In this paper we consider an explicit solution of an optimal stopping problem arising in connection with a dice game. An optimal stopping rule and the maximum expected reward in this problem can easily be computed by means of the distributions involved and the specific rules of the game

The characterization of the exponential distribution via the coefficient of the variation of the blocking time in a queueing system with an unreliable server, as given by Lin (1993), is improved by substantially weakening the conditions. Based on the coefficient of variation of certain random variables, including the blocking time, the normal service time and the minimum of the normal service and the server failure times, two new characterizations of the exponential distribution are obtained.

In this paper we obtain the large deviation principle for scaled queue lengths at a multi-buffered resource, and simplify the corresponding variational problem in the case where the inputs are assumed to be independent.

Erlang's function B(λ, C) gives the blocking probability that occurs when Poisson traffic of intensity λ is offered to a link consisting of C circuits. However, when dimensioning a telecommunications network, it is more convenient to use the inverse C(λ, B) of Erlang's function, which gives the number of circuits needed to carry Poisson traffic λ with blocking probability at most B. This paper derives simple bounds for C(λ, B). These bounds are close to each other and the upper bound provides an accurate linear approximation to C(λ, B) which is asymptotically exact in the limit as λ approaches infinity with B fixed