Two communication traffic streams with Poisson statistics arrive at a network node. These are to be transmitted across a channel with a total bandwidth capacity of C frequency slots. Messages not accepted at the node are assumed to be lost. Under the assumption of exponential service time distributions, the authors study the problem of dynamic allocation of available channel bandwidth among the two traffic types to minimize a weighted sum of blocking probabilities. Modeling the system as a two-dimensional Markov chain, they show by an application of dynamic programming principles that the optimal policy is characterized by a set of two switching curves.

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Conference Proceedings - Computer Networking Symposium.
Lambadaris, I, & Narayan, P. (P.). (1988). OPTIMAL CONTROL OF ARRIVALS AT A BLOCKING NODE. In Proceedings - Computer Networking Symposium (pp. 209–213).