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Station Assignment with Reallocation

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Abstract

We study a dynamic allocation problem that arises in various scenarios where mobile clients joining and leaving the system have to communicate with static stations via radio transmissions. Restrictions are a maximum delay, or laxity, between consecutive client transmissions and a maximum bandwidth that a station can share among its clients. We study the problem of assigning clients to stations so that every client transmits to some station, satisfying those restrictions. We consider reallocation algorithms, where clients are revealed at its arrival time, the departure time is unknown until they leave, and clients may be reallocated to another station, but at a cost proportional to the reciprocal of the client’s laxity. We present negative results for previous related protocols that motivate the study; we introduce new protocols that expound trade-offs between station usage and reallocation cost; we determine experimentally a classification of the clients attempting to balance those opposite goals; we prove theoretically bounds on our performance metrics; and we show through simulations that, for realistic scenarios, our protocols behave much better than our theoretical guarantees.

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Notes

  1. We consider an upstream model, but the same results apply to downstream communication.

  2. As a first step we consider a reallocation cost in terms of laxity. It is of interest to consider bandwidth in the cost and we leave this future work.

  3. To maintain station usage low, we will assume that the laxity can be relaxed during reallocation.

  4. Throughout, \(\log \) means \(\log _2\) unless otherwise stated.

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Acknowledgements

The authors thank the support from a Visiting Fellowship and the initiative Networks Sciences & Technologies (NeST) by School of EEE & CS, University of Liverpool, as well as Pace University NYFC SRC Award, Kenan Fund Award and The Royal Society Award # IES\(\setminus \)R3\(\setminus \)170293.

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Authors and Affiliations

  1. Computer Science Department, Pace University, New York, NY, USA

    Austin Halper & Miguel A. Mosteiro

  2. Computer Science Department, Kean University, Union, NJ, USA

    Yulia Rossikova

  3. Department of Computer Science, University of Liverpool, Liverpool, UK

    Prudence W. H. Wong

Authors
  1. Austin Halper
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  2. Miguel A. Mosteiro
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  3. Yulia Rossikova
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  4. Prudence W. H. Wong
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Corresponding author

Correspondence to Miguel A. Mosteiro.

Additional information

A preliminary version of this work appeared in SEA 2015 [34].

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Halper, A., Mosteiro, M.A., Rossikova, Y. et al. Station Assignment with Reallocation. Algorithmica 81, 1096–1125 (2019). https://doi.org/10.1007/s00453-018-0459-9

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