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

  • Vincenzo CianciaEmail author
  • Stephen Gilmore
  • Gianluca Grilletti
  • Diego Latella
  • Michele Loreti
  • Mieke Massink
Formal Methods for Transport Systems


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.


Spatio-temporal model checking Collective adaptive systems Smart transportation 

Mathematics Subject Classification

68N30 68Q60 03B70 



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.


  1. 1.
    Aiello, M.: Spatial reasoning: theory and practice. Ph.D. thesis, ILLC, University of Amsterdam (2002)Google Scholar
  2. 2.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  3. 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. 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)Google Scholar
  5. 5.
    Ben-Ari, M., Pnueli, A., Manna, Z.: The temporal logic of branching time. Acta Inform. 20(3), 207–226 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bortolussi, L., Nenzi, L.: Specifying and monitoring properties of stochastic spatio-temporal systems in signal temporal logic. In: VALUETOOLS (2014)Google Scholar
  7. 7.
    Buccafurri, F., Eiter, T., Gottlob, G., Leone, N.: On ACTL formulas having linear counterexamples. J. Comput. Syst. Sci. 62(3), 463–515 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 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)Google Scholar
  9. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 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)Google Scholar
  11. 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)Google Scholar
  12. 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)Google Scholar
  13. 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)Google Scholar
  14. 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)Google Scholar
  15. 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)Google Scholar
  16. 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. 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)CrossRefGoogle Scholar
  18. 18.
    Daganzo, C.F., Pilachowski, J.: Reducing bunching with bus-to-bus cooperation. Transp. Res. Part B Methodol. 45(1), 267–277 (2011)CrossRefGoogle Scholar
  19. 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)Google Scholar
  20. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 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)CrossRefGoogle Scholar
  23. 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. 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)CrossRefGoogle Scholar
  25. 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)Google Scholar
  26. 26.
    Grilletti, G.: Spatio-temporal model checking: Explicit and abstraction-based methods. Master’s thesis, Dipartimento di Matematica, Università di Pisa (2016)Google Scholar
  27. 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)CrossRefzbMATHGoogle Scholar
  28. 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)Google Scholar
  29. 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)CrossRefGoogle Scholar
  30. 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)CrossRefzbMATHGoogle Scholar
  31. 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)CrossRefGoogle Scholar
  32. 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)Google Scholar
  33. 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)Google Scholar
  34. 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)Google Scholar
  35. 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)CrossRefGoogle Scholar
  36. 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)Google Scholar
  37. 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)Google Scholar
  38. 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)Google Scholar
  39. 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)Google Scholar
  40. 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)Google Scholar
  41. 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)CrossRefGoogle Scholar
  42. 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)CrossRefGoogle Scholar
  43. 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)Google Scholar
  44. 44.
    Zhao, J., Dessouky, M., Bukkapatnam, S.: Optimal slack time for schedule-based transit operations. Transp. Sci. 40(4), 529–539 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Vincenzo Ciancia
    • 1
  • Stephen Gilmore
    • 4
  • Gianluca Grilletti
    • 3
  • Diego Latella
    • 1
  • Michele Loreti
    • 2
  • Mieke Massink
    • 1
  1. 1.Istituto di Scienza e Tecnologie dell’Informazione “A. Faedo”Consiglio Nazionale delle RicerchePisaItaly
  2. 2.Scuola di Scienze e TecnologieUniversità degli studi di CamerinoCamerinoItaly
  3. 3.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  4. 4.Laboratory for Foundations of Computer ScienceUniversity of EdinburghEdinburghScotland, UK

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