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PDF (DX094490.pdf) - White Rose Etheses Online

PDF (DX094490.pdf) - White Rose Etheses Online

R0 = 5, N = 16, then 148

R0 = 5, N = 16, then 148 = 5 * 5 mod 16 = 9 R2 = 5 * 9 mod 16 = 13 R = 5 * 13 mod 16 = 1 = 5 * 1 mod 16 = 5 The length of the cycle can be increased to such a value that would not allow any periodicity to the generated numbers to be observed. However, this value may be limited by the maximum integer value the computer accepts. One advantage of the pseudorandom processes is that if the same initial number is used the same sequence will result. Thus, exactly the same traffic flow conditions can be tested for each modification of the simulated system. 5.3 Production of the Desired Random Variate Figure 5.1 shows how the pseudorandom fractions can be converted to the desired distribution. The figure shows the cumulative probability distribution of variable X. The fraction generated by the method described above is interpreted as a probability and is used as an argument to enter the dis- tribution giving the value of X as the function. As an example, consider the conversion to a shifted negative exponential distribution. The cumulative form F(t) = P(h ^ t) is: - (t-t) /(t-T) F(t) = 1-e where : the mean headway (sec) t: headway (sec) r: the shift (sec) (eq. 5.2)

149 Let F(t) = r, the random fraction in the range 0 to 1. Taking logarithms of both sides of equation 5.2 - = = (l - r) = logR R 1 - r is equally random in the range 0 to 1. Solving the above for t t = T + ( t - T) (_logR) t = T + Ct - T) (log) Equating T with 0, equation 5.3 reduces to the negative exponential distribution t = tlog 5.4 The Program SIMC (eq. 5.3) (eq. 5.4) The current prc' 4ject is an improvement of a simulation model built previously (Natsinas, 1979). That model simulated a flared entry to a roundabout but did not take into account vehicle turning movements. This section will describe briefly that model, called SIMC. The assumptions incorporated in the model SIMC were: 1. The circulating flow is a negative exponential distribution. 2. The layout of the simulated entry consists of a two lane approach road flaring to four lanes at the stop line. Thus the row of vthicies at the stop line has 4 positions, the second row from the stop line has 3 positions, while subsequent rows have 2 positions. 3. There is a 2 sec minimum headway for each lane of the

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