A monotonicity result for a single-server loss system

Abstract

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 Σ j ≠i qij /(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.