Scheduling Packets with Values and Deadlines in Size-bounded Buffers

Motivated by providing quality-of-service differentiated services in the Internet, we consider buffer management algorithms for network switches. We study a multi-buffer model. A network switch consists of multiple size-bounded buffers such that at any time, the number of packets residing in each individual buffer cannot exceed its capacity. Packets arrive at the network switch over time; they have values, deadlines, and designated buffers. In each time step, at most one pending packet is allowed to be sent and this packet can be from any buffer. The objective is to maximize the total value of the packets sent by their respective deadlines. A 9.82-competitive online algorithm has been provided for this model (Azar and Levy. SWAT 2006), but no offline algorithms have been known yet. In this paper, We study the offline setting of the multi-buffer model. Our contributions include a few optimal offline algorithms for some variants of the model. Each variant has its unique and interesting algorithmic feature. These offline algorithms help us understand the model better in designing online algorithms.Comment: 7 page

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

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