An upper estimate of the probability density of d-parameter Wiener process with one barrier, already known for d = 2, is extended for general d.

In this paper the probability distribution of the discrete busy period of the 〈M, 1, GI/∞, 1〉 queue and some of its stability properties are given.

The busy period of the GI/D/∞ queue is determined as the time when at least one customer is served. Let v be the number of customers served during this period. The busy period of order n is defined as a busy period for which v ≧ n. In this paper we derive the exact distributions, integral equations, characteristic functions and all moments of those periods. Finally, some properties of the idle periods of order n are established.