The throughput of a series of buffers

Abstract

Messages are to be transmitted through a series of n nodes linked by communication channels. The lengths of successive messages are independent identically distributed random variables, and the time taken to transmit a message through a channel is determined by its length. Each node has a finite buffer, and when the number of messages at a node reaches the buffer size transmission from the preceding node is interrupted. This paper is concerned with the maximum rate at which messages can pass through the system, called the throughput. We investigate the asymptotic behaviour of throughput as the series length increases, and determine the rate at which buffer sizes should grow to ensure that throughput does not decline to 0.