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 $(\alpha + 2)/(\alpha + 1)$

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

Online algorithms for packet scheduling and buffer management

In this work, we study the problem of buffer management in network switches from an algorithmic perspective. In a typical switching scenario, packets with different service demands arrive at the input ports of the switch and are stored in buffers (queues) of limited capacity. Thereafter, they are transferred over the switching fabric to their corresponding output ports where they join other queues. Finally, packets are transmitted out of the switch through its outgoing links to their next destinations in the network.Due to limitations in the link bandwidth and buffer capacities, buffers may experience events of overflow and thus it becomes inevitable to drop some packets. In other switching models, packets that are sensitive to delay are dropped if they exceed a specific deadline inside the queue. We consider multiple models of switching with the goal of maximizing the throughput of the switch. If all packets are treated equally, i.e., corresponding to the best-effort concept of the Internet, we quantify the throughput as the number of packets that are successfully transmitted through the switch. In networks with Quality of Service (QoS) requirements, packets are assigned values that correspond to their levels of service, and the throughput in this case is equal to the total value of packets that are successfully transmitted. We present different algorithms for the problem of buffer management. In the buffering phase of these algorithms, we examine whether an arriving packet is accepted or rejected, and whether an already queued packet is preempted (dropped) to save space for more valuable packets. In the scheduling phase, we seek to answer questions of the kind "which packet to transfer from an input port to an output port in a given time step?'', and "which packet to transmit from an output buffer?''. An input instance for our algorithms is a finite sequence of packets arriving in an ``online'' manner, i.e., packets arrive one by one over time and an irrevocable decision has to be made on the fly before future arrivals become known. Such algorithms which need to cope with incomplete information about future and cannot undo their decisions are called online algorithms. It is known that packet arrivals do not adhere to any specific arrival distribution. In reality, packets tend to arrive "in bursts'' rather than in smooth Poisson-like distributions. Thus, we do not make any prior assumptions about the arrival process of packets. We therefore resort to the framework of competitive analysis which is the typical worst-case analysis used to assess the performance of online algorithms. In competitive analysis, the benefit of an online algorithm is compared to the benefit of an optimal algorithm which is assumed to know the entire input sequence in advance. An online algorithm is called c-competitive if for each input sequence, the benefit of the optimal algorithm is at most c times the benefit of the online algorithm. The value c is also called the competitive ratio of the online algorithm. We prove upper and lower bounds on the competitive ratio of several online algorithms, and show that some of these algorithms are optimal

Comparison-based buffer management in QoS switches

The following online problem arises in network devices, e.g., switches, with quality of service (QoS) guarantees. In each time step, an arbitrary number of packets arrive at a single buffer and only one packet can be transmitted. The differentiated service concept is implemented by attributing each packet with a non-negative value corresponding to its service level. The goal is to maximize the total value of transmitted packets. We consider two models of this problem, the FIFO and the bounded-delay model. In the FIFO model, the buffer can store a limited number of packets and the sequence of transmitted packets has to be a subsequence of the arriving packets. In this model, a buffer management algorithm can reject arriving packets and preempt buffered packets. In the bounded-delay model, the buffer has unbounded capacity, but each packet has a deadline and packets can only be transmitted before their deadlines. Here, a buffer management algorithm determines the packet to be sent in each time step. We study comparison-based buffer management algorithms, i.e., algorithms that make their decisions based solely on the relative order between packet values with no regard to the actual values. This kind of algorithm proves to be robust in the realm of QoS switches. Kesselman et al. (SIAM J Comput 33(3):563–583, 2004) present two deterministic comparison-based online algorithms, one for each model, which are 2-competitive. For a long time, it has been an open problem, whether a comparison-based online algorithm exists, in either model, with a competitive ratio below 2. In the FIFO model, we present a lower bound of 1+1/2–√≈1.7071+1/2≈1.707 on the competitive ratio of any deterministic comparison-based algorithm and give an algorithm that matches this lower bound in the case of monotonic sequences, i.e., packets arrive in a non-decreasing order according to their values. In the bounded-delay model, we show that no deterministic comparison-based algorithm exists with a competitive ratio below 2. In the special s-uniform case, where the difference between the arrival time and deadline of any packet equals s, we present a randomized comparison-based algorithm that is 5 / 3-competitive