Estimation of the Intensity of the Flow of Nonmonotone Refusals in the Queuing System $(≤ λ)/G/m$ - Kovalenko, I. N. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
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+ 1α1 m− 1α r− m+ 1), where α k is the kth moment of the service-time distribution.