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A Markov model is developed for a message processing node with batch arrivals and various flow control schemes. In particular, a credit allocation pacing control mechanism, previously modeled only by simulation, is represented analytically. The primary application is the network-independent flow control of messages between networks which may have quite different characteristics, via a gateway, but the approach is sufficiently general for modeling many servers or whole subnetworks in any queueing system. A closed form solution to the model's balance equations cannot be found, and direct solution is impracticable due to their number. However, by identifying invariants and making physically realistic approximations, the size of the state space is reduced to such an extent that direct numerical solution does become viable. In particular, the credit allocation scheme is shown to be equivalent to the node's operation in different modes, each with its own buffer capacity, so that credit control need not be modeled explicitly, and no approximation is incurred. Accuracy is assessed by comparison with the results of explicit simulations of a selection of nodes of this type with various parameterizations. Finally, we suggest applications for the model in the assessment and comparison of performance under various congestion control schemes and propose some new stabilizing mechanisms.
Date of Publication: Sep 1984