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2 results

  • A monotonicity result for a single-server loss system

  • Part of
  • Xiuli Chao, Liyi Dai
  • Journal:
    Journal of Applied Probability / Volume 32 / Issue 4 / December 1995
    Published online by Cambridge University Press:
    14 July 2016, pp. 1112-1117
    Print publication:
    December 1995

  • We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (λt (c), μt (c)) = (λct, μct), where (λt, μt) are governed by an irreducible Markov process with infinitesimal generator Q = (qij)m × m such that (λt, μt) = (λi, μi) when the Markov process is in state i. Based on matrix analysis we show that the blocking probability is decreasing in c in the interval [0, c∗], where c∗ = 1/maxi Σj≠iqij/(λi + μi). Two special cases are studied for which the result can be extended to all c. These results support Ross's conjecture that a more regular arrival (and service) process leads to a smaller blocking probability.