Consecutive customer losses in oscillating GI^(X)/M//n systems with state dependent services rates

Annals of Operations Research, 162(1) (2008), 143-158
http://dx.doi.org/10.1007/s10479-008-0313-6

We address the probability that k or more Consecutive Customer Losses take place during a busy period of a queue, the so-called k-CCL probability, for oscillating GI X /M//n systems with state dependent services rates, also denoted as GI X /M(m)?M(m)//n systems, in which the service rates oscillate between two forms according to the evolution of the number of customers in the system. We derive an efficient algorithm to compute k-CCL probabilities in these systems starting with an arbitrary number of customers in the system that involves solving a linear system of equations. The results derived are illustrated for specific sets of parameters.