Matthias Westermann

Considering suppressed packets improves buffer management in QoS switches

The following buffer management problem arises in network switches providing differentiated services: At the beginning of each time step, one packet can be sent, and afterwards an arbitrary number of new packets arrive. Packets that are not sent can be stored in a buffer. Each packet is attributed by a deadline, and a packet is automatically deleted from the buffer if it is still stored in the buffer by the end of its deadline. The differentiated service model is abstracted by attributing each packet with a value according to its service level. A buffer management strategy determines the packet to be sent in each time step. The goal of a buffer management strategy is to maximize the sum of the values of sent packets. We introduce the concept of suppressed packets and present a deterministic strategy that is based on this concept. We show that this strategy achieves a competitive ratio of 2√2--1 ≈ 1.828, which is the best known competitive ratio in the deterministic case. Further, we present a memoryless version of this strategy that achieves a competitive ratio of ≈ 1.893. This is the first memoryless strategy that achieves a competitive ratio less than 2, and the competitive ratio of this strategy is even better than the ratios of all previously known deterministic strategies. This demonstrates the potential of the concept of suppressed packets. In addition, we present a simple strategy that achieves the optimal competitive ratio of min{(1 + α)/α, 2α/(α+1)} ≤ √2, if only two packet values 1 and α > 1 are possible.

Exploiting locality for data management in systems of limited bandwidth

This paper deals with data management in computer systems in which the computing nodes are connected by a relatively sparse network. We consider the problem of placing and accessing a set of shared objects that are read and written from the nodes in the network. These objects are, e.g., global variables in a parallel program, pages or cache lines in a virtual shared memory system, shared files in a distributed file system, or pages in the World Wide Web. A data management strategy consists of a placement strategy that maps the objects (possibly dynamically and with redundancy) to the nodes, and an access strategy that describes how reads and writes are handled by the system (including the routing). We investigate static and dynamic data management strategies.

Lower and upper bounds on FIFO buffer management in QoS switches

We consider FIFO buffer management for switches providing differentiated services. In each time step, an arbitrary number of packets arrive, and only one packet can be sent. The buffer can store a limited number of packets, and, due to the FIFO property, the sequence of sent packets has to be a subsequence of the arriving packets. The differentiated service model is abstracted by attributing each packet with a value according to its service level. A buffer management strategy can drop packets. The goal is to maximize the sum of values of sent packets. For only two different packet values, we introduce the account strategy and prove that this strategy achieves an optimal competitive ratio of ≈ 1.282, if the buffer size tends to infinity, and an optimal competitive ratio of (√13-1)/2 ≈ 1.303, for arbitrary buffer sizes. For general packet values, the simple preemptive greedy strategy (PG) is studied. We show that PG achieves a competitive ratio of √3 ≈ 1.732 which is the best known upper bound on the competitive ratio of this problem. In addition, we give a lower bound of of 1+1/√2 ≈ 1.707 on the competitive ratio of PG which improves the previously known lower bound. As a consequence, the competitive ratio of PG cannot be further improved significantly.

Reordering buffer management for non-uniform cost models

A sequence of objects which are characterized by their color has to be processed. Their processing order influences how efficiently they can be processed: Each color change between two consecutive objects produces non-uniform cost. A reordering buffer which is a random access buffer with storage capacity for k objects can be used to rearrange this sequence in such a way that the total cost are minimized. This concept is useful for many applications in computer science and economics. We show that a reordering buffer reduces the cost of each sequence by a factor of at most 2k–1. This result even holds for cost functions modeled by arbitrary metric spaces. In addition, a matching lower bound is presented. From this bound follows that each strategy that does not increase the cost of a sequence is at least (2k–1)-competitive. As main result, we present the deterministic Maximum Adjusted Penalty (MAP) strategy which is O(log k)-competitive. Previous strategies only achieve a competitive ratio of k in the non-uniform model. For the upper bound on MAP, we introduce a basic proof technique. We believe that this technique can be interesting for other problems.

Lower and Upper Bounds on FIFO Buffer Management in QoS Switches

AbstractWe consider the management of FIFO buffers for network switches providing differentiated services. In each time step, an arbitrary number of packets arrive and only one packet can be sent. The buffer can store a limited number of packets and, due to the FIFO property, the sequence of sent packets has to be a subsequence of the arriving packets. The differentiated service model is abstracted by attributing each packet with a value according to its service level. A buffer management strategy can drop packets, and the goal is to maximize the sum of the values of sent packets.For only two different packet values, we introduce the account strategy and prove that this strategy achieves an optimal competitive ratio of

Approximation Algorithms for Data Management in Networks

\sqrt{2}-(\sqrt{5+4\sqrt{2}}-3)/2\approx 1.282

Reordering buffers for general metric spaces

if the buffer size tends to infinity and an optimal competitive ratio of

The Power of Reordering for Online Minimum Makespan Scheduling

(\sqrt{13}-1)/2\approx 1.303

Approximation algorithms for data management in networks

for arbitrary buffer sizes. For general packet values, the simple preemptive greedy strategy (PG) is studied. We show that PG achieves a competitive ratio of

Caching in Networks

\sqrt{3}\approx 1.732