Space filling and depletion

Yuliy Baryshnikov, E. G. Coffman, Predrag Jelenković

Research output: Contribution to journalArticlepeer-review


For a given k ≥ 1, subintervals of a given interval [0, X] arrive at random and are accepted (allocated) so long as they overlap fewer than k subintervals already accepted. Subintervals not accepted are cleared, while accepted subintervals remain allocated for random retention times before they are released and made available to subsequent arrivals. Thus, the system operates as a generalized many-server queue under a loss protocol. We study a discretized version of this model that appears in reference theories for a number of applications, including communication networks, surface adsorption-desorption processes, and reservation systems. Our primary interest is in steady-state estimates of the vacant space, i.e. the total length of available subintervals kX - σl i, where the l i0 are the lengths of the subintervals currently allocated. We obtain explicit results for k = 1 and for general k with all subinterval lengths equal to 2, the classical dimer case of chemical applications. Our focus is on the asymptotic regime of large retention times.

Original languageEnglish (US)
Pages (from-to)691-702
Number of pages12
JournalJournal of Applied Probability
Issue number3
StatePublished - Sep 2004
Externally publishedYes


  • Dimer packing
  • Many-server queue
  • Markov chain

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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