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92 section, this did not allow a conclusive decision. Table 4.13 includes the results for the same sets of initial values but for unweighted analysis. The predictions overall are worse than the ones of weighted analysis. However, standard deviations are much lower. Comparing the results of the two definitions, the results of analysis using the gap size (T) as the dependent variable are much better. The conclusion of these two sections is that best mean values are provided by weighted analysis while the standard deviation associated with the mean values is much smaller for unweighted analysis which assumes T as the dependent variable. 4.5.7 Effect of Sample Size - Another point investigated was the effect of reducing the sample size on the predictions and especially on the standard deviation of the mean over all the groups. The groups up to now consisted of 500 accepted gaps. However during a half-hour observation period the accepted gaps are usually much less. The groups of one set were divided up to form groups Of 200 vehicles. Table 4.14 shows the results. Table 4.15 is a collection of the respective results for a sample size of 500 vehicles. Comparison of the results shows that the reduction in sample size affected the prediction only by 0.01 sec while it increased the standard deviation by only a very small amount. Therefore the predictions based on a sample size of 200 are not significantly worse than those based on a sample size of 500.

93 4.5.8 The Effect of Assuming the Gap Characteristics not Constant Up to now the simulation assumed that cx and are the same for all drivers. This simplifying assumption was replaced by defining distributions of values for both the parameters. The distribution used was normal in each case. The simulation was carried out only for one set of initial values. Each entry vehicle was assigned its own critical gap and move-up time with the restricticn that no value should be outside the following range m + 2s > x ^ in - 2s where m is the input mean and s the input standard deviation. The accepted gaps were divided into 20 groups of 500 acceptances each. The analysis was performed as described previosuly. Tables 4.1 and 4.17 show the results of this set of simulation data. The predictions compare with the input values equally well as the predictions for constant cx and The standard deviation of the mean, however, is slightly larger than in the previous cases. (Compare Table 4.17 with Tables 4.14 and 4.15.) The increase is very small and does not invalidate the method when a and vary between drivers. 4.6 Comparison of the Simple Linear Model and Armitage and McDonald's Two-line Model As has been described in section 4.3, Armitage and McDonald have proposed a model which fits two straight lines to the data. This model is only slightly more complicated to apply once the data have been abstracted but requires the abstraction of rejected gaps. The simple linear model requires

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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

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where a: the critical gap (sec), NQ

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where = Q e cx e -1 17 the maximum

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19 The research carried out at TRRL

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take account of local operating con

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23 These types are illustrated in f

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25 exceeded by a considerable margi

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27 queues at the end and beginning

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29 TYPICAL CONVENTIONAL ROUNDABOUT

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- Page 49 and 50: 38 CHAPTER 3 COLLECTION 0F DATA
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- 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
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- Page 63 and 64: 61 CHAPTER 4 GAP ACCEPTANCE CHARACT
- Page 65 and 66: 63 this field. The conventions used
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- Page 69 and 70: 67 of drivers who accept such gaps,
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- Page 83 and 84: 81 The direct linear relationship i
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- Page 89 and 90: 87 the rejected gaps. The results o
- Page 91 and 92: 89 exclusion of top values decrease
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- 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
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- 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
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- 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
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- Page 127 and 128: 1 2 3 4 5 6 7 8 9 10 125 TABLE 4.21
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- Page 131 and 132: 129 TABLE 4.26 Time interval- (sec)
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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 -'-