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The smallness of PSL coefficient which equals to+0.27 indicates a so limited increase in V85 compara-ble with +2.1 in Ali et al. [6], +4.75 in Figueroa andTarko [7], and +0.98 in Fitzpatrick et al. [8]. Then,the effect of PSL on V85 is very low due to the baddriving behavior in Egypt. Although LW, NL, PW and MW have considerableeffect on operating speed, but they are excluded fromthe statistical model, because they are insignificant(P-value >0.05) in all models. Therefore, the modelingwith other technique is necessary to assure theseresults. ANN modelsFor ANN models (MLP); the input variables (seven variables)are in input layer. One hidden layer, and one desired variable(V85) is in output layer with 41 observations are used. Thearchitecture of the ANN model is shown in Fig. 2. Sites are di-vided into training data set that has 35 sites (85% of all obser-vations), and testing data set that has six sites (15% of allsites). So many trials are done to reach this percentage betweentraining and testing data. As in the literature, the training dataset varies from 70% to 90%. Therefore, 85% and 15% oftraining and testing data set respectively gives the best modelperformance in the present case of research. In addition, overfitting can be avoided by randomize the 41 sites before trainingthe network to reach the best performance for both trainingand testing data. The performance of testing data must begood as training data (R2must not be smaller than 0.5) [23].The number of neurons in hidden layer is about half of thetotal number of neurons at the input and output layers (threeneurons), which is set based on generally accepted knowledgein this field. Using of learning rule of (momentum) and the suit-able number of epochs (iterations) is 5000. The previous condi-tions are suitable for quick convergence of the problem [24].So many trials were done to reach the best model perfor-mance. As a result of training and testing processing, the per-formances of the best model for training (35 samples) andtesting (six samples) data set are presented in Table 2. The observed values are plotted versus predicted values asshown in Fig. 3. It is clearly that the ANN models give so bet-ter and most confidence results than regression models.In order to measure the importance of each explanatoryvariable, general influence (sensitivity about the mean or stan-dard deviation) is computed based on the trained weights ofANN. For specified independent variable, if this value (sensi-tivity about the mean) is higher than other variables. This indi-cates that the effect of this variable on dependent variable(V85) is higher than other variables. Fig. 4 shows the sensitivityof each explanatory variable in the selected model. It is foundthat the most influential variable on V85 is PW, followed byMW and SA while PSL has the lowest effect on V85.The relationships between each input variable and V85 areshown in Fig. 5. For PW MW, LW, and SW; V85 increaseswith the increase of these four variables. In addition, the exis-tence of SA leads to a considerable decrease of V85. Althoughthe average V85 at sites without SA is 95 km/h, the average V85at sites with SA is 66 km/h. Also, it is that the increase in NLleads to more V85 values. The average V85 for 2, 3, and 4 lanessite are equal to 69, 89, and 108 km/h, respectively. Finally, theeffect of PSL on V85 is very low and can be neglected due tothe bad driving behavior in Egypt. All the previous resultsare consistent with logic.Impact of post-speed limits on V85The previous models (especially ANN) show that, the PSL hasa very small effect on V85 and can be neglected. This may beFig. 4 Sensitivity for explanatory variable. due to the bad behavior of drivers are not to care with PSLsigns generally in Egypt. Table 3 shows the 85th percentilespeed (operating speed), the PSL, and the absolute differencebetween speed limit and the operating speed.Investigation of Table 3 shows that, The V85 is higher than PSL at 21 sites. The V85 speeds vary widely from site to site asfollows: At PSL 100 km/h, the maximum of 116.14 km/h anda minimum of 56.88 km/h. At PSL 90 km/h, the maximum of 106.27 km/h and aminimum of 54.7 km/h. At PSL 40 km/h, the maximum of 44.09 km/h and aminimum of 38.13 km/h. The V85 exceeding the speed limit at the studysites varies broadly from about 16.27 km/h, as in siteNo. 36, to about 0.51 km/h, as in site No. 28. The V85exceeding the speed limit by less than 10 km/h at 12sites, and more than 10 km/h at nine sites.Based on the above points and Table 3, the results showconsiderable changes in 85th percentile speed among the studysites despite that they are in the same class (i.e. rural multi-lanetwo-way). The road characteristics of straight section used inthe present paper such as pavement width and shoulder widthsurly have significant impact on the drivers’ choice of speed atstraight sections. This may explain also the variance in the ob-served speed data between the survey sites and assures the re-sults of the operating speed modeling in the present research.Fig. 6 shows the cumulative frequency distribution curvesfor sites 2 and 18. From this figure, it is obvious that thetwo cumulative distributions are completely different; i.e. thedifference between operating speeds (V85) is very large.