This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.

A discrete-time storage system with a general release rule and stationary nonnegative inflows is examined. A simple condition is found for the existence of a stationary storage and outflow for a general possibly non-monotone release function. It is also shown that in the Markov case (i.e. independent inflows) these distributions are unique under certain conditions. It is demonstrated that under these conditions the stationary behaviour in the Markov case varies continuously with parametric changes in the release rule. This result is used to prove convergence of a finite state space approximation for the Markov storage system.

In this case-study, an educational psychologist trained three primaryteachers to give feedback to three 11-12 year-old low progress readers whowere each tutoring one low progress classmate, with the Pause, Prompt andPraise procedures. After themselves learning the Pause, Prompt and Praiseprocedures the teachers were provided with written instructions, and thentrainer feedback on how to provide feedback for the peer tutors. Results ofthe eight week program indicated substantial gains for both tutees andtutors on the Dunedin Teachers College Informal Prose Inventory, and on thenumber of successive book levels read to criterion. With the writteninstructions alone, teachers use very intrusive prompts when giving feedbackto peer tutors. However, when teachers also received feedback on their ownperformance they used far less intrusive forms of prompts, encouragingtutors to remember and explain their own tutoring behaviours and implementthe procedures accurately without becoming dependent on teacher support orsupervision.