(Microsoft Word - \322\355\344\310 \307\341\336\355\323\355120- 130) Al-Khwarizmi Engineering Journal Al-Khwarizmi Engineering Journal,Vol. 13, No. 3, P.P. 120- 130 (2017) Travel Time Prediction Models and Reliability Indices for Palestine Urban Road in Baghdad City Zainab Ahmed Al-Kaissi Department of Highway and Transportation Engineering/ College of Engineering/ Al-Mustansiriyah University Email:dr.zainabalkaissi77@uomustansiriyah.edu.iq (Received 31 October 2016; accepted 29 January 2017) https://doi.org/10.22153/kej.2017.01.007 Abstract Travel Time estimation and reliability measurement is an important issues for improving operation efficiency and safety of traffic roads networks. The aim of this research is the estimation of total travel time and distribution analysis for three selected links in Palestine Arterial Street in Baghdad city. Buffer time index results in worse reliability conditions. Link (2) from Bab Al Mutham intersection to Al-Sakara intersection produced a buffer index of about 36% and 26 % for Link (1) Al-Mawall intersection to Bab Al- Mutham intersection and finally for link (3) which presented a 24% buffer index. These illustrated that the reliability get worst for link (2), (1) and (3) respectively during the peak period. Extra delay is observed on link(1), (2) and (3) in terms of 95% percentile travel time of about (301.9, 219.4, and 193.8)sec. for Link (1, 2 and 3) respectively. Higher value for 95% travel time is obtained for link (1). Travel time index (TTI) of 4.2 %, 4.9% and 4% is obtained for Link (1, 2 and 3) respectively. Maximum value for delay per km that obtained for link (1) which is about 266 sec/km and 268 sec./km for link (3) and 244 sec/km for link(2). Different predicted model for the three studied links of Palestine street have been developed based on the obtained field data. A best fit is presented as compared the predicted models with the observed field travel time data for all the models of studied links which illustrated that the predicted model can present the actual field data. Keywords: Delay, Buffer Index, Travel Time, predicted model, Reliability, Urban Arterial. 1. Research Objective The aim of this research is the estimation of total travel time and distribution analysis for three selected links in Palestine arterial street in Baghdad city which is considered as one of the most important residential and commercial area in Baghdad city due to dramatic change that produce potential pressure on daily trip generation and attraction. A statistical methods is needed to model travel time distribution on which reliability indices measurements including buffer index, buffer time and 95% percentile travel time were developed based on. 2. Introduction The travel time of urban arterial in urban city played an important role in measuring the performance of traffic transportation system. Different studies are employed to model the distribution for travel time, [1], [2], [3] and [4] concluded for a lognormal distribution. Polus, (1979) concluded for a Gamma distribution; Al- Deek and Eman (2006) proposed a Weibull one [5], [6]. In Taylor and Susilawati (2012) and Susilawati et.al. (2012) the Burr distribution is adopted [7], [8]. Federal Highway Administration (FHWA) has defined travel time reliability is as consistency or dependability in travel time as measure from day to day and across different times of the day [9]. The 95th percentile travel time and Buffer Index (BI) and Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 121 Planning Time Index (PTI) considered as performance indicators for travel time reliability. Travel time distribution and empirical based approach is the base for development of these indices. Study of travel time reliability can help in understanding the variation in travel time and aid in transportation system management [10]. 3. Study Area and Data Collected 3.1. Study Area Palestine street is one of the most important major arterial streets in Baghdad city due to the majority of surrounded area of different mix land uses; commercial, educational and residential that provide potential pressure of generation and attraction additional daily trips. Palestine street is located in the East of Baghdad and it runs parallel to the west of Army Canal between Al-Mustansiriyah Sequare through Beirut square to the end of it at Maysalone sequar; 6 divided lane carriageway 3-lane in each direction. Figure (1) presents the three links that have been considered in this research namely as Link(1); From Al-Mawall Intersection to Bab Al-Muatham Intersection of 1.03 Km length, Link (2); From Bab Al- Muatham Intersection to Al-Sachara Intersection of 520m length, and Link (3); From Al-Sachara Intersection to Beirut Intersection of 620 m length respectively. The selected corridor for Palestine street links passed through three signalized intersection (Bab Al-Mutham Intersection, Al-Sachara Intersection and Bairuit Intersection) which also take into consideration their impedance and delay effect on travel time variability, reliability and distribution estimation. 3.2. Data Collection The field data are collected for the selected sections of Palestine Street for Link (1), (2) and (3) respectively. Congestion of traffic conditions is taking the major part during peak hours of the day from (12:00 to 4:00 p.m.) on Monday 18 May and Tuesday 19 May 2016 which is selected to study the variations of total travel time and travel delay time for each link in the selected site of Palestine arterial street. GPS essentials measurement equipped with cell phone is applied to compute travel time with a 30 set of data point is recorded at peak period from (12:00 to 4:00 p.m.) on each selected link corridor. Figure (2) shows the control points for mapping the distance for acceleration and deceleration and starting of each link. 4. Results and Discussions 4.1. Analysis of Travel Time In this research a consideration to congestion of traffic conditions is taking the major part during peak hours of the day from (12:00 to 4:00 p.m.) is preferred to study the variations of total travel time and travel delay time for each link in the selected site of Palestine arterial street. Fig. 1. Study Area Urban Arterial Palestine Street with Selected Three Links. Fig. 2. Control Points for Deceleration, Acceleration and Stopping Time Measurement for Studied Links. Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 122 A number of sample run of 30 is provided for each link in the south direction as described from the link name in the previous section of site selection. Travel time analysis is required for measuring the performance and to have indication about the operation efficiency of Palestine arterial corridor. Figures (3), (4) and (5) clarified the variations of total travel time for each link including stop time and ( acceleration and deceleration time). Figure (6) and (7) illustrated the travel time delay for each link; Travel time delay estimated from total travel time minus ideal travel time for each link depend on posted speed limit and distance for each one. Based on the obtained results shown in figures, link (1) from Al-Mawall to Bab-Al- Mutham intersection produced the highest values for travel and delay time than other two links due to several reasons which can be referred to the surrounded of commercial, residential and educational mix land use that produced and attracted a large number of daily trips also its attributed to the traffic condition of the link itself which controlled by a check point at the start of the route for the link near Al- Mwaal intersection and cause excess delay during the peak hours reach about 5 minutes stopping causing the state of stop and slow moving conditions for vehicles. Also its appeared that travel time varied during the time period and three maximum peak point at (12:00- 1:00p.m), (1:30-2:30p.m) for all links and additional third peak point from (3:00-3:30) for link (1) were observed. Maximum travel time of 518.5 sec. and delay time of 457sec. which is about 88% of travel time is lost due to condition of traffic congestion on link (1). Also 238sec. total travel time for link (2) with delay time of 206sec. which is about 86% loss of travel time. And for link (3) a maximum travel time of 210 sec. and delay time of 172 sec. which is about 81.9% is lost due to delay congestion. GPS essentials equipped with cell phone is applied to compute the delay component (acceleration, deceleration and stopped delay) of signalized intersections at the selected site by determining the critical points for acceleration , deceleration and stopping then measure the required time, see Figure (2) of control points for each link. Since HCM used equation for estimate the control delay which is applied for fixed signalized signal during the day and this not achieved in our locally signalized intersection which almost managed by police man that organized the traffic movement at signalized intersections otherwise its produced error in the obtained results and not matching the reality conditions. Figures (8),(9) and (10) and tables (1), (2) and (3) presented the components of total delay for intersections in the selected site for ٣٠ sample run. It's clear that stopped delay compromise the major part of intersection delay for all links studied. Also the acceleration time delay is higher than deceleration time as shown in the obtained results due to the conflict vehicles in the intersection which make the driver more alert during passing the intersection and this take more time to accelerate. Fig. 3.Total Travel and Delay Time Variations During Peak period Time for Link (1). Fig. 4. Total Travel and Delay Time Variations During Peak Period Time for Link (2). Fig. 5. Total Travel and Delay Time Variations During Peak period Time for Link (3). Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 123 Fig. 6. Total Travel Time Variations During Peak period Time for Link (1), (2) and (3). Fig. 7. Travel Time Delay Variations During Peak period Time for Link (1), (2) and (3). Table 1, Delay Component Results for Sample Run of Bab Al-Mutham Intersection. Run No. Decelerat ion Delay (sec.) Acceleratio n Delay (sec.) Stopped Delay (sec.) Total Delay (sec.) 1 17 30 60 107 2 20 35 61 116 3 23 20 68 111 4 22 38 60 120 5 15 29 58 102 6 21 45 58 124 7 18 32 100 150 8 22 30 45 97 9 15 28 65 108 10 19 14 43 76 11 10 38 115 163 12 22 18 73 113 13 28 36 38 102 14 20 28 42 90 15 15 42 102 159 16 16 43 102 161 17 8 20 43 71 18 18 45 102 165 19 22 30 150 202 20 30 25 141 196 21 20 40 60 120 22 17 38 60 115 23 20 43 45 108 24 15 35 103 153 25 21 20 116 157 26 22 44 60 126 27 20 38 60 118 28 20 31 47 98 29 18 16 63 97 30 15 24 44 83 Fig. 8. Proportions of Total Delay at Intersection for Link (1). Table 2, Delay Component Results for Sample Run of Al- Sakara Intersection. Run No. Deceleration Delay (sec.) Acceleration Delay (sec.) Stopped Delay (sec.) Total Delay (sec.) 1 10 14 55 79 2 12 18 74 104 3 16 30 53 99 4 20 30 59 109 5 15 34 48 97 6 30 45 120 195 7 10 25 58 93 8 13 31 48 92 9 35 30 55 120 10 17 42 46 105 11 20 40 71 131 12 22 38 60 120 13 10 39 75 124 14 25 35 58 118 15 35 30 45 110 16 15 33 50 98 17 12 28 43 83 18 30 41 60 131 19 12 43 53 108 20 31 44 105 180 21 18 43 106 167 22 15 40 54 109 23 30 15 46 91 24 35 26 50 111 25 15 33 35 83 26 14 28 38 80 27 10 40 33 83 28 10 40 50 100 29 15 22 37 74 30 25 33 51 109 Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 124 Fig. 9. Proportions of Total Delay at Intersection for Link (2). Table 3, Delay Component Results for Sample Run of Bairuit Intersection. Run No. Decelerat ion Delay (sec.) Acceleration Delay (sec.) Stopped Delay (sec.) Total Delay (sec.) 1 12 40 40 92 2 20 43 55 118 3 16 50 60 126 4 21 48 50 119 5 20 60 53 133 6 30 47 75 152 7 38 70 80 188 8 24 55 60 139 9 13 48 91 152 10 18 65 62 145 11 12 44 45 101 12 14 30 37 81 13 10 70 40 120 14 25 35 58 118 15 17 30 45 92 16 15 28 50 93 17 12 55 43 110 18 23 56 60 139 19 18 70 53 141 20 15 56 105 176 21 25 44 70 139 22 10 49 54 113 23 22 30 46 98 24 20 55 60 135 25 15 28 95 138 26 14 47 38 99 27 18 22 45 85 28 10 39 46 95 29 14 50 36 100 30 25 30 51 106 Fig. 10. Proportions of Total Delay at Intersection for Link (3). 4.2. Estimation of Travel Time Distribution A 30 time data set of 15min. period is collected from field data using GPS essentials equipped with cell phone as explained earlier to study the behavior of travel time variation on the three links (1), (2) and (3) that provide significant variation and multimodal shape due to the delay at signalized intersection and impedance due to traffic jam at the selected links at peak period. A normal, lognormal distribution are applied and fitted for the field data using (SPSS ver.21 statistical software). The graphical representation of histogram with normal curve for travel time distributions are shown in Figures(10) to (12) for Link (1), (2) and (3) in this research. The travel time distribution is fitted to normal for Link (1) and , log-normal for Link(2) and (3).Based on normality test for Shapiro-Wilk column in Tables (4) to (9) for Link (1) ,(2) and (3) respectively which illustrated the significant level of p -value greater than 0.05. See Table (10). a) Normal Distribution Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 125 b) Log-normal Distribution Fig. 10. Normal and Log-Normal Travel Time Distribution for Link (1). Table 4, Descriptive Statistics of Normal Distribution for Travel Time for Link (1). Table 5, Test of Normality for Travel Time Distribution for Link (1). Table 6, Descriptive Statistics of Normal Distribution for Travel Time for Link (2). Table 7, Test of Normality for Travel Time Distribution for Link (2). a) Normal Distribution Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 126 b) Log- Normal Distribution Fig. 11. Normal and Log-Normal Travel Time Distribution for Link (2). Table 8, Descriptive Statistics of Normal Distribution for Travel Time for Link (3). Table 9, Test of Normality for Travel Time Distribution for Link (3). a) Normal Distribution b) Log- Normal Distribution Fig. 12. Normal and Log-Normal Travel Time Distribution for Link (3). Table 6, Test Statistics for Travel Time Distribution. 4.3. Travel Time Model Different predicted model for the three studied links of Palestine street have been made based on the obtained field data as shown below: Travel Time for Link (1): �� � 1.012�� � 67.87 � 0.939 � � 0.882 Travel Time for Link (2): �� � 1.148�� � 30.464 � 0.967 � � 0.936 Travel Time for Link (3): �� � 1.028�� � 30.432 � 0.985 � � 0.970 Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 127 Where: TT: Total Travel Time (sec.) DT: Delay Time at signalized Intersection (sec.) The summary of stepwise regression linear models are displayed in Tables (7) to (9) respectively for Link (1), link (2) and link (3). Table 7, Stepwise Regression Models Summary for Travel Time of Link (1). Table 8, Stepwise Regression Models Summary for Travel Time of Link (2). Table 9, Stepwise Regression Models Summary for Travel Time of Link (3). The validation of the three travel time model have been illustrated in Figures (13) to (15) between the estimated travel time and observed travel time from field data. An additional data have been measured and not included in the model building to complete the process of validations. Fig. 13. Predicted Travel Time Model Versus Field Travel Time for Link (1). Fig. 14. Predicted Travel Time Model Versus Field Travel Time for Link (2). Fig. 15. Predicted Travel Time Model Versus Field Travel Time for Link (3). A best fit is presented as compared the predicted model with the observed field travel time data for all the models of studied links which illustrated that the predicted model can present the actual field data. The goodness of fit for predicted model and field observed data have been checked using chi-square test as shown in Tables (10) to (12) for the study links. Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 128 Goodness of Fit: Chi-Square Test N=17 df=16 significant level α =0.05 Predicted Models �� ��������� Link(1) 24.71978 26.296 Link(2) 8.02577 26.296 Link (3) 2.719857 26.296 For �� < ��������� ; there are no significant difference between predicted model and observed field data. 4.4. Reliability Measurement The variability of travel time effect on its reliability measurement and then produced extra arrival time which had a real cost. Furthermore reliability of travel time is an important topics for increasing safety, quality life for road users, to produce less delay for their trips. Also it's a good indicators for improving the overall system operations and management. Buffer time reliability measure is explained as [9]: ������ !"�# $%& � '()* +��,�!)-.� /�01�. /-2� $3�,.&451��06� /�01�. /-2�$3�,.& 51��06� /�01�. /-2� $3�,.& ...(1) Figure (15) presented the reliability measurement for Palestine arterial street interms of the buffer time index for link (1), (2) and (3). Increasing the buffer time index results in worse reliability conditions. Link (2) produced a buffer index of about 36% and 26 % for Link (1) and finally for link (3) which present a 24% buffer index. These illustrated that the reliability get worst for link (2) (1) and (3) respectively. Also buffer time of (62 , 59, and 38 ) sec. for Link(1, 2and 3) respectively is obtained based on average travel time for each link, that mean additional 62, 59 and 38 sec. buffer time is provided from the average value to ensure 95% arrive on time at the destination of arterial corridor for link (1),(2) and (3). Also Figure (16) show the 95% percentile travel time for observed links which presents the extra delay that perceived on each link (301.9, 219.4, and 193.8)sec. for Link (1, 2 and 3) respectively. Higher value for 95% travel time is obtained for link (1). Figure (17) illustrated the travel time index which represent the average travel time divided by free flow time for the roadway study segments. A 4.2 %, 4.9% and 4% TTI is obtained for Link (1, 2 and 3) respectively. Increasing the Travel time index Fig. 15. Buffer Time Index for Link (1), (2) and (3). Fig. 16. 95% Percentile Travel Time Results for Link (1), (2) and (3). Greater than 1.0 meaning taking a longer travel time by about 420, 490 and 400 percent of free travel time to travel the three segment length respectively with the higher travel time index for Link(2) and link(1) and finally with link(3). This demonstrated the heavily congested conditions. Also Figure (18) prove the above statement interms of estimating the delay per travelling kilometer for each segment length (1.03, 0.520, and 0.620) Km for link (1, 2 and 3) respectively studied in this research. Figure (17) depicted the maximum value for delay per km that obtained for link(1) which is about 266 sec/km and 268 sec./km for (3) and 244 sec/km for link (2). Fig. 17. Travel Time Index Results for Link (1), (2) and (3). Zainab Ahmed Al-Kaissi Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 120- 130 (2017) 129 Fig. 18. Average Delay per Kilometer Results for Link (1), (2) and (3). 5. Conclusions It can be drawn the following points: 1. Maximum travel time of 518.5 sec. and delay time of 457sec. which is about 88% of travel time for link (1); also 238sec. total travel time for link (2) with delay time of 206sec. which is about 86% loss of travel time. For link (3) a maximum travel time of 210 sec. and delay time of 172 sec. which is about 81.9% is lost due to delay congestion. 2. Stopped delay compromise the major part of intersection delay for all links studied. Also the acceleration time delay is higher than deceleration time due to the conflict vehicles in the intersection. 3. Buffer time index results in worse reliability conditions. Link (2) produced a buffer index of about 36% and 26 % for Link (1) and finally for link (3) which presented a 24% buffer index. 4. The 95% percentile travel time of about (301.9, 219.4, and 193.8) sec. for Link (1, 2 and 3) respectively. Higher value for 95% travel time is obtained for link (1). 5. Travel time index TTI of 4.2 %, 4.9% and 4% is obtained for Link (1, 2 and 3) respectively. Higher travel time index for Link (2) and link (1) and finally with link (3) respectively. 6. Maximum value for delay per km that obtained for link(1) which is about 266 sec/km and 268 sec./km for (3) and 244 sec/km for link(2). 6. Refrences [1] Richardson A. J. and Taylor, M.A.P. (1978):" Travel time variability on commuter journeys". High Speed Ground Transportation Journal. 6. pp. 77–79. [2] Rakha, H., El-Shawarby, I., M. Arafeh & Dion, F. (2006):" Estimating Path Travel- Time Reliability". Proceedings of the IEEE ‐ITSC 2006. Toronto, Canada. September 17-20. [3] Arezoumandi, M. (2011):"Estimation of Travel Time Reliability for Freeways Using Mean and Standard Deviation of Travel Time". Journal of transp. Syst. Engineering and info. Tech. Volume 11. Issue 6. [4] Pu, W. (2010): "Analytic relationships between travel time reliability measures. Compendium of Papers TRB". 90th Annual Meeting. Washington, D.C., USA. [5] Polus, A. (1979): "A study of travel time and reliability on arterial routes. Transportation". 8. pp. 141–151. [6] Al-Deek, H. & Emam, E.B. (2006): "New methodology for estimating reliability in transportation networks with degraded link capacities". Journal of Intelligent Transportation Systems. pp. 117–129. [7] Taylor, M. & Susilawati, S. (2012):" Modeling travel time reliability with the Burr distribution". Procedia - Social and Behavioral Sciences. Volume 54. 4 October 2012. pp. 75–83. [8] Susilawati, S., Taylor, M.A.P. & Somenahalli, S.V.C. (2012):" Distributions of travel time variability on urban roads". Journal of Advanced [9] Federal Highway Administration. (2005):" Traffic congestion and reliability: Trends and advanced strategies for congestion mitigation". Cambridge Systematic Inc. and Texas Transportation Institute, College Station, TX. [10] Chen, C., Skabardonis, A., and Varaiya, P. (2003). “Travel Time Reliability as a Measure of Service.” In Transportation Research Record: Journal of the Transportation Research Board, 1855, pp. 74–79. )2017( 120-130، صفحة 3د، العد13دجلة الخوارزمي الهندسية المجلم زينب احمد القيسي 130 نة بغدادشارع فلسطين شرياني حضري في مديالتنبؤ لزمن الرحلة ومؤشرات الوثوقية ل نماذج زينب أحمد القيسي كلية الهندسة / الجامعة المستنصرية قسم هندسة الطرق والنقل / dr.zainabalkaissi77@uomustansiriyah.edu.iq:البريد االلكتروني الخالصة رحالت تخطيط النقل. الهدف للشبكة المرورية ولتوزيع أفضل لحساب زمن الرحلة وحسابات الوثوقية هي عوامل مهمة لتحسين كفاءة التشغيل واألمان واحد دد والذي يعمقاطع مختارة من شارع فلسطين الشرياني في مدينة بغدا ةمن الرحلة الكلي وتحليل التوزيع لزمن الرحلة لثالثزمن هذا البحث هو حساب لد ضغط إضافي من الشوارع المهمة التي تمر في المناطق السكنية والتجارية في مدينة بغداد نتيجة التطور السريع الحاصل في استعماالت األرض والذي يو لتوليد وجذب الرحالت اليومية. . ١من زمن الرحلة بسبب طبيعة زدحام المرور في المقطع رقم %٨٨ثانية حيث يتم ضياع ٤٥٧ثانية وزمن التأخير ٥١٨٫٥أعلى قيمة لزمن الرحلة . وبالنسبة للمقطع اً تأخيربوصفه %٨٦ثانية أي يتم ضياع من الوقت بحوالي ٢٠٦ثانية وزمن تأخير بحدود ٢٣٨, ٢وزمن الرحلة المستغرق للمقطع رقم تم الحصول عليه ٣٨, ٥٩, ٦٢ Bufferبالوقت بسبب تأخير الزدحام. زمن ضياع %٨١٫٩ثانية ويمثل حوالي ١٧٢أعلى زمن رحلة مستغرق هو ٣رقم ً على التوالي. هذا يعني وقت ١٬٢٬٣بالنسبة للمقطع رقم ً إضافي ا على التوالي من معدل زمن الرحلة للحصول ١٫٢٫٣لكل من المقطع ٥٩٬٣٨.,٦٢بحدود ا من باب المعظم إلي ٢أظهرت سوء الوثوقية. المقطع رقم Bufferللوصول غاية الرحلة في نهاية الطريق الشرياني. نتائج مؤشرات زمن %٩٥على دقة مؤشر وثوقية $٢٤من تقاطع الموال إلى تقاطع باب المعظم وأخيرا ١قية بالنسبة لمقطع رقم مؤشر وثو %٢٦مؤشر وثوقية و %٣٦تقاطع الصخرة أعطى , ٣٠١على التوالي. زمن تأخير إضافي بحدود ١٬٢٬٣من تقاطع الصخرة إلى تقاطع ساحة بيروت. هذه النتائج تدل على سوء مؤشرات الوثوقية لمقطع رقم تم الحصول من النتائج على .١زمن الرحلة للمقطع رقم %٩٥على التوالي. تم الحصول على أعلى قيمة ل ١٬٢٬٣ثانية للمقطع رقم ١٩٣٫٨, ٢١٩٫٤ يدل على استغراق وقت إضافي ١٫٠على التوالي. زيادة مؤشر زمن الرحلة اكبر من ١٬٢٬٣للمقطع رقم %٤, و ٤٫٩, ٤٫٢مؤشر زمن الرحلة حوالي . اعلى قيمة لنتائج ٣وأخيرا للمقطع رقم ٢رقم و مقطع رقم ١اطع الثالثة المدروسة مع اعلى مؤشر زمن رحلة للمقطع للرحلة عن الوقت الحر المثالي للمق نماذجأيضا تم تطوير . ٢ثانية /كلم للمقطع رقم ٢٤٤و ٣كلم /ثانية للمقطع رقم ٢٦٨ثانية /كلم و ٢٦٦بحوالي ١التأخير لكل كم طول كانت للمقطع رقم مقارنة لزمن الرحلة للمقاطع الثالثة في منطقة الدراسة لشارع فلسطين اعتمادا على البيانات الحقلية المستحصلة. تم الحصول على توافق جيد عندالتنبؤ للبيانات الحقلية. النماذجمع البيانات الحقلية لزمن الرحلة مما يبين قابلية تمثيل ا النماذج