Queuing network models of modern computing systems must consider a large number of components (e.g., Web servers, DB servers, application servers, firewall, routers, networks) and hundreds of customers with very different resource requirements. The complexity of such models makes the application of exact solution techniques prohibitively expensive, motivating research on approximate methods. This paper proposes an interpolation-matching framework that allows a unified view of approximate solution techniques for closed product-form queuing networks. Depending upon the interpolating functional form and the matching populations selected, a large versatile family of new approximations can be generated. It is shown that all the known approximation strategies, including Linearizer, are instances of the interpolation-matching framework. Furthermore, a new approximation technique, based on a third-order polynomial, is obtained using the interpolation-matching framework. The new technique is shown to be more accurate than other known methods.

Store-and-forward deadlock in store-and-forward networks may be avoided by forwarding messages from buffer to buffer in accordance with a loop-free directed buffer graph which accommodates all the desired message routes. Schemes for designing such buffer graphs are presented, together with methods for using them to forward the messages in an efficient and deadlock-free manner. These methods can be implemented by a set of counters at each node. Such an implementation increases the efficiency of buffer use, and simplifies jumping between normal lowoverhead operation when deadlock is far and more careful operation when deadlock is near. The proposed deadlock avoidance mechanism works for any network topology and any finite routing algorithm.

This paper describes the construction of loop-free buffer graphs which avoid four types of buffer deadlocks in store-and-forward networks. 1) Progeny deadlock, where original messages spawnother ones, and buffer contention occurs between the original and progeny messages. This occurs when positive or negative acknowledgments are created, e.g., if messages reverse direction after encountering a path failure. 2) Copy-release deadlock, where a message copy is stored at the source node and the buffer is not released until an acknowledgment is received from the destination node. Buffer contention may arise among the original messages, stored copies, and acknowledgments. 3) Pacing deadlock, where a local flow control protocol is used between a network node and attached terminals. Buffer contention may arise between the message flows into and out of the terminal, preventing the transmission of go-ahead commands. 4) Reassembly deadlock, whereby reassembly of packetized messages at the destination node cannot be completed. The solution presented here has the novel features of not requiring preallocation of reassembly buffers before transmission of multiple packets of a multipacket message, and not requiring dedication of buffer space at intermediate nodes for individual messages. These schemes are believed to have modest buffer requirements at each node, and if adequate buffer pools are provided, will incur negligible performance degradations under normal conditions, with overhead increasing under heavy buffer usage when deadlock is near.