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Shortest Path Distance in Manhattan Poisson Line Cox Process

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Abstract

While the Euclidean distance characteristics of the Poisson line Cox process (PLCP) have been investigated in the literature, the analytical characterization of the path distances is still an open problem. In this paper, we solve this problem for the stationary Manhattan Poisson line Cox process (MPLCP), which is a variant of the PLCP. Specifically, we derive the exact cumulative distribution function (CDF) for the length of the shortest path to the nearest point of the MPLCP in the sense of path distance measured from two reference points: (i) the typical intersection of the Manhattan Poisson line process (MPLP), and (ii) the typical point of the MPLCP. We also discuss the application of these results in infrastructure planning, wireless communication, and transportation networks.

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Acknowledgements

This work is supported by the US National Science Foundation (Grant IIS-1633363) and UK Engineering and Physical Sciences Research Council (Grant EP/N002458/1). The authors would like to thank an anonymous reviewer for the constructive feedback that helped in improving this paper. All the code required to reproduce the numerical results is available on GitHub [36].

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Authors and Affiliations

  1. Wireless@VT, Department of ECE, Virginia Tech, Blacksburg, VA, USA

    Vishnu Vardhan Chetlur & Harpreet S. Dhillon

  2. School of Mathematics, University of Bristol, Bristol, UK

    Carl P. Dettmann

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  1. Vishnu Vardhan Chetlur
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  2. Harpreet S. Dhillon
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  3. Carl P. Dettmann
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Correspondence to Vishnu Vardhan Chetlur.

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Communicated by Eric A. Carlen.

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Chetlur, V.V., Dhillon, H.S. & Dettmann, C.P. Shortest Path Distance in Manhattan Poisson Line Cox Process. J Stat Phys 181, 2109–2130 (2020). https://doi.org/10.1007/s10955-020-02657-2

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  • DOI: https://doi.org/10.1007/s10955-020-02657-2

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