Discriminatory Processor Sharing models play important role in analysing bandwidth allocation schemes in packet based communication systems. Users in such systems usually have access rate limitations which also influence their bandwidth shares. This paper is concerned with DPS models which incorporate these access rate limitations in a bandwidth economical manner. In this paper the interlock between access rate limited Discriminatory Processor Sharing (DPS) models and some constrained optimization problems is investigated. It is shown, that incorporating the access rate limit into the DPS model is equivalent to extending the underlying constrained optimization by constraints on the access rates. It also means that the available bandwidth share calculation methods for the access rate limited DPS are also non-conventional solution methods for the extended constrained optimization problem. We also foreshadow that these results might be important steps towards obtaining efficient pricing and resource allocation mechanism when users are selfish and subject to gaming behavior when competing for communication resources.
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