Abstract
We introduce a new approach to model and analyze Mobility. It is fully based on discrete mathematics and yields a class of mobility models, called the Markov Trace Model. This model can be seen as the discrete version of the Random Trip Model: including all variants of the Random Way-Point Model [14].
We derive fundamental properties and explicit analytical formulas for the stationary distributions yielded by the Markov Trace Model. Such results can be exploited to compute formulas and properties for concrete cases of the Markov Trace Model by just applying counting arguments.
We apply the above general results to the discrete version of the Manhattan Random Way-Point over a square of bounded size. We get formulas for the total stationary distribution and for two important conditional ones: the agent spatial and destination distributions.
Our method makes the analysis of complex mobile systems a feasible task. As a further evidence of this important fact, we first model a complex vehicular-mobile system over a set of crossing streets. Several concrete issues are implemented such as parking zones, traffic lights, and variable vehicle speeds. By using a modular version of the Markov Trace Model, we get explicit formulas for the stationary distributions yielded by this vehicular-mobile model as well.
Partially supported by the Italian MIUR COGENT.
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References
Koberstein, J., Peters, H., Luttenberger, N.: Graph-based mobility model for urban areas fueled with real world datasets. In: Proc. of the 1st SIMUTOOLS 2008, pp. 1–8 (2008)
Aldous, D., Fill, J.: Reversible Markov Chains and Random Walks on Graphs (2002), http://stat-www.berkeley.edu/users/aldous/RWG/book.html
Camp, T., Boleng, J., Davies, V.: A survey of mobility models for ad hoc network research. Wireless Communication and Mobile Computing 2(5), 483–502 (2002)
Baccelli, F., Brémaud, P.: Palm Probabilities and Stationary Queues. Springer, Heidelberg (1987)
Bettstetter, C., Resta, G., Santi, P.: The Node Distribution of the Random Waypoint Mobility Model for Wireless Ad Hoc Networks. IEEE Transactions on Mobile Computing 2, 257–269 (2003)
Camp, T., Navidi, W., Bauer, N.: Improving the accuracy of random waypoint simulations through steady-state initialization. In: Proc. of 15th Int. Conf. on Modelling and Simulation, pp. 319–326 (2004)
Clementi, A., Monti, A., Pasquale, F., Silvestri, R.: Information spreading in stationary markovian evolving graphs. In: Proc. of 23rd IEEE IPDPS, pp. 1–12 (2009)
Clementi, A., Pasquale, F., Silvestri, R.: MANETS: High mobility can make up for low transmission power. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 387–398. Springer, Heidelberg (2009)
Clementi, A., Monti, A., Silvestri, R.: Modelling Mobility: A Discrete Revolution. Techn. Rep. arXiv.org, Tech. Rep. arXiv:1002.1016v1 (2010)
Clementi, A., Monti, A., Silvestri, R.: Fast Flooding over Manhattan. In: Proc. of 29th ACM PODC (to appear, 2010)
Crescenzi, P., Di Ianni, M., Marino, A., Rossi, G., Vocca, P.: Spatial Node Distribution of Manhattan Path Based Random Waypoint Mobility Models with Applications. In: Kutten, S. (ed.) SIROCCO 2009. LNCS, vol. 5869, pp. 154–166. Springer, Heidelberg (2009)
Diaz, J., Perez, X., Serna, M.J., Wormald, N.C.: Walkers on the cycle and the grid. SIAM J. Discrete Math. 22(2), 747–775 (2008)
Diaz, J., Mitsche, D., Perez-Gimenez, X.: On the connectivity of dynamic random geometric graphs. In: Proc. of the 19th ACM-SIAM SODA 2008, pp. 601–610 (2008)
Le Boudec, J.-Y., Vojnovic, M.: The Random Trip Model: Stability, Stationary Regime, and Perfect Simulation. IEEE/ACM Transaction on Networking 16(6), 1153–1166 (2006)
Le Boudec, J.-Y.: Understanding the simulation of mobility models with Palm calculus. Performance Evaluation 64, 126–147 (2007)
Le Boudec, J.-Y., Vojnovic, M.: Perfect simulation and the stationarity of a class of mobility models. In: Proc. of the 24th IEEE INFOCOM, pp. 2743–2754 (2005)
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Clementi, A.E.F., Monti, A., Silvestri, R. (2010). Modelling Mobility: A Discrete Revolution. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_41
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DOI: https://doi.org/10.1007/978-3-642-14162-1_41
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