Abstract
The co-car anomaly appears in the study of circular traffic queues. An unfolding of the corresponding coloured net is proved to be isomorphic to a particular cycloid. Then the anomaly is reduced to a combinatorial property of path lengths in the cycloid. Methods of the cycloid algebra are used to derive iterations of cycloids. Different such iterations correspond to different models of traffic queues, but only those with observable co-traffic items show the anomaly.
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Notes
- 1.
For the notion of occurrence mode of a coloured net see [2], page 35.
- 2.
This also follows from the Chinese remainder theorem as discussed in Sect. 5.
- 3.
An elementary cycle is a cycle where all nodes are different.
- 4.
\(u, a, b, c, \cdots \) denote the points in the Petri space, while the vectors \(\boldsymbol{u},\boldsymbol{a},\boldsymbol{b},\boldsymbol{c},\cdots \) are pointing to them when originated in the origin (0, 0), respectively.
- 5.
\(\chi _{_{0}}(a,b\oplus _g j)\) would be insufficient in case of \(c > g\).
References
Attiya, H., Welch, J.: Distributed Computing. McGraw-Hill, New York (1998)
Girault, C., Valk, R. (eds.): Petri Nets for System Engineering - A Guide to Modelling, Verification and Applications. Springer, Berlin (2003) https://doi.org/10.1007/978-3-662-05324-9
Jones, G.A., Jones, J.M.: Elementary Number Theory. SUMS, pp. 163–189. Springer, London (1998). https://doi.org/10.1007/978-1-4471-0613-5_9
Petri, C.A.: Nets, Time and Space. Theor. Comput. Sci. 153, 3–48 (1996)
Valk, R.: On the Structure of cycloids introduced by Carl Adam Petri. In: Khomenko, V., Roux, O.H. (eds.) PETRI NETS 2018. LNCS, vol. 10877, pp. 294–314. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-91268-4_15
Valk, R.: Formal Properties of Petri’s Cycloid Systems. Fundamenta Informaticae 169, 85–121 (2019)
Valk, R.: Circular traffic queues and Petri’s cycloids. In: Janicki, R., Sidorova, N., Chatain, T. (eds.) PETRI NETS 2020. LNCS, vol. 12152, pp. 176–195. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51831-8_9
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Valk, R. (2021). Deciphering the Co-Car Anomaly of Circular Traffic Queues Using Petri Nets. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_22
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