536 research outputs found

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

    Get PDF
    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

    Online packet scheduling for CIOQ and buffered crossbar switches

    Get PDF
    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

    Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop

    Get PDF
    We consider the problem of managing the buffer of a shared-memory switch that transmits packets of unit value. A shared-memory switch consists of an input port, a number of output ports, and a buffer with a specific capacity. In each time step, an arbitrary number of packets arrive at the input port, each packet designated for one output port. Each packet is added to the queue of the respective output port. If the total number of packets exceeds the capacity of the buffer, some packets have to be irrevocably rejected. At the end of each time step, each output port transmits a packet in its queue and the goal is to maximize the number of transmitted packets. The Longest Queue Drop (LQD) online algorithm accepts any arriving packet to the buffer. However, if this results in the buffer exceeding its memory capacity, then LQD drops a packet from the back of whichever queue is currently the longest, breaking ties arbitrarily. The LQD algorithm was first introduced in 1991, and is known to be 2-competitive since 2001. Although LQD remains the best known online algorithm for the problem and is of practical interest, determining its true competitiveness is a long-standing open problem. We show that LQD is 1.707-competitive, establishing the first (2-?) upper bound for the competitive ratio of LQD, for a constant ? > 0

    Effiziente Algorithmen

    Get PDF
    [no abstract available

    Competitive Management of Non-preemptive Queues with Multiple Values

    Full text link
    We consider the online problem of active queue management. In our model, the input is a sequence of packets with values v ∈ [1, α] that arrive to a queue that can hold up to B packets. Specifically, we consider a FIFO non-preemptive queue, where any packet that is accepted into the queue must be sent, and packets are sent by the order of arrival. The benefit of a scheduling policy, on a given input, is the sum of values of the scheduled packets. Our aim is to find an online policy that maximizes its benefit compared to the optimal offline solution. Previous work proved that no constant competitive ratio exists for this problem, showing a lower bound of ln(α)+1 for any online policy. An upper bound of e⌈ln(α) ⌉ was proved for a few online policies. In this paper we suggest and analyze a RED-like online policy with a competitive ratio that matches the lower bound up to an additive constant proving an upper bound of ln(α) + 2 + O(ln 2 (α)/B). For large values of α, we prove that no policy whose decisions are based only on the number of packets in the queue and the value of the arriving packet, has a competitive ratio lower than ln(α) + 2 − ɛ, for any constant ɛ> 0. Submitted to the regular track. Nir Andelman is a full time student at Tel-Aviv University.
    • …
    corecore