  In this paper, we focus on a multi-queue buffer management in which packets
of different values are segregated in different queues. Our model consists of m
packets values and m queues. Recently, Al-Bawani and Souza (arXiv:1103.6049v2
[cs.DS] 30 Mar 2011) presented an online multi-queue buffer management
algorithm Greedy and showed that it is 2-competitive for the general m-valued
case, i.e., m packet values are 0 < v_{1} < v_{2} < ... < v_{m}, and
(1+v_{1}/v_{2})-competitive for the two-valued case, i.e., two packet values
are 0 < v_{1} < v_{2}. For the general m-valued case, let c_i = (v_{i} +
\sum_{j=1}^{i-1} 2^{j-1} v_{i-j})/(v_{i+1} + \sum_{j=1}^{i-1}2^{j-1}v_{i-j})
for 1 \leq i \leq m-1, and let c_{m}^{*} = \max_{i} c_{i}. In this paper, we
precisely analyze the competitive ratio of Greedy for the general m-valued
case, and show that the algorithm Greedy is (1+c_{m}^{*})-competitive.
