Skip to main content
SpringerLink
Log in

Spatio-temporal model checking of vehicular movement in public transport systems

  • Formal Methods for Transport Systems
  • Published:
International Journal on Software Tools for Technology Transfer Aims and scope Submit manuscript

Abstract

We present the use of a novel spatio-temporal model checker to detect problems in the data and operation of a collective adaptive system. Data correctness is important to ensure operational correctness in systems which adapt in response to data. We illustrate the theory with several concrete examples, addressing both the detection of errors in vehicle location data for buses in the city of Edinburgh and the undesirable phenomenon of “clumping” which occurs when there is not enough separation between subsequent buses serving the same route. Vehicle location data are visualised symbolically on a street map, and categories of problems identified by the spatial part of the model checker are rendered by highlighting the symbols for vehicles or other objects that satisfy a property of interest. Behavioural correctness makes use of both the spatial and temporal aspects of the model checker to determine from a series of observations of vehicle locations whether the system is failing to meet the expected quality of service demanded by system regulators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Notes

  1. A collective adaptive system consists of multiple cooperating components with decentralised control—these may be human or non-human—and adapts itself to unexpected problems arising from the environment in which it operates.

  2. Note that in general any kind of basic propositions may be chosen. For example, they may be values representing concentrations of chemical substances or probabilities as shown in the various case studies presented in [11, 14].

  3. In this paper, the points have been selected artificially, in order to present a clear working example, but use of the spatial model checker does not differ when dealing directly with the vehicle location data supplied by Lothian Buses.

  4. See http://topochecker.isti.cnr.it/, and https://github.com/vincenzoml/topochecker; an earlier prototype is available at https://github.com/cherosene/ctl_logic.

  5. Further information on the dot notation and the graphviz toolkit can be found at http://www.graphviz.org/Documentation.php.

  6. More than one time step can be required. This can be achieved by repeated nesting of applications of E X operators. We did not do so for the sake of clarity in Fig. 11.

  7. The source code, written in the programming language OCaml, is available as a free and open source software in the source code repository of topochecker.

  8. States are numbered in the implementation and output for each state can be directly viewed without navigating the Kripke structure.

References

  1. Aiello, M.: Spatial reasoning: theory and practice. Ph.D. thesis, ILLC, University of Amsterdam (2002)

  2. Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)

    MATH  Google Scholar 

  3. Bartocci, E., Gol, E.A., Haghighi, I., Belta, C.: A formal methods approach to pattern recognition and synthesis in reaction diffusion networks. IEEE Trans. Control Netw. Syst. PP, 1–12 (2016)

    Google Scholar 

  4. Belmonte, G., Ciancia, V., Latella, D., Massink, M.: From collective adaptive systems to human centric computation and back: spatial model checking for medical imaging. In: Proceedings of the Workshop on FORmal Methods for the Quantitative Evaluation of Collective Adaptive SysTems, FORECAST@STAF 2016, Vienna, Austria, 8 July 2016, volume 217 of EPTCS, pp. 81–92 (2016)

  5. Ben-Ari, M., Pnueli, A., Manna, Z.: The temporal logic of branching time. Acta Inform. 20(3), 207–226 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bortolussi, L., Nenzi, L.: Specifying and monitoring properties of stochastic spatio-temporal systems in signal temporal logic. In: VALUETOOLS (2014)

  7. Buccafurri, F., Eiter, T., Gottlob, G., Leone, N.: On ACTL formulas having linear counterexamples. J. Comput. Syst. Sci. 62(3), 463–515 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Caires, L.: Behavioral and spatial observations in a logic for the \(\pi \)-calculus. In: Proceedings of the 7th International Conference on Foundations of Software Science and Computation Structures (FOSSACS’04), volume 2987 of LNCS, pp. 72–87. Springer (2004)

  9. Cardelli, L., Gardner, P.: Processes in space. Theor. Comput. Sci. 431(0), 40–55 (2012). Modelling and Analysis of Biological Systems Based on papers presented at the Workshop on Membrane Computing and Bio-logically Inspired Process Calculi (MeCBIC) held in 2008 (Iasi), 2009 (Bologna) and 2010 (Jena)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cardelli, L., Gordon, A.D.: Anytime, anywhere: modal logics for mobile ambients. In: Proceedings of the 30th SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL’00), pp. 365–377 (2000)

  11. Ciancia, V., Grilletti, G., Latella, D., Loreti, M., Massink, M.: An experimental spatio-temporal model checker. In: Software Engineering and Formal Methods—SEFM 2015 Collocated Workshops, volume 9509 of Lecture Notes in Computer Science, pp. 297–311. Springer (2015)

  12. Ciancia, V., Latella, D., Loreti, M., Massink, M.: Specifying and verifying properties of space. In: Springer (ed.) The 8th IFIP International Conference on Theoretical Computer Science, TCS 2014, Track B, volume 8705 of Lecture Notes in Computer Science, pp. 222–235 (2014)

  13. Ciancia, V., Latella, D., Loreti, M., Massink, M.: Model checking spatial logics for closure spaces. Log. Methods Comput. Sci. 12(4), 1–51 (2016)

  14. Ciancia, V., Latella, D., Massink, M., Paskauskas, R., Vandin, A.: A tool-chain for statistical spatio-temporal model checking of bike sharing systems. In: Margaria, T., Steffen, B. (eds.) Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques—7th International Symposium, ISoLA 2016, Imperial, Corfu, Greece, 10–14 October 2016, Proceedings, Part I, volume 9952 of Lecture Notes in Computer Science, pp. 657–673 (2016)

  15. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Logic of Programs, volume 131 of Lecture Notes in Computer Science, pp. 53–71. Springer (1986)

  16. Clarke, E.M., Veith, H.: Counterexamples revisited: principles, algorithms, applications. In: Dershowitz, N. (ed.) Verification: Theory and Practice, Essays Dedicated to Zohar Manna on the Occasion of His 64th Birthday, volume 2772 of Lecture Notes in Computer Science, pp. 208–224. Springer, Berlin (2003)

    Google Scholar 

  17. Daganzo, C.F.: A headway-based approach to eliminate bus bunching: systematic analysis and comparisons. Transp. Res. Part B Methodol. 43(10), 913–921 (2009)

    Article  Google Scholar 

  18. Daganzo, C.F., Pilachowski, J.: Reducing bunching with bus-to-bus cooperation. Transp. Res. Part B Methodol. 45(1), 267–277 (2011)

    Article  Google Scholar 

  19. De Angelis, F.L., Di Marzo Serugendo, G.: Towards a spatial language for run-time assessments in self-organizing systems. In: 2015 IEEE 9th International Conference on Self-Adaptive and Self-Organizing Systems, Cambridge, MA, USA, 21–25 September 2015, pp. 174–175. IEEE Computer Society (2015)

  20. De Nicola, R., Katoen, J.-P., Latella, D., Loreti, M., Massink, M.: Model checking mobile stochastic logic. Theor. Comput. Sci. 382(1), 42–70 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. Del Bimbo, A., Vicario, E., Zingoni, D.: Symbolic description and visual querying of image sequences using spatio-temporal logic. IEEE Trans. Knowl. Data Eng. 7(4), 609–622 (1995)

    Article  Google Scholar 

  22. Dobson, S.A., Viroli, M., Fernandez-Marquez, J.L., Zambonelli, F., Stevenson, G., Di Marzo Serugendo, G., Montagna, S., Pianini, D., Ye, J., Castelli, G., Rosi, A.: Spatial awareness in pervasive ecosystems. Knowl. Eng. Rev. 31(4), 343–366 (2016)

    Article  Google Scholar 

  23. Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science (Vol. B), pp. 995–1072. MIT Press, Cambridge (1990)

    Google Scholar 

  24. Fathi, A., Krumm, J.: Detecting road intersections from GPS traces. In: Fabrikant, S.I., Reichenbacher, T., van Kreveld, M., Schlieder, C. (eds.) Geographic Information Science, Lecture Notes in Computer Science, vol. 6292, pp. 56–69. Springer, Berlin (2010)

    Chapter  Google Scholar 

  25. Gol, E.A., Bartocci, E., Belta, C.: A formal methods approach to pattern synthesis in reaction diffusion systems. In: 53rd IEEE Conference on Decision and Control, pp. 108–113 (2014)

  26. Grilletti, G.: Spatio-temporal model checking: Explicit and abstraction-based methods. Master’s thesis, Dipartimento di Matematica, Università di Pisa (2016)

  27. Grosu, R., Smolka, S.A., Corradini, F., Wasilewska, A., Entcheva, E., Bartocci, E.: Learning and detecting emergent behavior in networks of cardiac myocytes. Commun. ACM 52(3), 97–105 (2009)

    Article  MATH  Google Scholar 

  28. John III, J.B., Clark, R.J., Williamson, D.W., Eisenstein, D.D., Platzman, L.K.: Building a self-organizing urban bus route. In: Sixth IEEE International Conference on Self-Adaptive and Self-Organizing Systems Workshops, SASOW 2012, Lyon, France, 10–14 September 2012, pp. 66–70. IEEE Computer Society (2012)

  29. John III, J.B., Eisenstein, D.D.: A self-coordinating bus route to resist bus bunching. Transp. Res. Part B Methodol. 46(4), 481–491 (2012)

    Article  Google Scholar 

  30. John, M., Ewald, R., Uhrmacher, A.M.: A spatial extension to the pi calculus. Electron. Notes Theor. Comput. Sci. 194(3), 133–148 (2008). Proceedings of the First Workshop From Biology To Concurrency and back (FBTC 2007)

    Article  MATH  Google Scholar 

  31. Kontchakov, R., Kurucz, A., Wolter, F., Zakharyaschev, M.: Spatial logic + temporal logic = ? In: Aiello, M., Pratt-Hartmann, I., van Benthem, J. (eds.) Handbook of Spatial Logics, pp. 497–564. Springer, Berlin (2007)

    Chapter  Google Scholar 

  32. Letchner, J., Krumm, J., Horvitz, E.: Trip router with individualized preferences (TRIP): incorporating personalization into route planning. In: Proceedings of the 18th Conference on Innovative Applications of Artificial Intelligence—volume 2, IAAI’06, pp. 1795–1800. AAAI Press (2006)

  33. Nenzi, L., Bortolussi, L., Ciancia, V., Loreti, M., Massink, M.: Qualitative and quantitative monitoring of spatio-temporal properties. In: Runtime Verification—6th International Conference, RV 2015 Vienna, Austria, 22–25 September 2015. Proceedings, volume 9333 of Lecture Notes in Computer Science, pp. 21–37. Springer (2015)

  34. Newell, G.F., Potts, R.B.: Maintaining a bus schedule. In: Proceedings of 2nd Australian Road Research Board, volume 2, pp. 388–393 (1964)

  35. Ordoñez, C., Martínez, J., Rodríguez-Pérez, J., Reyes, A.: Detection of outliers in GPS measurements by using functional-data analysis. J. Surv. Eng. 137(4), 150–155 (2011)

    Article  Google Scholar 

  36. Reijsbergen, D., Gilmore, S.: Formal punctuality analysis of frequent bus services using headway data. In: Horváth, A., Wolter, K. (eds.) Computer Performance Engineering—11th European Workshop, EPEW 2014, Florence, Italy, 11–12 September 2014. Proceedings, volume 8721 of Lecture Notes in Computer Science, pp. 164–178. Springer (2014)

  37. Ruan, Mi., Lin, J.: An investigation of bus headway regularity and service performance in Chicago bus transit system. In: Transport Chicago, Annual Conference, vol. 14 (2009)

  38. Strathman, J.G., Kimpel, T.J., Callas, S.: Headway deviation effects on bus passenger loads: analysis of Tri-Met’s archived AVL-APC data. Technical Report PR126, Portland State University, Centre for Urban Studies, Oregon (2003)

  39. Tsigkanos, C., Kehrer, T., Ghezzi, C.: Modeling and verification of evolving cyber-physical spaces. In: Proceedings of the 2017 11th Joint Meeting on Foundations of Software Engineering, ESEC/FSE 2017, Paderborn, Germany, 4–8 September 2017, pp. 38–48. ACM (2017)

  40. Tsigkanos, C., Pasquale, L., Ghezzi, C., Nuseibeh, B.: Ariadne: topology aware adaptive security for cyber-physical systems. In: 2015 IEEE/ACM 37th IEEE International Conference on Software Engineering, volume 2, pp. 729–732 (2015)

  41. van Benthem, J., Bezhanishvili, G.: Modal logics of space. In: Aiello, M., Pratt-Hartmann, I., van Benthem, J. (eds.) Handbook of Spatial Logics, pp. 217–298. Springer, Berlin (2007)

    Chapter  Google Scholar 

  42. Xuan, Y., Argote, J., Daganzo, C.F.: Dynamic bus holding strategies for schedule reliability: optimal linear control and performance analysis. Transp. Res. Part B Methodol. 45(1), 1831–1845 (2011)

    Article  Google Scholar 

  43. Yan, Z.: Traj-ARIMA: a spatial-time series model for network-constrained trajectory. In: Proceedings of the Second International Workshop on Computational Transportation Science, IWCTS ’10, pp. 11–16. ACM, New York (2010)

  44. Zhao, J., Dessouky, M., Bukkapatnam, S.: Optimal slack time for schedule-based transit operations. Transp. Sci. 40(4), 529–539 (2006)

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank Bill Johnston of Lothian Buses and Stuart Lowrie of the City of Edinburgh council for providing access to the data related to bus positions.

Author information

Authors and Affiliations

  1. Istituto di Scienza e Tecnologie dell’Informazione “A. Faedo”, Consiglio Nazionale delle Ricerche, Pisa, Italy

    Vincenzo Ciancia, Diego Latella & Mieke Massink

  2. Scuola di Scienze e Tecnologie, Università degli studi di Camerino, Camerino, Italy

    Michele Loreti

  3. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Gianluca Grilletti

  4. Laboratory for Foundations of Computer Science, University of Edinburgh, Edinburgh, Scotland, UK

    Stephen Gilmore

Authors
  1. Vincenzo Ciancia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephen Gilmore
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gianluca Grilletti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Diego Latella
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Michele Loreti
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mieke Massink
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vincenzo Ciancia.

Additional information

This work is partially supported by the EU project QUANTICOL: A Quantitative Approach to Management and Design of Collective and Adaptive Behaviours, 600708.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ciancia, V., Gilmore, S., Grilletti, G. et al. Spatio-temporal model checking of vehicular movement in public transport systems. Int J Softw Tools Technol Transfer 20, 289–311 (2018). https://doi.org/10.1007/s10009-018-0483-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10009-018-0483-8

Keywords

Mathematics Subject Classification

Search

Navigation