توسعه مفهوم كوتاه‌ترين درخت گسترش و كاربرد آن در تحليل شبكه‌هاي حمل و نقل

Minimum Spanning Tree Concept Development and its Application in Transportation Network Analysis

چكيده- از جمله مسايل مهم جريان در شبكه، براي تحليل ساختار و عملكرد آن، مسيله كوتاه‌ترين درخت گسترش است. بررسي پيوستگي شبكه و اولويت بندي كمان هاي شبكه از جمله كاربردهاي اين مسيله است. معيار محاسبه و تعيين كوتاه‌ترين درخت گسترش مفهوم هزينه كمان است كه تا به حال در اكثر مطالعات مربوطه از مفهوم زمان سفر آزاد استفاده شده است. در مقاله جاري، اين مفهوم به حالت عام زمان سفر تحت بار تقاضا و محدوديت ظرفيت توسعه يافته و كاربرد آن در تحليل شبكه هاي حمل و نقل بررسي مي شود. با توجه به ضرورت تعريف و بررسي اثر هزينه اي كه در شرايط مختلف بتواند هزينه كل واقعي را نشان دهد، در اين مقاله، هزينه كمان، براي محاسبه كوتاه‌ترين درخت گسترش، زمان سفر كمان تحت بار جريان در شبكه تعريف شده و مسيله براي مطالعه موردي راه هاي شرياني استان تهران فرمول بندي و حل مي شود. نتايج نشان مي دهد كه با تعريف هزينه به صورت زمان سفر تعادلي كمان و حل مجدد مسيله هزينه كل شبكه از 25973 به 28081 ثانيه (8 درصد) افزايش و كمان هاي تشكيل‌دهنده نيز حدود 30 درصد تغيير مي كنند. در صورت استفاده از كوتاه‌ترين درخت گسترش اوليه (بدون بار) براي مسيله تحت بار تقاضا، هزينه شبكه برابر 30232 ثانيه مي شود كه معادل 17 درصد افزايش در هزينه و 9 درصد خطاست.

Abstract: Minimum Spanning Tree (MST) is a well-known problem for analyzing the structure and performance of transportation networks. In this problem, cost is usually considered just as a function of supply (transportation network) properties, like Free Flow Travel Time (FFTT) which is independent of traffic volume. This is a simple and ideal presumption that neglects the effect of traffic volume on links travel time. Although network performance is a result of demand and supply interaction in reality, this assumption which simplifies the solution neglects the sensitivity of this problem to demand. Therefore MST estimation would be more accurate and realistic by using real travel time instead of Free Flow Travel Time (FFTT). In this paper, MST problem is solved by substituting FFTT with the cost related to the effect of congestion on link travel time. This modified cost is achieved through assigning origin-destination demand matrix to the network, based on Deterministic User Equilibrium (DUE) assignment procedure by means of VISUM software package®. Then, this new cost is utilized to formulate and solve MST problem using WinQSB software package®. The solution of DUE problem is based on the behavioral assumption that each motorist travels on the path that minimizes the travel time from origin to destination. This choice rule implies that at equilibrium, the link-flow pattern is such that the travel times on all used paths connecting any given O-D pair, will be equal. The effect of travel behavior of choosing the shortest path is reflected in equal travel times between each O-D. Thus in this study the effect of the aggregate travel demand on the individual behavior is considered in the loaded version of MST problem. In this way the dependence of each individual decision when entering the network (marginally) on the decision of all the previous travelers who have entered the network is taken into account. The proposed concept is applied to the case of Tehran province network, consisting of 56 nodes and 75 links. For this purpose Iran country intercity origin-destination demand matrix of the year 2007 is assigned to the arterial roads of entire country network consisting of 854 nodes, 1147 links and 56 traffic analysis zones for 4 different travel modes (1- passenger, 2- air, 3- train, 4- bus and freight) and travel time on Tehran province network is derived to calculate the MST. Results show that by developing cost concept to the loaded condition, despite decreasing MST link numbers from 54 to 51 and also decreasing its length from 718 km to 701 km (with 627 km common to both) total cost has 2144 seconds increased from The amount of dissipated plastic energy in frames with composite beams and/or rigid connections is lower than that of other frames. By replacing the simple connections with rigid connections and also steel beams with composite beams, plastic energy dissipation will be reduced in the joints. But it will be increase in other members, especially in column bases and beams. In view of the above results, the highest rate of plastic energy dissipation is in steel frames with simple connections. The results also show that composite frames with rigid connections have the lowest plastic energy dissipation capacity. This is due to the weakness of concrete and its plastic failure that imposes a sudden stress concentration in the weld and causes connection failure. Distribution of compressive stresses in the rigid connection model is transferred in a concentrated form to the outer face of the column flange. But in the simple connection model, the distribution in the outer flange of the column is more uniform. It can be said that in the case of the middle connection, the direct effect of mechanism 1 is greater than that of mechanism 2. The concrete surrounding the steel columns in composite beams causes additional stiffness in this area and has a negative effect on the nonlinear behavior of theses frames. This accelerates the formation of plastic hinges in composite beams and results in sudden brittle failures, especially at the welded connections. Consequently the structure can not achieve higher energy dissipation. So it can be concluded that composite frames with rigid connections cause a reduction in the natural period and the capacity of plastic energy dissipation and result in failure mechanisms in frame.