Buffer Overflow in a Store-and-Forward Network Node

Equilibrium behavior of a store-and-forward network node with finite buffer capacity is studied via a network-of-queues model. The positive acknowledgment protocol is explicitly modeled and consumes part of the buffer pool. The principal results are the buffer overflow probability, the mean delays, and the distribution of queue lengths as functions of the buffer capacity and traffic levels. Introduction Previous queuing analyses of store-and-forward (S&F) networks assume node independence, Poisson arrivals to each node, and infinite buffer capacity at each node [ 1, 21. These assumptions, justified for low traffic levels, lead to convenient decoupled M / G / 1 queuing models for each line or channel. This paper examines the case of finite nodal buffer capacity. Since we retain the assumptions of node independence and Poisson arrivals to each node, our results are valid for moderate traffic levels or nodes with several input lines. To relax these assumptions requires solution of various network functional dependencies. Our main results are the buffer overflow probability, mean delays, and distribution of queue lengths as functions of the buffer capacity and traffic levels at the S&F node. The main differences between our model and models of finite-capacity statistical multiplexors or de-multiplexors [3, 41 are the incorporation of blocking by neighboring nodes and explicit employment of a portion of the buffer pool for packet retention until receipt of positive acknowledgment (ACK) ; numerical calculations show that these processes may contribute significantly to buffer usage. A similar finite-capacity buffer allocation model without the ACK protocol is under investigation by Irland [ 51. For a detailed description of one set of protocols, and for acknowledgment and flow control, see the ARPANET documentation [6, 71.