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

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## 5.1 Introduction 146

5.1 Introduction 146 Computer simulation models have been developed ever since general-purpose computers became readily available in the mid-50's. Short historical summaries are given by Lewis and Michael (1963) and Gerlough and Huber (1975). Lewis and Michael reported that already in 1956, three digital computer simulations were published in the traffic engineering literature. Drew (1968) defined computer simulation as a dynamic representation of some part of the real world, achieved by building a computer model and moving it through time. The term computer model denotes a model which is not intended to be solved analytically but rather to be simulated on an electronic computer. Simulation is a working analogy. It involves the construction of a working model presenting similarity of prop- erties or relationships to the real problem under study. Thus complex traffic situations can be studied in the laboratory rather than the field. This allows the study of longer periods than it would be possible in reality; the repetition of certain combinations of relevant parameters with only slight modifications to determine the precise contribution to the problem of each parameter; and the comparison of alternative solutions for specific problems without the expense of in-situ long-term testiriq. 5.2 Generation of Random Numbers One of the most important features of simulating traffic is the ability to generate random events. Such a generation takes place in two steps: First, a random number

147 following a uniform (rectangular) distribution is generated. second, this random number is treated as a probability to substitute into an appropriate distribution function in order to solve for the associated event. (Gerlough and Huber, 1975; Gordon, 1969) Any phenomenon whose behaviour Is not predictable by any obvious deterministic law and whose numerical values satisfy several tests of randomness, to ensure, for example, that each decimal digit occurs with equal frequency without any serial correlation, is accepted as random. Programs for computers can be written which will output a sequence of numbers which satisfy the various statistical tests of randomness that have been devised. Random numbers generated in a non-random fashion are called pseudorandom numbers. The following is such a process. An assumed starting number, R0 , is multiplied by an appropriate multiplier, k. The remainder of the division by an integer M is the next random nymber, R 1 , which is used to generate a subsequent random number. The relationship can.be expressed as R = kR modM m rn-i (eq. 5.1) The above will give a sequence of pseudorandom numbers in the range 1 to (N-i). R must be an odd integer in the range 1 to (M-l). If the numbers of the sequence are divided by M they will give a sequence of random fractions in the region o to 1. The cycle of random numbers is repeated after M/4 operations of equation 5.1. The following is an example of the operation of the routine. If the initial values of the parameters are: k = 5,

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