Shortest Path Distance in Manhattan Poisson Line Cox Process

Vishnu Vardan Chetlur; Harpreet S. Dhillon; Carl P Dettmann

doi:10.1007/s10955-020-02657-2

Shortest Path Distance in Manhattan Poisson Line Cox Process

Vishnu Vardan Chetlur^*, Harpreet S. Dhillon, Carl P Dettmann

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Original language	English
Pages (from-to)	2109-2130
Number of pages	22
Journal	Journal of Statistical Physics
Volume	181
DOIs	https://doi.org/10.1007/s10955-020-02657-2
Publication status	Published - 21 Oct 2020

Keywords

Stochastic geometry
Manhattan
Poisson line process
Manhattan Poisson line Cox Process
Path distance
Shortest path

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10.1007/s10955-020-02657-2

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Dettmann , C. P. (Principal Investigator)
1/11/15 → 18/03/19
Project: Research

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@article{c25f3555bfa642638e6a112358a44c8f,

title = "Shortest Path Distance in Manhattan Poisson Line Cox Process",

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.",

keywords = "Stochastic geometry, Manhattan, Poisson line process, Manhattan Poisson line Cox Process, Path distance, Shortest path",

author = "Chetlur, {Vishnu Vardan} and Dhillon, {Harpreet S.} and Dettmann, {Carl P}",

year = "2020",

month = oct,

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doi = "10.1007/s10955-020-02657-2",

language = "English",

volume = "181",

pages = "2109--2130",

journal = "Journal of Statistical Physics",

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TY - JOUR

T1 - Shortest Path Distance in Manhattan Poisson Line Cox Process

AU - Chetlur, Vishnu Vardan

AU - Dhillon, Harpreet S.

AU - Dettmann , Carl P

PY - 2020/10/21

Y1 - 2020/10/21

N2 - 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.

AB - 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.

KW - Stochastic geometry

KW - Manhattan

KW - Poisson line process

KW - Manhattan Poisson line Cox Process

KW - Path distance

KW - Shortest path

U2 - 10.1007/s10955-020-02657-2

DO - 10.1007/s10955-020-02657-2

M3 - Article (Academic Journal)

SN - 0022-4715

VL - 181

SP - 2109

EP - 2130

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

ER -

Shortest Path Distance in Manhattan Poisson Line Cox Process

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Keywords

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