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The stability properties of the bandwidth allocation algorithm First Fit are analyzed for the distributions concentrated on three sizes for the requests and the bin equal to 5. To analyze these processes we introduce the notion of a smooth initial state. Starting from a smooth initial state the fluid limits of these systems are investigated.
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Faiza Belarbi, Amina A. Bouchentouf, Study of the maximal throughput of multiclass queueing systems. Port. Math. 65 (2008), no. 4, pp. 535–568