On Economies of Scale and Integration of Services in Certain Queued Information Transmission Systems

This paper discusses two aspects of the performance and design of certain queued or buffered information transmission systems. Examples are buffered multiplexers and message-switching systems. The first part of the paper examines the theoretical performance of such a system as its output channel capacity and the number of its speed-limited information sources are increased proportionately. The aspects of performance considered are time delay and probability of overflow of the system's finite buffer capacity. Under the assumptions made (described in the text), system performance almost always improves as the size of the system is increased. The second portion of the paper considers the design of a communication system that must serve two classes of users, the two classes differing in average message length. Here the question is that of superiority of integrated or segregated communication system design under a channel-capacity constraint. Using average delay as a performance criterion it is shown that the integrated system is not always superior but becomes superior if there is sufficient excess capacity.