined the assumed linear relationship of capacity and the weaving proportion in Wardrop's formula with data from two sites in Sheffield. There was no correlation between the two variables, with a slope not significantly different from zero at either site. The observed capacities were considerably different from both the full arid 80% practical capacity values. Ashworth and Laurence (1974) pursued further the examination of the application of Wardrop's formula. Obser- vations from 21 weaving sections were used. The conclusion of the study were that: (1) The capacity of roundabouts is not affected by the proportion of weaving traffic. (2) Observed capacities were approximately 70% of the maximum theoretical capacity as a whole. However, there was considerable scatter for individual entries indicating that Wardrop's formula was no longer reliable. (3) If the weaving proportion was assumed to equal 1.0, the practical capacity predictions were approx- imately correct overall, but they still produced considerable scatter for individual entries.

12 Since then a number of alternative formulaehave been produced to predict the capacity. They are described in the subsequent sections. 2.5 Gap Acceptance Models Before 1966, Tanner (1962) had developed a model of operation of T-junctions based on the gap acceptance behaviour of drivers. Once the operation of roundabouts became similar to that of T-junctions, his model and the gap acceptance para- meters formed the basis of a large portion of the research to develop new formulae relating to roundabout performance. Tanner (1962, 1967) derived the following capacity formula for priority junctions: q2 = q 1 (1 - q 1 (ct- 1 ) -2q1 e (1-e with the following assumptions (eq. 2.3) (1) The major stream flow consists of a single traffic stream equal to q1(veh/s); there is a minimum headway, (sec), between successive vehicles in the major stream. (2) The entering vehicles arrive at the intersection at a rate greater than q 2 (veh/s), where q 2 is the entry capacity. (3) 2(sec) is . the minimum headway of successive entering vehicles. (4) The critical gap, a(sec) is assumed constant for all drivers. The above formula formed the basis of a significant portion of the subsequent research on the capacity of roundabouts. Wohl and Martin (1967) considered roundabouts

• Page 1: A COMPUTER SIMULATION STUDY OF THE
• Page 4 and 5: 11 SUMMARY This thesis reports on a
• Page 8 and 9: 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
• Page 10 and 11: viii LIST OF TABLES 3.1 Observed Fl
• Page 12 and 13: 1.1 Roundabout Design 1 Intersectio
• Page 14 and 15: 3 a modified formula was introduced
• Page 16 and 17: CHAPTER 2 LITERATURE REVIEW: CAPACI
• Page 18 and 19: (Wardrop, 1957). The investigation
• Page 20 and 21: 9 They looked also at ways of impro
• Page 24 and 25: 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 and 76:

73 They related the gap-acceptance

• Page 77 and 78:

75 advance which rejected gaps shcu

• 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

• Page 127 and 128:

1 2 3 4 5 6 7 8 9 10 125 TABLE 4.21

• Page 129 and 130:

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

• Page 131 and 132:

129 TABLE 4.26 Time interval- (sec)

• Page 133 and 134:

No. of passing vehicles 0. 1 2 3 4

• Page 135 and 136:

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

• Page 137 and 138:

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

• Page 139 and 140:

tag ..engfñLf Weaving Width •3/

• Page 141 and 142:

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

• Page 143 and 144:

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

• Page 145 and 146:

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

• Page 147 and 148:

145 CHAPTER 5 THE SIMULATION PROGRA

• Page 149 and 150:

147 following a uniform (rectangula

• Page 151 and 152:

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

• Page 153 and 154:

151 5. Entering or alternatively up

• Page 155 and 156:

153 (b) Three initial numbers for t

• Page 157 and 158:

155 vehicles are not of such length

• Page 159 and 160:

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

• Page 161 and 162:

159 CHAPTER 6 RESULTS AND COMMENTS

• Page 163 and 164:

161 equivalent to the capacity of a

• Page 165 and 166:

163 parameters. It was found that a

• Page 167 and 168:

165 least 50% straight ahead traffi

• Page 169 and 170:

167 left-turning vehicles, is not u

• Page 171 and 172:

169 exhibit a minimum average delay

• Page 173 and 174:

171 not operating at or near capaci

• Page 175 and 176:

Input 500 1000 1500 2000 2500 3000

• Page 177 and 178:

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

• Page 179 and 180:

177 1. Ashworth and Laurence (1977)

• Page 181 and 182:

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

• Page 183 and 184:

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

• Page 185 and 186:

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

• Page 187 and 188:

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

• Page 189 and 190:

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

• Page 191 and 192:

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

• Page 193 and 194:

C) •1 > 0 L. > 10 5 191 ST 101 =

• Page 195 and 196:

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

• Page 197 and 198:

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

• Page 199 and 200:

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

• Page 201 and 202:

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

• Page 203 and 204:

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

• Page 205 and 206:

0 60 40 IT 203 cx = 2.50 sec 500 =

• Page 207 and 208:

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

• Page 209 and 210:

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

• Page 211 and 212:

0 0 60 40 120 209 Beta Q1 = 3000 ve

• Page 213 and 214:

.0 60 40 11 1.5 211 Alpha Q1 = 1000

• Page 215 and 216:

C) Co 60 40 20 213 ALpha Q1 = 3000

• Page 217 and 218:

215 A computer simulation model has

• Page 219 and 220:

217 hou1d. Therefore any change in

• Page 221 and 222:

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

• Page 223 and 224:

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

• Page 225 and 226:

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

• Page 227 and 228:

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

• Page 229 and 230:

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

• Page 231 and 232:

DOUBLE PRECISION R INTEGER*4 I A =

• Page 233 and 234:

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

• Page 235 and 236:

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

• Page 237 and 238:

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

• Page 239 and 240:

82 2 237 sui entries of lane tar

• Page 241 and 242:

108 106 CONTINUE 109 CONTINUE DO 10

• Page 243 and 244:

CAP CAP+CA(N3) 125 CONTINUE 00 128

• Page 245 and 246:

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

• Page 247 and 248:

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

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