A monotonicity result for a single-server loss system

We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (lambda(i)(c), mu(t), (c))=(lambda(ct), mu(ct)), where (lambda(t), mu(t)) are governed by an irreducible Markov process with infinitesimal generator Q=(q(ij))(mxm) such that (lambda(t), mu(t))=(lambda(i), mu(i)) 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/max, Sigma(j not equal i) q(tj)/(lambda(i)+mu(i)). 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.