Superimposed renewal processes and storage with gradual input

In systems for data handling, buffers are often applied for temporary storage of messages. The storage process at the buffer may be considered as a queueing process with gradual input, being a process which until now has been hardly studied. The present study provides for several models of this type an analytic description, it shows that existing results of queueing theory can be used. The results obtained provide also important information for the determination of the buffer capacity. A number of new and interesting problems originate from the present model and the results so far obtained.