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Traffic modelling is interpreted as «application of methods of casual tests to the determined and probabilistic problems». Therefore the estimation with a confidential interval is often applied to calculation of a template of average value from results of imitation. More shortly an interval, above - an estimation.
Confidence limit is calculated by classifying the simulation results in appropriate groups. The main methods of evaluation of the measurement results should be attributed copy method, the method of the middle group and the regenerative method.
On fig. 19 concepts of these techniques are illustrated.
On a copying method a quantity of independent imitations is carried out, and the confidential interval is calculated by negation of results of an initial transitive phase agrees to following procedures:
1) Imitation is started from a certain initial condition, using the aprioristic information, for example, about an equilibrium state;
2) The data is denied till some predetermined time T beginning from an empty initial condition.
Though it is desirable to carry out the preliminary test for definition T, this time is usually established by supervision or heuristically, and process of negation of the initial data is called as negation of initial influence.
If observable values X1, X2, …, Xn for sizes X, tell number of calls in system, are independent the confidential interval [ma +, ma-] average size m = E {X} with probability (1 - a) is calculated as follows.
Believing that s2 - a dispersion X, from the central limiting theorem and population mean model
formula (69)
Approximately normal distribution N (m, s2/n) with average value m and a dispersion s2/n follows at n ® ¥. Using this theorem, confidential limits ma + and ma - with probability (1 - a) ´ 100 % are defined as formula (70)
Where ua / 2 - value from normal distribution, such that formula (71)
Usually s2 - it is unknown, and consequently from imitating result the dispersion model is calculated formula (72)
On a method of average group n выборок, received at imitation performance, break on M groups on n ¢ = n / M выборок in everyone. Then average value and a confidential interval are calculated on each of M groups. Believing Xmi i model in m th group, we set average value in group as
formula (73)
And the full model of a population mean is set as formula (74)
The quantity of groups M can be such big what the central limiting theorem supports. Though it is represented desirable that some data between groups has been rejected to eliminate correlation between groups, it is known that dispersions of samples can be reduced more truly, using this data. Therefore, if in most cases, mentioned above, data processing proceeds after negation of the data during initial stage T according to a method of average group in most cases all data is used.
In practice it is known that with n ¢> 25 correlation between groups becomes insignificant, and the group average approximately follows normal distribution N (m, s2/n ¢), where m and s2 an average and a dispersion from X, accordingly. From here (70) confidential limits are similar are calculated as
formula (75). Where s2m - a dispersion.
If s2m it is unknown, and substitution formula (76). It is used, value ta / 2 M - 1 in tab. 1 is still used instead of ua / 2 as it became above.
The regenerative method is based on a principle that groups are formed between regenerative epoch, and has advantages in stochastic processing. For example, we can define duration of time of the computer modelling, necessary to receive the set accuracy of imitating result. However here there are some problems with application of this method to practical models, for example, how to define regenerative epoch?
Stochastic process {X (t); t ³ 0} is called as regenerative process if it arrives in conformity with likelihood rules irrespective of last history during series {tn} which concern regenerative epoch. For example, in system with delay if we will put that {tn} are epoch of receipt of a call when the system is empty, new quantity of the calls which have again arrived in system, makes regenerative process with regenerative epoch {tn}.
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