Average Number of Recirculations in SDL Constructions of Optical Priority Queues

Cheng, Jai-Hong; Huang, Xuan-Chao; Cheng, Chih-Heng; Chou, Hsin-Hung; Chang, Cheng-Shang; Lee, Duan-Shin

doi:10.1109/lcomm.2011.062211.110893

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Proof (Proof Of Theorem 6)1

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“…Therefore, we see that the first inequality in (25) follows from U k ≥ m ℓ−s−1 = 2 (ℓ−s−1) log 2 m in (31) and ℓ ≥ M log 2 (2s + 2)/((2s + 1)m log 2 m) − 6 log 2 (2s + 2)/ log 2 m in (33). Similarly, we see that the second inequality in (25) follows from U k ≤ 8m ℓ+1 = 2 (ℓ+1) log 2 m+3 in (32) and ℓ ≤ M log 2 (2s + 2)/((2s + 1)m log 2 m) + s + 2 in (34).…”

Section: Proof (Proof Of Theorem 6)mentioning

confidence: 90%