Abstract
The classical route optimization problem of a network focuses on the shortest or fastest route mainly under the assumption that all roads will not fail. In fact, the capacities of roads in a transportation network are not determinate but random because of the traffic accidents, maintenance or other activities. So a most reliable route from source to sink under the time threshold may be more important than the shortest or fastest route sometimes. This paper describes a stochastic Petri net-based simulation approach for reliability-based route optimization of a transportation network. The capacities of arcs may be in a stochastic state following any discrete or continuous distribution. The transmission time of each arc is also not a fixed number but stochastic according to its current capacity and demand. To solve this problem, a capacitated stochastic colored Petri net is used for modeling the system behavior. By the simulation, the optimal route with highest reliability can be obtained. Finally, an example of a transportation network with random arc capacities is given.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahuja, R.K.: Minimum cost-reliability ratio problem. Computers and Operations Research 16, 83–89 (1998)
Bodin, L.D., Golden, B.L., Assad, A.A., Ball, M.O.: Routing and scheduling of vehicles and crews: The state of the art. Computers and Operations Research 10, 63–211 (1998)
Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. Journal of ACM 34, 596–615 (1987)
Golden, B.L., Magnanti, T.L.: Deterministic network optimization: A bibliography. Networks 7, 149–183 (1977)
Park, C.K., Lee, S., Park, S.: A label-setting algorithm for finding a quickest path. Computers and Operations Research 31, 2405–2418 (2004)
Ramirez-Marquez, J.E., Coit, D.: A Monte-Carlo simulation approach for approximating multi-state two-terminal reliability. Reliability Engineering and System Safety 87, 253–264 (2005)
Lin, J.S., Jane, C.C., Yuan, J.: On reliability evaluation of a capacitated-flow network in terms of minimal pathsets. Networks 3, 131–138 (1995)
Yeh, W.C.: A simple approach to search for all d-MCs of a limited-flow network. Reliability Engineering and System Safety 71, 15–19 (2001)
Lin, Y.K.: Study on the multicommodity reliability of a capacitated-flow network. Comput. Math. Appl. 42, 255–264 (2011)
Lin, Y.K.: Two-commodity reliability evaluation for a stochastic-flow network with node failure. Computers and Operations Research 29, 1927–1939 (2002)
Lin, Y.K.: Two-commodity reliability evaluation of a stochastic-flow network with varying capacity weight in terms of minimal paths. Computers and Operations Research 36, 1050–1063 (2009)
Lin, Y.K.: Performance evaluation for the logistics system in case that capacity weight varies from arcs and types of commodity. Applied Mathematics and Computation 190, 1540–1550 (2007)
Yeh, W.C.: A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability. Reliability Engineering and System Safety 93, 125–136 (2008)
Lin, Y.K.: Routing policy of stochastic-flow networks under time threshold and budget constraint. Expert Systems with Applications 36, 6076–6081 (2009)
Lin, Y.K.: System reliability of a stochastic-flow network through two minimal paths under time threshold. Int. J. Production Economics. 124, 382–387 (2010)
Lin, Y.K.: An algorithm to evaluate the system reliability for multicommodity case under cost constraint. Computers and Mathematics with Applications 48, 805–812 (2004)
Zhou, Y., Meng, Q.: Improving efficiency of solving d-MC problem in stochastic-flow network. Reliability Engineering and System Safety 92, 30–39 (2007)
Lin, Y.K.: Time version of the shortest path problem in a stochastic-flow network. Journal of Computational and Applied Mathematics 228, 150–157 (2009)
Janssens, G.K., Caris, A., Ramaekers, K.: Time Petri nets as an evaluation tool for handling travel time uncertainty in vehicle routing solutions. Expert Systems with Applications 36, 5987–5991 (2009)
Petri, C.A.: Kommunikation mit automaten. PhD thesis (1962) (in German)
Molloy, M.H.: Performance analysis using stochastic Petri nets. IEEE Trans. Comp. C-31, 913–917 (1982)
Tolba, C., Lefebvre, D., Thomas, P., Moudni, A.: Continuous and timed Petri nets for the macroscopic and microscopic traffic flow modelling. Simulation Modelling Practice and Theory 13, 407–436 (2005)
de Athayde Prata, B., Nobre Jr., E.F., Barroso, G.C.: A stochastic colored petri net model to allocate equipments for earth moving operations. ITcon 13, 476–490 (2008)
Jensen, K.: Colored Petri nets: Basic concepts, analysis methods and practical use, vol. 1. Springer, New York (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, T., Guo, B., Tan, Y. (2011). Reliability-Based Route Optimization of a Transportation Network with Random Arc Capacities and Time Threshold. In: Tang, Y., Huynh, VN., Lawry, J. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2011. Lecture Notes in Computer Science(), vol 7027. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24918-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-24918-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24917-4
Online ISBN: 978-3-642-24918-1
eBook Packages: Computer ScienceComputer Science (R0)