716 research outputs found
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
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 output ports. The shared memory of size
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 -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
Comparison-based FIFO 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 FIFO buffer and only one packet can be transmitted. Packets may be kept in the buffer of limited size and, due to the FIFO property, the sequence of transmitted packets has to be a subsequence of the arriving packets. The differentiated service concept is implemented by attributing each packet with a non-negative value corresponding to its service level. A buffer management algorithm can reject arriving packets and preempt buffered packets. The goal is to maximize the total value of transmitted packets.
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 algorithms proves to be robust in the realm of QoS switches. Kesselman et al. (SIAM J. Comput., 2004) present a comparison-based algorithm that is 2-competitive. For a long time, it has been an open problem whether a comparison-based algorithm exists with a competitive ratio below 2. We present a lower bound of 1 + 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
Bounded Delay Scheduling with Packet Dependencies
A common situation occurring when dealing with multimedia traffic is having
large data frames fragmented into smaller IP packets, and having these packets
sent independently through the network. For real-time multimedia traffic,
dropping even few packets of a frame may render the entire frame useless. Such
traffic is usually modeled as having {\em inter-packet dependencies}. We study
the problem of scheduling traffic with such dependencies, where each packet has
a deadline by which it should arrive at its destination. Such deadlines are
common for real-time multimedia applications, and are derived from stringent
delay constraints posed by the application. The figure of merit in such
environments is maximizing the system's {\em goodput}, namely, the number of
frames successfully delivered.
We study online algorithms for the problem of maximizing goodput of
delay-bounded traffic with inter-packet dependencies, and use competitive
analysis to evaluate their performance. We present competitive algorithms for
the problem, as well as matching lower bounds that are tight up to a constant
factor. We further present the results of a simulation study which further
validates our algorithmic approach and shows that insights arising from our
analysis are indeed manifested in practice
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