 Original Paper
 Open Access
Derivation of level of service by artificial neural networks at horizontal curves: a case study in Egypt
 Ahmed Mohamed Semeida^{1}Email author
https://doi.org/10.1007/s1254401401522
© The Author(s) 2015
 Received: 7 January 2014
 Accepted: 9 November 2014
 Published: 27 January 2015
Abstract
Purpose
Multilane highways represent the majority of the total length of highway network at many countries. The geometric design of such facilities and the traffic volume which includes heavy vehicles percentage (HV) are considered the most important factors affecting the level of service (LOS), especially on the horizontal curves.
Methods
This paper aims to explore the relationship between the road geometric characteristics including horizontal curve properties and traffic volume including average annual daily traffic (AADT) and HV in one hand and LOS in the other hand by two methods. First is generalized linear modeling (GLM) procedure and second is the artificial neural networks (ANNs) procedure. In this research, the traffic and road geometric data are collected on 78 horizontal curves that are distributed on four multilane highways in Egypt. Two of them are located in desert area and the others in agricultural area.
Results
The Analyses showed that the ANNs procedure give the best models for estimating LOS. Also, the most influential variables on LOS are AADT, HV, and radius of horizontal curve (R). Finally, the derived models have statistics within the acceptable regions and, also, they are conceptually reasonable.
Conclusions
The previous inferences are so important for road authorities in Egypt as they can consider them as a first step for origination of Egyptian highway capacity manual.
Keywords
 Level of service
 Highway geometry
 Horizontal curves
 Generalized linear modeling
 Artificial neural networks
1 Introduction
The transportation system in Egypt is suffered from limited roadway infrastructure and the lack of operation and management experience. Among the most critical issues in highway planning and management is to explore the effectiveness of road geometric characteristics and the percentage of heavy vehicles (HV) in traffic composition on LOS at multilane rural highways. Rural multilane highways are an important type of uninterrupted flow facilities in which there is no obstructions to the movement of vehicles along the road. Such facilities represent the majority of the highway system in Egypt. Highway Capacity Manual (HCM) [1] uses traffic density (Density), in terms of passenger cars per kilometer per lane as the primary level of service (LOS) measure for multilane highways. AbdulMawjoud and Sofia [2] indicate that horizontal curves have long been recognized as having a significant effect on vehicle speeds. Therefore, it is necessary and important to be taken into consideration in the present analysis. Hence, this paper aims to evaluate LOS on horizontal curves at multilane highways by two modeling techniques. First is generalized linear modeling (GLM) technique and the second is artificial neural networks (ANNs) technique.
Field data on multilane highways in Egypt are used in this investigation. The analysis considers 78 horizontal curves that are distributed on four multilane highways. Two of them are located in desert area (CairoAlexandria and CairoIsmailia desert highways), and the other two are located in agricultural area (Cairo Alexandria and TantaDamietta agricultural roads). Then, the paper includes two separate relevant analyses. The first analysis uses GLM procedure to investigate the relationships between Density as dependent variable, and horizontal curve properties, roadway factors, traffic volume, and HV as independent variables. The horizontal curve properties include radius of curve, deflection angle, and superelevation. The road factors for each curve are lane and pavement width, lateral clearance, and number of lanes in each direction. In addition the traffic volume is expressed by average annual daily traffic (AADT). The second analysis uses ANNs procedure to explore the previous relationships and comparing the results. According to the objectives of this research, road authorities in Egypt can determine LOS for different horizontal curves on multilane highways and improve the traffic performance of them in the future.
2 Background studies
Several researches have been carried out to analyze the effect of road geometry and traffic composition on LOS for multilane highways. Kerner [3] confirmed that the determination of LOS for any highway is one of the most important applications of any traffic theory. Some previous theories and empirical researches focused on the interrelationships among the influence of LOS, traffic features and geometric elements on uninterrupted multilane highways [4–7]. The Indonesian highway capacity manual [8] mentioned that travel speed as the main measure of LOS of road segments.
Reinfurt et al. [9] tackled the speed changes which lead to LOS variation over the horizontal curves. They found that, as curves become sharper, there is a proportionally greater increase in speed reduction on a curve. The study findings support the debate of drivers cutting the curve short, which can result in runoff road crashes on the inside of the curve as well as headon and opposite directionsideswipe crashes with oncoming vehicles.
Arasan and Arkatkar [10] studied the effect of variation of traffic composition, road width, magnitude of upgrade and its length on Indian highways capacity and LOS, and subsequent it was concluded that highway performance significantly changes with change in traffic volume composition, width of roadway, magnitude of upgrade and its length.
Sakai et al. [11] used an empirical approach to produce LOS measure for basic expressway segments in Japan incorporating Customer Satisfaction (CS). It was concluded that LOS and CS were confirmed to have a nonlinear relation.
Shawky and Hashim [12] studied the effect of horizontal alignment on traffic performance at twolane rural highways. The follower density was used as a promising measure of traffic performance. The results show that the horizontal alignment characteristics have a significant effect on the follower density, especially curve radius value, by decreasing radius, the follower density increases (i.e., traffic performance decreases).
In Egypt, there were so few concerned with LOS due to lack of road geometric, horizontal curve, traffic flow and speed data. The most important research in this direction is published by Semeida [13]. The analysis in this paper used 45 different tangent sites from four main multilane rural highways. Two modeling techniques were used. First was multiple linear regression and second was ANNs. Results showed that the ANN modeling gives the best models for estimating LOS. The most influential variables on LOS are lane width, HV, and existence of side access. This analysis was limited to tangent sections. Hence, the present paper extends and improves the analysis to include LOS on horizontal curves.
3 Study sites and field data
This research concerns with horizontal curves at rural multilane highways in Egypt. Therefore the analysis of this paper uses 78 horizontal curves (Sections) from four main multilane highways in Egypt. These roads include CairoAlexandria Agricultural Highway, Tanta Damietta Agricultural Highway, CairoAlexandria Desert Highway, and CairoIsmailia Desert Highway. The collected data are divided into three types as road geometric characteristics including horizontal curves, vehicles speed, and traffic volume data including AADT and HV.
3.1 Road geometry data
Statistical analysis and symbols of all collected variables
Variable  Variable Symbol  Max.  Min.  Avg.  S.D. 

1 Lane Width in meters  LW  3.65  3  3.61  0.1 
2 Pavement Width in one direction in meters  PW  14.6  6  8.36  1.82 
3 Lateral Clearance in meters  LC  3.6  1.2  1.84  0.41 
4 No of lanes in each direction in lanes  NL  4  2  –  – 
5 Radius of curve in meters  R  780  40  402.5  231.7 
6 Deflection Angle in Degree  DA  70.6  14.3  27.9  16.7 
7 Superelevation %  e  12  2  4.7  3.5 
3.2 Vehicles speed data
Average travel speed data (ATS_{pc}) for passenger cars
Curve No.  ATS_{pc} (m)  Curve No.  ATS_{pc} (m)  Curve No.  ATS_{pc} (m)  Curve No.  ATS_{pc} (m) 

1  44.33  21  78.09  41  58.39  61  56.35 
2  36.65  22  79.79  42  67.9  62  39.28 
3  47.36  23  47.9  43  73.03  63  80.31 
4  46.2  24  62.17  44  74.9  64  76.91 
5  26.27  25  53.18  45  72.57  65  88.19 
6  46.24  26  54.61  46  78.44  66  75.29 
7  26.95  27  38.93  47  25.43  67  86.3 
8  29.11  28  61.19  48  65.68  68  72.51 
9  39.88  29  85.14  49  70.74  69  62.44 
10  69.22  30  83.8  50  48.78  70  79.5 
11  78.13  31  61.58  51  64.32  71  71.82 
12  81.99  32  73.38  52  66.77  72  74.58 
13  79.55  33  68.72  53  70.64  73  61.34 
14  75.97  34  73.38  54  50.34  74  70.65 
15  73.2  35  71.21  55  50.6  75  78.69 
16  77.63  36  74.1  56  66.17  76  64.31 
17  79.79  37  73.23  57  66.36  77  58.14 
18  25.02  38  73.71  58  73.63  78  24.35 
19  25.86  39  68.71  59  65.54  
20  78.59  40  74.45  60  60.17 
3.3 Traffic volume data
Values of DF and SF for roads under research
Factors  Cairo – Alexandria (agricultural highway)  Tanta – Damietta (agricultural highway)  Cairo – Alexandria (desert highway)  Cairo – Ismailia (desert highway)  

Daily Factor (DF)  Saturday  1.05  1.03  1.00  1.01 
Sunday  0.96  0.98  1.01  1.03  
Monday  0.98  0.96  0.97  0.99  
Tuesday  0.93  0.94  0.99  0.98  
Wednesday  0.97  0.97  1.03  1.02  
Thursday  1.01  1.05  1.06  1.04  
Friday  1.1  1.13  0.98  0.93  
Seasonal Factor (SF)  January  0.82  0.84  0.71  0.74 
February  0.94  0.96  0.65  0.68  
March  0.89  0.88  0.74  0.71  
April  0.91  0.93  0.87  0.84  
May  0.87  0.89  0.94  0.96  
June  1.11  1.08  1.29  1.25  
July  1.21  1.24  1.38  1.41  
August  1.29  1.32  1.61  1.58  
September  1.14  1.18  1.19  1.14  
October  1.08  1.06  1.03  1.01  
November  0.89  0.91  0.84  0.87  
December  0.85  0.82  0.79  0.81 
Traffic count data, density, and LOS values for all horizontal curves
Curve No.  Traffic count in both direction per hour  AADT  Dir. V  HV (%)  Density  LOS 

1  1593  18,060  1084  20.5  18.16  D 
2  2298  26,053  1563  32.6  36.09  E 
3  641  7267  436  12.5  4.14  A 
4  663  7516  451  12.5  4.39  A 
5  1200  13,604  816  20.5  15.39  C 
6  768  13,341  800  20.5  12.23  C 
7  1000  17,371  1042  21  27.5  E 
8  1033  17,944  1077  20.5  17.43  D 
9  692  12,021  721  13.8  7.87  B 
10  3175  55,152  3309  20.5  22.52  E 
11  3191  55,430  3326  20.5  19.95  D 
12  3163  54,944  3297  20.5  19.02  D 
13  3098  53,815  3229  20.5  19.6  D 
14  3212  55,795  3348  20.5  20.52  D 
15  3181  55,256  3315  20.5  21.3  D 
16  3185  55,326  3320  20.5  20.08  D 
17  3171  55,083  3305  20.5  19.54  D 
18  1640  28,488  1709  22  32.74  E 
19  1591  27,637  1658  29.4  33.29  E 
20  1348  23,416  1405  12.7  7.67  B 
21  3175  55,152  3309  20.5  19.97  D 
22  3258  56,594  3396  20.5  19.54  D 
23  1665  28,922  1735  20.5  25.6  E 
24  1348  23,416  1405  18.4  10.39  B 
25  1448  25,153  1509  18.4  12.15  C 
26  1376  23,902  1434  18.4  11.83  C 
27  1586  27,550  1653  29.3  33.05  E 
28  3175  55,152  3309  33.2  43.79  E 
29  852  15,902  954  12  3.76  A 
30  864  16,126  968  12  3.87  A 
31  1037  15,920  955  18.4  11.24  C 
32  1056  16,212  973  18.4  9.61  B 
33  1037  15,920  955  18.4  10.07  B 
34  1101  16,903  1014  18.4  9.61  B 
35  1037  15,920  955  18.4  9.72  B 
36  1082  16,611  997  16.4  9.29  B 
37  1037  15,920  955  18.4  9.45  B 
38  1044  16,027  962  16.4  9.34  B 
39  1037  15,920  955  18.4  10.08  B 
40  1086  16,672  1000  14.8  9.07  B 
41  1022  15,690  941  18.4  11.86  C 
42  1051  16,135  968  18.4  10.38  B 
43  1032  15,843  951  18.4  9.48  B 
44  1065  16,350  981  13.8  8.9  B 
45  1024  15,720  943  14  9.05  B 
46  1063  16,319  979  13.8  8.5  B 
47  1076  16,519  991  21  28.57  E 
48  311  4774  286  5.7  2.73  A 
49  297  4560  274  12  2.76  A 
50  316  4851  291  12.5  4.02  A 
51  291  4467  268  12  3.04  A 
52  316  4851  291  7.7  2.76  A 
53  310  4759  286  12  2.76  A 
54  323  4959  298  12  3.87  A 
55  352  5404  324  12.5  3.88  A 
56  318  4882  293  5.5  2.7  A 
57  312  4790  287  6.5  2.74  A 
58  325  4989  299  5  2.41  A 
59  330  5066  304  12  2.98  A 
60  328  5035  302  12  3.24  A 
61  314  4821  289  12  3.47  A 
62  802  12,312  739  20.5  13.97  C 
63  806  12,374  742  12.7  6.25  A 
64  817  12,543  753  12.7  6.62  A 
65  806  12,374  742  12.7  5.69  A 
66  817  12,543  753  12.7  6.76  A 
67  637  9779  587  12.5  4.59  A 
68  551  8459  508  12.7  4.74  A 
68  637  9779  587  12.7  6.36  A 
70  551  8459  508  12.5  4.31  A 
71  637  9779  587  12.7  5.53  A 
72  551  8459  508  12.7  4.61  A 
73  817  12,543  753  13.8  8.41  B 
74  823  12,635  758  12.7  7.2  B 
75  811  12,450  747  12.7  6.47  A 
76  806  12,374  742  12.7  7.81  B 
77  817  12,543  753  18.4  9.38  B 
78  795  12,205  732  20.5  22.36  E 
 V:

design hourly volume (typically, the 30th highest annual hourly volume)
 AADT:

Average Annual Daily Traffic in vehicle per day and
 K:

factor used to convert annual average daily traffic to a specified annual hourly volume. (K = 0.1 for rural roads).
Note that D = 0.6 for rural roads as stated by HCM 2010 [1]. Dir. V values for all sites are recorded in Table 4. Finally, HV is extracted from the recorded manual counting as there is a classification of vehicles for passenger cars and HV. These values are indicated in Table 4.
3.4 Determination of LOS for horizontal curves under study
 Dir. V:

hourly volume in one direction (veh/h)
 PHF:

peakhour factor (PHF = 0.88 for rural roads)
 N:

number of lanes in the selected direction
 f_{HV} :

heavyvehicle adjustment factor (0.97–0.9) depending on HV value, and
 f_{p} :

driver population factor (1) as the driver is familiar with the highway.
Consequently, LOS is determined for each curve from Density value which reflects the degree of vehicles congestion on each curve. The LOS and Density for all curves are determined and listed in Table 4.
4 Methodology
The methodology of LOS prediction in the present research is divided into two main procedures: GLM procedure and ANNs procedure. It is concluded from the previous researches that the ANNs provide a better model is highlighted by better predictions for lower values, the normality of the residuals and their independence from the predicted variable. Several authors have reported greater performance of ANNs compared to GLM. The advantage of ANNs over GLM is that ANNs can directly take into account any nonlinear relationships between the dependent variables and each independent variable. ANNs have another advantage in that the ANN modeling approach is fast and flexible. Finally, ANNs model can be easily use by engineers.
4.1 GLM procedure
 X_{n} :

Explanatory variables from 1 to 9
 β_{ o } :

Regression constant; and
 βn :

Regression coefficient.
 (1).
This model must yield logical results (non negative). Also, at Xi = 0; Density must be zero.
 (2).
The existing of logarithmic link function that can linearize this form for the purpose of coefficient estimation.
This model form is executed using the generalized linear model procedure PROC GENMOD in the SAS statistical software [19]. SAS user’s manual [20] applies the maximum loglikelihood technique to estimate the regression coefficients, standard errors, Wald Chisquared statistics, pvalues. In addition, the R^{2} (coefficient of determination) and (infinity norm of error vector) ║δ║ values are calculated for each model as Varagouli et al. [18]. Finally, the model with minimum ║δ║ and highest R^{2} value is selected.
4.2 ANNs procedure
In general, ANNs consist of 3 layers, namely, the input, the hidden and the output layers. In statistical terms, the input layer contains the independent variables and the output layer contains the dependent variables. ANNs typically start out with randomized weights for all their neurons. When a satisfactory level of performance is reached the training is ended and the network uses these weights to make a decision (Singh et al., 2011) [21].
The experience in this field is extracted from Semeida [13, 22, 23]. In his researches, the multilayer perceptron (MLP) neural network models give the best performance of all models. In addition, this network is usually preferred in engineering applications because many learning algorithm might be used in MLP. One of the commonly used learning algorithms in ANN applications is back propagation algorithm (BP) [24], which is also used in this work.
The overall dataset of 78 curve sections is divided into a training dataset and a testing dataset. As in the literature, the training data set varies from 70 % to 90 % and the testing data set varies from 10 % to 30 %. Model performances are and R^{2} for testing and training data set in one hand and for all data set in the other hand (Voudris, 2006) [25].
So many trials are done to reach the suitable percentage between training and testing data that gives the best performance for cars and trucks speed models. In addition, over fitting can be avoided by randomize the 78 curves before training the network to reach the best performance for both training and testing data. The performance of testing data must be good as training data (R^{2} must not be smaller than 0.7) (Tarefder et al., 2005) [26].
5 Data analysis and results
5.1 Correlation analysis
Correlations between Density and independent variables
D  NL  LW  PW  LC  AADT  R  DA  e  HV  

Density  PC  1.000  −0.214  −0.253*  0.190  −0.331**  0.871**  −0.914**  0.887**  0.849**  0.907** 
Sig.  0.060  0.025  0.095  0.003  0.000  0.000  0.000  0.000  0.000  
NL  PC  1  −0.285*  0.992**  0.519**  −0.24*  −0.305**  0.179  0.254*  0.195  
Sig.  0.011  0.000  0.000  0.034  0.007  0.116  0.025  0.088  
LW  PC  1  −0.165  0.021  0.35**  0.368**  −0.256*  −0.187  −0.291**  
Sig.  0.149  0.855  0.002  0.001  0.024  0.1  0.01  
PW  PC  1  0.538**  −0.204  −0.268*  0.151  0.24*  0.166  
Sig.  0.000  0.073  0.018  0.188  0.035  0.146  
LC  PC  1  0.195  0.19  −0.343**  −0.31**  0.021  
Sig.  0.088  0.095  0.002  0.006  0.855  
AADT  PC  1  0.189  −0.179  −0.204  −0.151  
Sig.  0.094  0.116  0.073  0.188  
R  PC  1  −0.811**  −0.823**  0.21  
Sig.  0.000  0.000  0.065  
DA  PC  1  0.72**  0.179  
Sig.  0.000  0.116  
e  PC  1  0.19  
Sig.  0.095  
HV  PC  1  
Sig. 
5.2 Analysis and results of GLM procedure
Model estimation results for the best GLM models
GLM Models  

Variable  GLM 1  GLM 2  GLM 3  
Coeff.  Chisquare  pvalue  Coeff.  Chisquare  pvalue  Coeff.  Chisquare  pvalue  
Constant  3.86  531.6  0.0001  5.05  753.4  0.0001  4.8  544.4  0.0001 
AADT  0.136  97.1  0.0001  0.086  32.26  0.0001  0.108  39.77  0.0001 
R  −0.505  2847  0.0001  −0.311  572.1  0.0001  −0.294  421.3  0.0001 
HV  –  –  –  0.999  538.1  0.0001  0.99  514.3  0.0001 
LC  –  –  –  –  –  –  −0.136  8.04  0.0046 
R^{2}  0.877  0.96  0.962  
║δ║  0.258  0.142  0.123 
(Whereas, R^{2} = 0.962, and δ = 0.123)

The third model in Eq. (9) is better than the other three as it has higher R^{2}, and lower ║δ║.

In the best model, it is concluded that the negative sign of the coefficient for R means that Density decreases with the increase of R. The horizontal curves that have greater radii encourage the drivers to increase their speed on them than with smaller radii. These curves are safer for drivers. Thus, the greater R improves LOS on horizontal curves.

In addition for the third model, the positive sign of the coefficient for AADT means that Density increases with the increase of traffic volume. The increase of traffic volume makes the road section more crowded with vehicles and consequently, the number of vehicles per km clearly increases. This implies to the decrease of LOS. Also, this result is rational.

In the same model, the positive sign of the coefficient for HV means that Density increases with the increase of HV. The horizontal curves with higher HV are more congestive and the drivers of passenger cars are annoyed with HV which force them to decrease their speed. This implies to the decrease of LOS. Also, this result is rational.

In the best model, it is found that the negative sign of the coefficient for LC means that Density moderately decreases with the increase of LC. In other word, the wider lateral clearance encourages the drivers to increase their speed on horizontal curve as the maneuvering is easier at wider road cross section and then Density decreases. Consequently, the wider LC slightly improves LOS on horizontal curves. This result is consistent with logic.
5.3 Analysis and results of ANNs procedure
Performances for the best three trials of ANNs model
Trial number  Performance  Number of Training samples  Number of Testing samples  Overall Model 

1  68  10  
R^{2}  0.931  0.894  0.928  
║δ║  0.134  0.211  0.186  
2  63  15  
R^{2}  0.996  0.965  0.993  
║δ║  0.044  0.167  0.102  
3  58  20  
R^{2}  0.882  0.863  0.879  
║δ║  0.193  0.234  0.205 

Density decreases with the increase of R. The increase of R from 134 m to 617 m leads to a decrease of Density from 15.7 pc/km/lane to 5.6 pc/km/lane. In other words, the LOS improves form C to A. The relation between the two variables is nearly linear and clearly inverse.

Density increases with the increase of HV. The increase of HV from 16 % to 22 % leads to an increase of Density from 9.8 pc/km/lane to 18 pc/km/lane. This implies that LOS deteriorates from B to D. Moreover, Density is nearly constant with HV less than 16 %. This implies that HV effect on traffic moving starts at percentage more than 16 %. Less than this value, this effect is feeble.

Density increases with the increase of AADT. The increase of AADT from 8000 veh. /h to 38,000 veh. /h leads to an increase of Density from 7.7 pc/km/lane to 12.8 pc/km/lane. This indicates that LOS retreats from B to C. The relation between the two variables in this zone is linear. Density is nearly constant with AADT less than 8000 veh./ h. This proves that AADT is not effective on traffic flow less than this value.

Although the effect of the other variables (LC, DA, and e) on Density is limited, but it is discussed for more knowledge. Density decreases with the increase of LC. The increase of LC from 1.4 m to 2.3 m leads to a decrease of Density from 10.5 pc/km/lane to 9 pc/km/lane. This implies that no change in LOS B. In addition, the same conclusion is resulted for DA and e as the same LOS B is existed with variable change. Therefore, the effect of these variables on Density is weak and can be neglected.
In addition, Density increases with the increase of both HV and AADT. These results are more accurate than the regression models and rational.
6 Conclusions
 1.
The ANNs procedure gives so better, more confident and consistent with logic results than GLM procedure in terms of predicting Density.
 2.
The best ANNs model gives R^{2} and δ equal to 0.993 and 0.102, respectively compared with the best GLM model for the same horizontal curves gives R^{2} and ║δ║ equal to 0.962, and 0.123, respectively.
 3.
For ANN model: The most influential variable on Density is R, followed by HV and AADT.
 4.
Also, the increase of R from 134 m to 617 m leads to a decrease of Density from 15.7 pc/km/lane to 5.6 pc/km/lane. In other words, the LOS improves form C to A.
 5.
In addition, the increase of HV from 16 % to 22 % leads to an increase of Density from 9.8 pc/km/lane to 18 pc/km/lane. This implies that LOS deteriorates from B to D.
 6.
Finally, the increase of AADT from 8000 veh. /h to 38,000 veh. /h leads to an increase of Density from 7.7 pc/km/lane to 12.8 pc/km/lane. This indicates that LOS retreats from B to C.
These results are so important for road authorities in Egypt as they can determine LOS for different horizontal curves and improve the traffic performance of them in the future. Also, they can consider these results as a first step for origination of Egyptian highway capacity manual. Finally, future research should be conducted to extend all aspects of this research using comprehensive field data including more multilane rural roads and vertical alignment. In addition, capacity for multilane highways is the main target in the Egyptian future research.
Declarations
Acknowledgments
The author acknowledges the support of the General Authority of Roads, Bridges, and Land Transport, (GARBLT) for their assistance with the acquisition of traffic count data. Also, the author acknowledges Eng. Nasser Abdalla, Department of Civil Engineering, Faculty of Engineering, AlAzhar University for his assistance with the acquisition of horizontal curve properties at sites under research.
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Authors’ Affiliations
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