A ϕ\phi-Competitive Algorithm for Scheduling Packets with Deadlines

In the online packet scheduling problem with deadlines (PacketScheduling, for short), the goal is to schedule transmissions of packets that arrive over time in a network switch and need to be sent across a link. Each packet has a deadline, representing its urgency, and a non-negative weight, that represents its priority. Only one packet can be transmitted in any time slot, so, if the system is overloaded, some packets will inevitably miss their deadlines and be dropped. In this scenario, the natural objective is to compute a transmission schedule that maximizes the total weight of packets which are successfully transmitted. The problem is inherently online, with the scheduling decisions made without the knowledge of future packet arrivals. The central problem concerning PacketScheduling, that has been a subject of intensive study since 2001, is to determine the optimal competitive ratio of online algorithms, namely the worst-case ratio between the optimum total weight of a schedule (computed by an offline algorithm) and the weight of a schedule computed by a (deterministic) online algorithm. We solve this open problem by presenting a $\phi$-competitive online algorithm for PacketScheduling (where $\phi\approx 1.618$ is the golden ratio), matching the previously established lower bound.Comment: Major revision of the analysis and some other parts of the paper. Another revision will follo

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

A 4/3-competitive randomized algorithm for online scheduling of packets with agreeable deadlines

In 2005 Li et al. gave a phi-competitive deterministic online algorithm for scheduling of packets with agreeable deadlines with a very interesting analysis. This is known to be optimal due to a lower bound by Hajek. We claim that the algorithm by Li et al. can be slightly simplified, while retaining its competitive ratio. Then we introduce randomness to the modified algorithm and argue that the competitive ratio against oblivious adversary is at most 4/3. Note that this still leaves a gap between the best known lower bound of 5/4 by Chin et al. for randomised algorithms against oblivious adversary.Comment: 11 pages, 3-4 figures; new version due to STACS submissio

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

A φ-competitive algorithm for scheduling packets with deadlines

In the online packet scheduling problem with deadlines (PacketScheduling, for short), the goal is to schedule transmissions of packets that arrive over time in a network switch and need to be sent across a link. Each packet has a deadline, representing its urgency, and a non-negative weight, that represents its priority. Only one packet can be transmitted in any time slot, so, if the system is overloaded, some packets will inevitably miss their deadlines and be dropped. In this scenario, the natural objective is to compute a transmission schedule that maximizes the total weight of packets which are successfully transmitted. The problem is inherently online, with the scheduling decisions made without the knowledge of future packet arrivals. The central problem concerning PacketScheduling, that has been a subject of intensive study since 2001, is to determine the optimal competitive ratio of online algorithms, namely the worst-case ratio between the optimum total weight of a schedule (computed by an offline algorithm) and the weight of a schedule computed by a (deterministic) online algorithm. We solve this open problem by presenting a ϕ-competitive online algorithm for PacketScheduling (where ϕ ≈ 1.618 is the golden ratio), matching the previously established lower bound