Unicast and Multicast Qos Routing with Soft Constraint Logic Programming

For all these reasons, the routing problem has naturally been extended to include and to guarantee QoS requirements [Younis and Fahmy 2003;Xiao and Ni 1999;Paul and Raghavan 2002], and consequently is usually abbreviated to QoS routing. As defined in [Crawley et al. 1998], QoS is “a set of service requirements to be met by the network while transporting a flow”, where a flow is “a packet stream from source to a destination (unicast or multicast) with an associated Quality of Service (QoS)”. To be implemented and subsequently satisfied, service requirements have to be expressed in some measurable QoS metrics, such as bandwidth, number of hops, delay, jitter, cost and loss probability of packets.

This paper combines and extends the two works presented in [Bistarelli et al. 2002] and [Bistarelli et al. 2007]. First, we detail the modelling procedure to represent and solve plain Shortest Path (SP) [Cormen et al. 1990] problems with Soft Constraint Logic Programming (see Sec. 2). We consider several versions of SP problems, from the classical one to the multi-criteria case (i.e. many costs to be optimized), from partially-ordered problems to those that are based on modalities associated to the use of the arcs (i.e. modality-based ), and we show how to model and solve them via SCLP programs. The basic idea is that the paths represent network routes, edge costs represent QoS metric values, and our aim is to guarantee the requested QoS on the found unicast routes, by satisfying the QoS constraints and optimizing the cost of the route at the same time. The different criteria can be, for example, maximizing the global bandwidth and minimizing the delay that can be experienced on a end-to-end communication.

Then, extending the unicast solution, we suggest a formal model to represent and solve the multicast routing problem in multicast networks (i.e. networks supporting the multicast delivery schema) that need QoS support. To attain this, we draw the network adapting it to a weighted and-or graph [Martelli and Montanari 1978], where the weight on a connector corresponds to the cost of sending a packet on the network link modelled by that connector. Then, we translate the hypergraph in a SCLP program and we show how the semantic of this program computes the best tree in the corresponding and-or graph. We apply this result to find, from a given source node in the network, the multicast distribution tree having the minimum cost and reaching all the destination nodes of the multicast communication. The • 3 costs of the connectors can be described as vectors (multidimensional costs), each component representing a different QoS metric value. We show also how modalities can be added to multicast problems, and how the computational complexity of this framework can be reduced. Therefore, in this paper we present a complete formal model to represent and solve the unicast/multicast QoS routing problem.

SCLP programs are logic programs where each ground atom can be seen as an instantiated soft constraint [Bistarelli et al. 1995;1997b] and it can be associated with an element taken from a set. Formally, this set is a c-semiring [Bistarelli 2004] (or simply semiring in the following), that is, a set plus two operations, + and ×, which basically say how to combine constraints and how to compare them. The presence of these two operations allows to replace the usual boolean algebra for logic programming with a more general algebra where logical and and logical or are replaced by the two semiring operations. In this way, the underlying logic programming engine provides a natural tool to specify and solve combinatorial problems, while the soft constraint machinery provides greater expressivity and flexibility.

The most important features of the adopted framework are: first, is that SCLP is a declarative programming environment and, thus, is relatively easy to specify a lot of different problems, ranging from paths to tree

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