The steady state content Z of a finite dam in discrete time is investigated for small absolute values of the expected net input and correspondingly large values of the dam capacity. It is shown that under general conditions Z has, asymptotically, a truncated exponential distribution, a result that supplements previous knowledge in queueing theory.

An alternative proof of a result of Blomqvist on the “heavy-traffic” problem for the two-barrier random walks using weak convergence methods is indicated.

The present paper investigates the limiting distribution of the number of busy channels (queue size) and the remaining lengths of holding times at an epoch of departure for a loss system with general holding times and exponentially distributed interarrival times. Further, it is established that for this loss system in the limit an interdeparture interval length is independent of the queue size at the end of the interval and is distributed according to an exponential distribution with mean λ–1. It is also seen that in the limit interdeparture times are mutually independent.

This paper presents an algorithm to determine whether a stochastic matrix is regular. The main theorem is the following. Hypothesis: An n-by-n stochastic matrix has at least one positive entry off the main diagonal in every row and column. There is at most one row with n — 1 zeros and at most one column with n — 1 zeros. There are no j-by-k submatrices consisting entirely of zeros, where j and k are integers greater than 1, with j + k = n. Conclusion: The matrix is regular. Similar results hold for strongly connected digraphs.