Estimation of the Intensity of the Flow of Nonmonotone Refusals in the Queuing System $(≤ λ)/G/m$

Abstract

We consider a queuing system (≤ λ)/G/m, where the symbol (≤ λ) means that, independently of prehistory, the probability of arrival of a call during the time interval dtdoes not exceed λdt. The case where the queue length first attains the level r≥ m+ 1 during a busy period is called the refusal of the system. We determine a bound for the intensity μ₁(t) of the flow of homogeneous events associated with the monotone refusals of the system, namely, μ₁(t) = O(λ ^{r+ 1}α₁ ^{m− 1}α _{r− m+ 1}), where α _k is the kth moment of the service-time distribution.