Real-Time Message Routing and Scheduling

Abstract

Exchanging messages between nodes of a network (e.g., embedded computers) is a fundamental issue in real-time systems involving critical routing and scheduling decisions. In order for messages to meet their deadlines, one has to determine a suitable (short) origin-destination path for each message and resolve conflicts between messages whose paths share a communication link of the network. With this paper we contribute to the theoretic foundations of real-time systems. On the one hand, we provide efficient routing strategies yielding origin-destination paths of bounded dilation and congestion. In particular, we can give good a priori guarantees on the time required to send a given set of messages which, under certain reasonable conditions, implies that all messages can be scheduled to reach their destination on time. Finally, for message routing along a directed path (which is already N P-hard), we identify a natural class of instances for which a simple scheduling heuristic yields provably optimal solutions. ⋆⋆ supported by DFG Focus Program 1307 within the project "Algorithm Engineering for Real-time Scheduling and Routing".

Packet Routing: Complexity and Algorithms

“…Since there are algorithms known to determine paths for routing the packets (see [28,18] or simply take shortest paths) we will also consider the packet routing problem with fixed paths. An instance of this problem is a tripel (G, M, P) such that G is a (directed or undirected) graph, M is a set of packets and P is a set of predefined paths.…”

“…There are also some local algorithms for this problem (algorithms in which each node must take the scheduling decisions for its packets without knowing the packets in the rest of the network) needing O (C) +(log [28] present an algorithm that solves the packet routing problem with variable paths with a constant approximation factor. This algorithm was recently improved by Koch et al [18] for the more general message routing problem (where each message consists of several packets).…”

A Simpler Proof for $O(\textrm{Congestion} + \textrm{Dilation})$ Packet Routing

“…If we generalize the problem to finding paths plus schedules, then constant factor approximation algorithms are still possible due to Srinivasan and Teo [ST00] (using the fact that it suffices to find paths that minimize the sum of congestion and dilation). Koch et al [KPSW09] extend this to a more general setting, where messages consisting of several packets have to be sent. The Leighton-Maggs-Rao result, apart from being quite involved, has the disadvantage of being a non-local offline algorithm.…”

Competitive Packet Routing with Priority Lists

“…A fundamental combinatorial optimization problem that has received considerable attention in the past (cf. [4,14,17,18,21,24]) is packet routing in graphs. We are given a set of packets, which may, for example, correspond to unit-sized messages/bits in a communication network.…”