A Tight Upper Bound on Online Buffer Management for Multi-Queue Switches with Bicodal Buffers

Abstract

SUMMARYThe online buffer management problem formulates the problem of queuing policies of network switches supporting QoS (Quality of Service) guarantee. In this paper, we consider one of the most standard models, called multi-queue switches model. In this model, Albers et al. gave a lower bound e e−1 , and Azar et al. gave an upper bound e e−1 on the competitive ratio when m, the number of input ports, is large. They are tight, but there still remains a gap for small m. In this paper, we consider the case where m = 2, namely, a switch is equipped with two ports, which is called a bicordal buffer model. We propose an online algorithm called Segmental Greedy Algorithm (S G) and show that its competitive ratio is at most

Competitive buffer management for multi-queue switches in QoS networks using packet buffering algorithms

“…Furthermore, he showed a lower bound e e−1 (≈ 1.581) of deterministic online algorithms for any B and large enough m, and a lower bound 1.465 of randomized online algorithms for any B and large enough m. Azar and Litichevskey [8] showed a e e−1 (≈ 1.58)-competitive deterministic algorithm for large enough B > log m. Schmidt [36] claimed he showed a 3/2-competitive randomized algorithm, whose flaw was pointed out in [13]. Also, in the case of m = 2, Schmidt [36] showed a lower bound of 16/13 ≈ 1.230 for any online algorithm for large enough B. Bienkowski and Madry [12] and Kobayashi et al [32] proved 16/13-competitive algorithms for the randomized and deterministic cases respectively. Bienkowski [13] showed a lower bound of e e−1 for any online algorithm for any B and large enough m. As for the single-queue models, the current upper and lower bounds on competitive ratios are summarized in Table 2.…”

“…In this section, we use, as subroutines of DS and SS, the deterministic algorithm Segmental Greedy (SG) for M 1 for m = 2 [32]. Its competitive ratios for several values of B are given in the second column of Table 4 as c. The values of c for 1 ≤ B ≤ 8 are not explicitly written in the paper [32] but implied by its appendix. Table 4.…”

An Optimal Lower Bound for Buffer Management in Multi-Queue Switches

“…By taking the algorithm Frac-Waterlevel and applying the fractional-to-deterministic reduction mentioned above, Azar and Litichevskey [AL06] obtained a deterministic e e−1 • (1 + H m + 1 /B)-competitive algorithm (which we call Det-Waterlevel). Again, the results can be improved for particular cases: when B = 2, then the Semi-Greedy algorithm achieves the optimal competitive ratio of 13/7 ≈ 1.857 [AS05]; when m = 2, the optimal ratio 16/13 ≈ 1.231 was achieved by the algorithm Segmental Greedy by Kobayashi et al [KMO08].…”

Tight analysis of priority queuing for egress traffic

“…In this model, the task of an algorithm is to manage its buffers and to schedule packets. The problem of designing only a scheduling algorithm in multi-queue switches is considered in [4,8,13,34,14]. Moreover, Albers and Jacobs [3] performed an experimental study for the first time on several online scheduling algorithms for this model.…”