Bounds and inequalities for single server loss systems (Q915290)

The authors consider a single server loss system at which the customers arrive according to a doubly stochastic Poisson process, with an intensity \(\lambda_ t\). \textit{S. M. Ross} [see J. Appl. Probab. 15, 602- 609 (1978; Zbl 0383.60092)] conjectured that the loss probability of the system is larger than the loss probability in a single server loss system in which the arrivals are Poisson with fixed rate and he supposed that the successive service times are independently drawn from a distribution G with mean \(\mu^{-1}.\) The present authors study a special case of the model, where the system has zero buffer capacity, and the successive times are independently drawn from an exponential distribution with mean \(\mu^{-1}\).