Read e-book online Flows in Transportation Networks PDF

By Renfrey B. Potts

ISBN-10: 0125636504

ISBN-13: 9780125636506

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14. 14. 51 Cheapest Routes Cheapest Routes ( a ) Appraisal of Algorithms There is an extensive literature on the problem of determining the cheapest routes on a network; the bibliography prepared by Murchland [2] lists about one hundred references. Many algorithms have been proposed, some have subsequently been shown to be incorrect, others have proved inferior to earlier ones, and indeed the literature presents a very confusing picture. This has been greatly clarified by a recent article by Dreyfus [3] which gives an appraisal of algorithms proposed for networks without turn penalties.

The general step is in two parts. The last node permanently labeled is scanned in the following way: for all nodes to which links from this node are directed the following comparison is made. Is the sum of the cost label on the node being scanned and the link cost less than the tentative node label? If the answer is yes, the node being scanned becomes the new tentative predecessor node label and the lesser cost the new tentative cost label. All other tentative labels are left unchanged.

3,withN'= {l,2,3},L1={(1,2),(2,2),(2,3),(l,3)}. 3. Compressed network obtained by combining nodes 2 and 3 of the network in Fig. 2(a). , there is a renumbering of nodes. Similarly links (1,2), ( I , 3) in L are replaced by (1,2) in L', links (2,4) and (3,4) in L by (2,3) in L' and links (2,3), (3,2), and (3,3) in L by (2,2) in L'. The compressibility equations are f;Z = f i 2 + f 1 3 = 3, (34) f;3 =f14 = 3, (35) 79 (36) f;2 =f23 +f32 +f33 = f;3 =f*4+f34 = 3. (37) 38 11. Elements of Network Theory It will be noted that the production and attraction at the new node 2 are the sums of the productions and attractions for the original nodes 2,3.

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Flows in Transportation Networks by Renfrey B. Potts

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