2011 **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. It can be viewed as the discrete version of the Random Trip model: including all variants of the Random Way-Point model [15]. We derive fundamental properties and explicit analytical formulas for the stationary probability distributions yielded by the Markov Trace model. Besides having a per-se interest, such results can be exploited to compu…

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(19 citation statements)

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“…The stationary (agent) spatial distribution gives the probability that an agent lies in a position (x, y) and it has been derived in [12]. The stationary (agent) destination distribution gives the probability that an agent, conditioned to lie in position (x0, y0), is traveling toward destination (x, y) and it has been determined in [10]. Theorem 1.…”

confidence: 99%

“…The stationary (agent) spatial distribution gives the probability that an agent lies in a position (x, y) and it has been derived in [12]. The stationary (agent) destination distribution gives the probability that an agent, conditioned to lie in position (x0, y0), is traveling toward destination (x, y) and it has been determined in [10]. Theorem 1.…”

confidence: 99%

“…Explicit formulas for the stationary spatial and destination probability distributions have been derived in [12,10]. The stationary distributions of some other versions of the RWP have been obtained in [4,6,19,21].…”

confidence: 99%

“…Torkestani (2012) [130] present a mobility prediction model based on Gauss-Markov and used learning automata for a boundless simulation area with no obstacles. Clementi et al (2011) [131] develop a Markov trace model to analyze mobility in complex mobility systems (e.g., vehicular-mobile systems) using discrete mathematics. A limited attempt is made to relate Markov models to real-world situations.…”

confidence: 99%

“…Helpful guidelines for traffic engineers about the study and application of counting distributions are also contained in Gerlough and Huber (1975) and in May (1990). After a few decades theoretical research has restarted and some works in the field have been produced by Jabari and Liu (2012), Clementi, Monti and Silvestri (2011) and Cao, Tai and Chan (2012) who have analysed some statistical models for counting distributions.…”

confidence: 99%