Delay Bounds for Multiclass FIFO

FIFO is perhaps the simplest scheduling discipline. For single-class FIFO, its delay guarantee performance has been extensively studied: The well-known results include a stochastic delay bound for GI/GI/1 by Kingman [2] and a deterministic delay bound for D/D/1 by Cruz [3]. However, for multiclass FIFO, few such results are available. To fill the gap, we prove delay bounds for multiclass FIFO in this work, considering both deterministic and stochastic cases. Specifically, delay bounds are presented for D/D/1, G/D/1, GI/D/1, and GI/GI/1, all under multiclass FIFO.