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Rendezvous Search on the Line with Limited Resources: Maximizing the Probability of Meeting

Author

Listed:
  • Steve Alpern

    (Mathematics Department, London School of Economics, London, WC2A 2AE, England)

  • Anatole Beck

    (Mathematics Department, University of Wisconsin, Madison, Wisconsin 53706)

Abstract

Two players are placed on a line at a distance d which is drawn from a known distribution F . The players have no common notion of direction on the line, and each has a resources bound on the total distance he can travel. If F is bounded and the resources are sufficiently large, then the players can ensure a meeting. The expected time minimization problem in that case has been studied by the authors in a previous paper. Aside from that case the most the players can do is maximize the probability that they meet. This is the problem studied here, for general and specific distributions. This problem generalizes that of Foley et al. (1991), where one of the players is stationary (zero resources).

Suggested Citation

  • Steve Alpern & Anatole Beck, 1999. "Rendezvous Search on the Line with Limited Resources: Maximizing the Probability of Meeting," Operations Research, INFORMS, vol. 47(6), pages 849-861, December.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:6:p:849-861
    DOI: 10.1287/opre.47.6.849
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    References listed on IDEAS

    as
    1. Wei Shi Lim & Steve Alpern & Anatole Beck, 1997. "Rendezvous Search on the Line with More Than Two Players," Operations Research, INFORMS, vol. 45(3), pages 357-364, June.
    2. R. D. Foley & T. P. Hill & M. C. Spruill, 1991. "Linear search with bounded resources," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 555-565, August.
    3. Shmuel Gal, 1999. "Rendezvous Search on the Line," Operations Research, INFORMS, vol. 47(6), pages 974-976, December.
    4. J. V. Howard, 1999. "Rendezvous Search on the Interval and the Circle," Operations Research, INFORMS, vol. 47(4), pages 550-558, August.
    5. Alpern, Steve & Beck, Anatole, 1997. "Rendezvous search on the line with bounded resources: expected time minimization," European Journal of Operational Research, Elsevier, vol. 101(3), pages 588-597, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Leone, Pierre & Buwaya, Julia & Alpern, Steve, 2022. "Search-and-rescue rendezvous," European Journal of Operational Research, Elsevier, vol. 297(2), pages 579-591.
    2. Steve Alpern & Wei Shi Lim, 2002. "Rendezvous of three agents on the line," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 244-255, April.
    3. Pierre Leone & Steve Alpern, 2022. "A Symbolic Programming Approach to the Rendezvous Search Problem," SN Operations Research Forum, Springer, vol. 3(1), pages 1-29, March.
    4. Edward J. Anderson & Sándor P. Fekete, 2001. "Two Dimensional Rendezvous Search," Operations Research, INFORMS, vol. 49(1), pages 107-118, February.
    5. Pierre Leone & Steve Alpern, 2018. "Rendezvous search with markers that can be dropped at chosen times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 449-461, September.
    6. Steve Alpern, 2002. "Rendezvous Search: A Personal Perspective," Operations Research, INFORMS, vol. 50(5), pages 772-795, October.

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    Keywords

    search and surveillance; rendezvous search;

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