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We present a discretized learning automaton (LA) solution to the capacity assignment (CA) problem which focuses on finding the best possible set of capacities for the links that satisfy the traffic requirements in a prioritized network while minimizing the cost. Most approaches consider a single class of packets flowing through the network, but in reality, different classes of packets with different average packet lengths and different priorities are transmitted over the networks. This generalized model is the focus of this paper. Although the problem is inherently NP-hard, a few approximate solutions have been proposed in the literature. Marayuma and Tang (1977) proposed a single algorithm composed of several elementary heuristic procedures. Other solutions tackle the problem by using modern-day artificial intelligence (AI) paradigms such as simulated annealing and genetic algorithms (GAs). In 2000, we introduced a new method, superior to these, that uses continuous LA. In this paper, we present a discretized LA solution to the problem. This solution uses a meta-action philosophy new to the field of LA, and is probably the best available solution to this extremely complex problem.