# SYSTEM OPTIMUM FRAMEWORK FOR EVALUATION AND EFFICIENCY OF ROAD NETWORK

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3 road network will achieved the same result between the both approaches. The efficiency, in the context of modeling, was obtained from different ratio of system cost between the both approaches. 2.1 User Equilibrium (UE) Wardrop (1952) assuming that on all parts of the network, all drivers have an identical perception of cost, proposed principles of route choice in accordance with the two codes of behaviour as follows: 1. The costs on all routes used between any given pair of end poitns are equal and not greater than the cost experienced by a single vehicle on any unused route between them. 2. The average journey cost over all routes used is the minimum possible. It is generally considered that in practice Wardrop s first principle is the more likely basis for network equilibrium. Similarly, most theoretical work has attempted to produce solutions in accordance with this principle, subject usually to additional constraints. Beckmann et al. (1956) showed that, assuming that the cost on any link a is a function of the flow on link a only, i.e.: C a = c a (V a ) (1) And that the c a (V a ) are increasing functions, then the flows V a satisfying Wardrop s first principle are unique and are the same as those which: minimize Z = c ( v) dv (2) If the requirement, that c a (V a ) is an increasing function of V a is relaxed to allow it to be a non-decreasing function, then the c a remain unique but the V a may not be. 2.2 System Optimum (SO) A solution satisfying Wardrop s second principle is unlikely because of its requirement that drivers should sacrifice self-interest for the common good. However, such a solution provides the minimum value for the total costs available under the specified conditions and is a useful benchmark for comparison purposes. A system optimum solution is obtained by: minimize C = V c (3) where: p id = a path from i to d V pid = the flow from i to d on path p id C pid = the cost in path p id One way to solve the SO routing problem can be described as follows by introducing the marginal cost of travel: dca c a '( Va ) = cava + Va (4) dva where dc a /dv a is the differential of c a (V a ) with respect to V a, and substituting c a for c a in Z in equation (2), the system optimum solution may be obtained by minimizing Z provided that id a Va 0 pid a pid pid 909

9 DKI Jakarta Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 5, pp , 2005 Serang Pandeglang Tangerang Bekasi Rangkasbitung Bogor Cianjur Sukabumi Indramayu Jepara Karawang Pati Rembang Tuban Gresik Kudus Lamongan Demak Pekalongan Blora Cirebon Surabaya Subang Tegal Batang Kendal Semarang Purwodadi Bojonegoro Purwakarta Majalengka Mojokerto Brebes Pemalang Temanggung Salatiga Sragen Ngawi Nganjuk Sidoarjo Sumedang Kuningan Jombang Bandung Banjarnegara Surakarta Karanganyar Purbalingga Magelang Madiun Ciamis Purwokerto Boyolali Garut Sukoharjo Kediri Sleman Purworejo Ponorogo Malang Klaten Blitar Wonogiri Tasikmalaya Wates Yogyakarta Kebumen Trenggalek Cilacap Tulungagung Bantul Wonosari Pacitan Pasuruan Lumajang Probolinggo Panarukan Bondowoso Banyuwangi Jember Figure 5. Road Network of Java Island Figure 5 depicts a land transport network in Java Island, Indonesia. In this study only land transport (road and rail) were considered, as a limitation to the implementation and analysis stage. In the base condition road was categorized depending on its function for carrying freight transport. First category is primary route, i.e. PANTURA (Pantai Utara) or the Java north coast corridor. Second category is secondary route, i.e. JALUR SELATAN or south corridor and JALUR TENGAH or middle corridor. And third category is the alternative routes Do Nothing Case/Base Case In this case, it was evaluated existing condition of multimodal freight transport network in Java Island using UE (User Equilibrium) and SO (System Optimum) method. In this case only land transport (road and rail) were considered. The equilibrium solutions for the existing Java multimodal network are summarized in Table 4, together with the benefits that may be available if optimal control is put in place. From Table 4 can be seen that, when comparing assignment results of UE and SO, the SO routing results in a 5.19% of road mode usage, in terms of ton-km, diverting to rail. The SO condition yields a benefit of 2% of the total transport cost relative to the base UE condition. Table 4. Equilibrium Solutions for the Java Network - Base Case JAVA NETWORK BASE CASE Cost Road Usage Rail Usage (ton.hr.) ton.km % ton.km % User Equilibrium , ,22 System Optimum , ,41 Benefit 2,00% Figure 6 depicts the pattern under UE condition for the Java network base case. It can be seen that PANTURA and JALUR SELATAN were most used. Road network Figure 6. Flow Pattern (Base Condition) Rail network 915

11 Road network Figure 7. Flow Pattern (Do Something A) Rail network Table 8. Optimum Solutions for the Java Network Railroad Investment - Do Something B JAVA NETWORK RAILWAYS INVESTMENT Cost Road Usage Rail Usage (ton.hr.) ton.km % ton.km % Do Nothing , ,22 Do Something , ,44 Saving 7,11% From Table 8 can be seen that, when comparing optimum results of do nothing and do something B, the railroad investment scenario achieves a better solution. The do something B results in a 3.22% road mode usage, in terms of ton-km, diverting to rail. This yields a different of 7.11% of the total transport cost relative to the base condition. Figure 8 show flow pattern for Java network in do something B scenario. Road network Figure 8. Flow Pattern (Do Something B) Rail network In the do something scenario, the railroad investment scenario has a higher saving than the road investment scenario. 5. CONCLUSION From implementation s result on artificial network was tested above can summarized that there are inefficient on the network, which can got from UE condition relative to SO condition, in term of system cost total (veh.sec/hour). Level of inefficient for the artificial network is 8.69%. 917

12 On freight transport network in Java Island, for base condition case, there are inefficient of mode usage. It can be seen that the SO routing results in a 5.19% of road mode usage, in terms of ton-km, diverting to rail. The SO condition yields a benefit of 2% of the total transport cost relative to the base UE condition. In the do something A condition, there are 0.99% rail mode usage, in term of ton-km, diverting to road. This yields a different of 0.50% of the total transport cost relative to the base condition. And in the do something B condition, there are 3.22% road mode usage, in term of ton-km, diverting to rail. This yields a different of 7.11% of the total transport cost relative to the base condition. Based on result of implementation above, it can achieved a conclusion that equilibrium approach only reproduce assign traffic flow optimally from user side. But it can t represent optimal condition in context of network system. So, in the road network system models need to done evaluation using SO method that can achieve the better solution. Practically, implementation of SO method can be applied on traffic management scheme, i.e.: road pricing, link directional, parking policy, etc. REFERENCES Beckmann, M., McGuire, C. and Winsten, C. (1956) Studies in the Economics of Transportation. Yale University Press, New Haven. Directorate of Urban Road Development (1997) Indonesian Highway Capacity Manual. Directorate General Bina Marga, Jakarta. Ortuzar, J.D., Willumsen, L.G. (1990) Modelling Transport. John Wiley&Sons, Chichester. Prasetyo, L.B.B. (1999) Modelling Intermodal Transfers of Freight Transportation Network. Master Thesis, Sistem dan Teknik Jalan Raya, ITB. Sheffi, Y. (1985) Urban Transportation Network. Prentice-Hall, New Jersey. Wardrop, J.G. (1952) Some Theoretical Aspects of Road Traffic Research, Proc. Inst. Civ. Eng., Part II, 1, pp

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