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We study a friction-controlled slide of a body excited by random motions of the foundation it is placed on. Specifically, we are interested in such quantities as displacement, traveled distance, and energy loss due to friction. We assume that the random excitation is switched off at some time (possibly infinite) and show that the problem can be treated in an analytic, explicit, manner. Particularly, we derive formulas for the moments of the displacement and distance, and also for the average energy loss. To accomplish that we use the Pugachev-Sveshnikov equation for the characteristic function of a continuous random process given by a system of SDEs. This equation is solved by reduction to a parametric Riemann boundary value problem of complex analysis.

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The non-preemptive priority queuing with a finite buffer is considered. We introduce a randomized push-out buffer management mechanism which allows to control very efficiently the loss probability of priority packets. The packet loss probabilities for priority and non-priority traffic are calculated using the generating function approach. For the particular case of the standard non-randomized push-out scheme we obtain explicit analytic expressions. The theoretical results are illustrated by a numerical example.