If an n × n stochastic matrix has a column with no zeros, one can immediately conclude that the chain is ergodic and the state corresponding to that column is persistent and aperiodic. In this paper it is shown that it is decidable whether or not some power of a finite stochastic matrix has a positive column. Some problems regarding positive columns in infinite stochastic matrices are also considered.

Necessary and sufficient conditions are obtained for the weak convergence of the sample range of i.i.d. random variables as the number of observations tends to infinity.

A technique is derived providing for the analysis of busy period processes in the queueing models M/Mn/1 and Mn/M/1; queueing models with state dependent service and arrival rates respectively. A single treatment covers both models and no separate analysis is required.

This paper provides simple proofs of two standard results for the stable GI/G/1 queue on the structure of the distribution functions of the stationary virtual waiting time and the stationary queue-length Our argument is applicable to more general single server systems than the queue GI/G/1.

This paper obtains the probability and the expectation of the length of the busy and idle periods in a discrete-time service system by means of two-component Markov chains and their first passage times. The M/G/1 model is discussed as a special case.

The results obtained by Lehoczky on the first emptiness of a dam subject to random outputs are extended to a more general model.