Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

On a Coverage Process Ranging from the Boolean Model to the Poisson-Voronoi Tessellation with Applications to Wireless Communications

François Baccelli and Bartłomiej Błaszczyszyn
Advances in Applied Probability
Vol. 33, No. 2 (Jun., 2001), pp. 293-323
Stable URL: http://www.jstor.org/stable/1428254
Page Count: 31
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On a Coverage Process Ranging from the Boolean Model to the Poisson-Voronoi Tessellation with Applications to Wireless Communications
Preview not available

Abstract

We define and analyse a random coverage process of the d-dimensional Euclidean space which allows us to describe a continuous spectrum that ranges from the Boolean model to the Poisson-Voronoi tessellation to the Johnson-Mehl model. As for the Boolean model, the minimal stochastic setting consists of a Poisson point process on this Euclidean space and a sequence of real valued random variables considered as marks of this point process. In this coverage process, the cell attached to a point is defined as the region of the space where the effect of the mark of this point exceeds an affine function of the cumulative effect of all marks. This cumulative effect is defined as the shot-noise process associated with the marked point process. In addition to analysing and visualizing this spectrum, we study various basic properties of the coverage process such as the probability that a point or a pair of points be covered by a typical cell. We also determine the distribution of the number of cells which cover a given point, and show how to provide deterministic bounds on this number. Finally, we also analyse convergence properties of the coverage process using the framework of closed sets, and its differentiability properties using perturbation analysis. Our results require a pathwise continuity property for the shot-noise process for which we provide sufficient conditions. The model in question stems from wireless communications where several antennas share the same (or different but interfering) channel(s). In this case, the area where the signal of a given antenna can be received is the area where the signal to interference ratio is large enough. We describe this class of problems in detail in the paper. The results obtained allow us to compute quantities of practical interest within this setting: for instance the outage probability is obtained as the complement of the volume fraction; the law of the number of cells covering a point allows us to characterize handover strategies, and so on.

Page Thumbnails

  • Thumbnail: Page 
293
    293
  • Thumbnail: Page 
294
    294
  • Thumbnail: Page 
295
    295
  • Thumbnail: Page 
296
    296
  • Thumbnail: Page 
297
    297
  • Thumbnail: Page 
298
    298
  • Thumbnail: Page 
299
    299
  • Thumbnail: Page 
300
    300
  • Thumbnail: Page 
301
    301
  • Thumbnail: Page 
302
    302
  • Thumbnail: Page 
303
    303
  • Thumbnail: Page 
304
    304
  • Thumbnail: Page 
305
    305
  • Thumbnail: Page 
306
    306
  • Thumbnail: Page 
307
    307
  • Thumbnail: Page 
308
    308
  • Thumbnail: Page 
309
    309
  • Thumbnail: Page 
310
    310
  • Thumbnail: Page 
311
    311
  • Thumbnail: Page 
312
    312
  • Thumbnail: Page 
313
    313
  • Thumbnail: Page 
314
    314
  • Thumbnail: Page 
315
    315
  • Thumbnail: Page 
316
    316
  • Thumbnail: Page 
317
    317
  • Thumbnail: Page 
318
    318
  • Thumbnail: Page 
319
    319
  • Thumbnail: Page 
320
    320
  • Thumbnail: Page 
321
    321
  • Thumbnail: Page 
322
    322
  • Thumbnail: Page 
323
    323