This paper deals with optimal stopping rules for a sampling process with uncertain recall, i.e. the probability that a past observation is currently available declines exponentially with the time elapsed since it was last observed. The main result of this paper is that for such sampling processes, and for any utility function, if a solicitation of a past observation incurs the same cost as a new draw, then it is never optimal to continue the sampling when the observation solicited is found to be available. This result applies to both bounded and unbounded sequential decision procedures.

In this paper we consider the general birth-and-death queueing model of Natvig (1975). Define the input and output processes by the steady-state behaviour of respectively successive input and output intervals. Ignoring balking customers, two cases are considered. In the first case we treat a lost customer neither as an input nor as an output, then secondly as both. For both cases we show the input and output processes to be reverse processes. One mistake and two erroneous comments in Natvig (1975) are also corrected.

Moments of the delay distribution and other measures of performance for a multi-channel queue are shown to be bounded above by corresponding quantities for one or a collection of single-channel queues.