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

In the online packet buffering problem (also known as the unweighted FIFO variant of buffer management), we focus on a single network packet switching device with several input ports and one output port. This device forwards unit-size, unit-value packets from input ports to the output port. Buffers attached to input ports may accumulate incoming packets for later transmission; if they cannot accommodate all incoming packets, their excess is lost. A packet buffering algorithm has to choose from which buffers to transmit packets in order to minimize the number of lost packets and thus maximize the throughput. We present a tight lower bound of e/(e-1) ~ 1.582 on the competitive ratio of the throughput maximization, which holds even for fractional or randomized algorithms. This improves the previously best known lower bound of 1.4659 and matches the performance of the algorithm Random Schedule. Our result contradicts the claimed performance of the algorithm Random Permutation; we point out a flaw in its original analysis

Buffer Overflow Management with Class Segregation

We consider a new model for buffer management of network switches with Quality of Service (QoS) requirements. A stream of packets, each attributed with a value representing its Class of Service (CoS), arrives over time at a network switch and demands a further transmission. The switch is equipped with multiple queues of limited capacities, where each queue stores packets of one value only. The objective is to maximize the total value of the transmitted packets (i.e., the weighted throughput). We analyze a natural greedy algorithm, GREEDY, which sends in each time step a packet with the greatest value. For general packet values $(v_1 < \cdots < v_m)$, we show that GREEDY is $(1+r)$-competitive, where $r = \max_{1\le i \le m-1} \{v_i/v_{i+1}\}$. Furthermore, we show a lower bound of $2 - v_m / \sum_{i=1}^m v_i$ on the competitiveness of any deterministic online algorithm. In the special case of two packet values (1 and $\alpha > 1$), GREEDY is shown to be optimal with a competitive ratio of $(\alpha + 2)/(\alpha + 1)$

The Longest Queue Drop Policy for Shared-Memory Switches is 1.5-competitive

We consider the Longest Queue Drop memory management policy in shared-memory switches consisting of $N$ output ports. The shared memory of size $M\geq N$ may have an arbitrary number of input ports. Each packet may be admitted by any incoming port, but must be destined to a specific output port and each output port may be used by only one queue. The Longest Queue Drop policy is a natural online strategy used in directing the packet flow in buffering problems. According to this policy and assuming unit packet values and cost of transmission, every incoming packet is accepted, whereas if the shared memory becomes full, one or more packets belonging to the longest queue are preempted, in order to make space for the newly arrived packets. It was proved in 2001 [Hahne et al., SPAA '01] that the Longest Queue Drop policy is 2-competitive and at least $\sqrt{2}$-competitive. It remained an open question whether a (2-\epsilon) upper bound for the competitive ratio of this policy could be shown, for any positive constant \epsilon. We show that the Longest Queue Drop online policy is 1.5-competitive

Greedy Algorithms for Multi-Queue Buffer Management with Class Segregation

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.Comment: 19 page

Online packet scheduling for CIOQ and buffered crossbar switches

We consider the problem of online packet scheduling in Combined Input and Output Queued (CIOQ) and buffered crossbar switches. In the widely used CIOQ switches, packet buffers (queues) are placed at both input and output ports. An N×N CIOQ switch has N input ports and N output ports, where each input port is equipped with N queues, each of which corresponds to an output port, and each output port is equipped with only one queue. In each time slot, arbitrarily many packets may arrive at each input port, and only one packet can be transmitted from each output port. Packets are transferred from the queues of input ports to the queues of output ports through the internal fabric. Buffered crossbar switches follow a similar design, but are equipped with additional buffers in their internal fabric. In either model, our goal is to maximize the number or, in case the packets have weights, the total weight of transmitted packets. Our main objective is to devise online algorithms that are both competitive and efficient. We improve the previously known results for both switch models, both for unweighted and weighted packets. For unweighted packets, Kesselman and Rosén (J. Algorithms 60(1):60–83, 2006) give an online algorithm that is 3-competitive for CIOQ switches. We give a faster, more practical algorithm achieving the same competitive ratio. In the buffered crossbar model, we also show 3-competitiveness, improving the previously known ratio of 4. For weighted packets, we give 5.83- and 14.83-competitive algorithms with an elegant analysis for CIOQ and buffered crossbar switches, respectively. This improves upon the previously known ratios of 6 and 16.24

An Experimental Study of New and Known Online Packet Buffering Algorithms

We present the first experimental study of online packet buffering algorithms for network switches. The design and analysis of such strategies has received considerable research attention in the theory community recently. We consider a basic scenario in which m queues of size B have to be maintained so as to maximize the packet throughput. A Greedy strategy, which always serves the most populated queue, achieves a competitive ratio of only 2. Therefore, various online algorithms with improved competitive factors were developed in the literature. In this paper we first develop a new online algorithm, called HSFOD, which is especially designed to perform well under real-world conditions. We prove that its competitive ratio is equal to 2. The major part of this paper is devoted to the experimental study in which we have implemented all the proposed algorithms, including HSFOD, and tested them on packet traces from benchmark libraries. We have evaluated the experimentally observed competitivess, the running times, memory requirements and actual packet throughput of the strategies. The tests were performed for varying values of m and B as well as varying switch speeds. The extensive experiments demonstrate that despite a relatively high theoretical competitive ratio, heuristic and greedy-like strategies are the methods of choice in a practical environment. In particular, HSFOD has the best experimentally observed competitiveness