The k-splittable flow model and a heuristic algorithm for minimizing congestion in the MPLS networks

Abstract

In the multiple protocol label-switched (MPLS) networks, the commodities (packets) are transmitted by the labelswitched paths (LSPs). For the sake of reducing the total cost and strengthening the central management, the MPLS networks restrict the number of paths that a commodity can use. For maintaining the quality of service (QoS) of the users, the demand of each commodity must be satisfied. Under the above conditions, some links of the network may be too much loaded, which affecting the performance of the whole network drastically. For this problem, we first establish two mathematical models, namely the arc-path and arc-flow model. Second, we design a heuristic algorithm which quickly finds paths for each commodity, and then allocate demands for them. In the last, the computational results are tested on a set of medium-sized instances to show the effectiveness of our approach.

A Fast Heuristic Algorithm for Minimizing Congestion in the MPLS Networks

“…Find the smallest α such that there exists a feasible flow satisfying the demands and the path restrictions if all capacities are multiplied by α . In [1], we first propose two different mathematical models, namely the arc-path and arc-flow model. In this paper, we also use the two models to describe our problem.…”

“…may not transform to a feasible flow satisfying all demands in the original graph. For example, a graph with five nodes 1 , s t have demands 5 and 4, respectively. We add a super source node s as mentioned above and a super sink node t .…”

“…The main contribution of this paper is as follows: for the single-source multi-commodity k-splittable flow problem, we propose a new heuristic algorithm, different from the old algorithm that is proposed in [1]. The new algorithm reduces the original problem to a small scale of mixed-integer linear programming.…”

A matheuristic approach for the Quickest Multicommodity k-Splittable Flow Problem

“…Similarly, in the context of emergency transport, it is desirable to obtain evacuation plans where the number of subgroups for each population is limited, in order to prevent interferences, turbulences, and congestions that may drastically affect the transportation process [6]. In telecommunication, the use of a very large number of paths for a quick transmission of data packets can decrease the overall performance of the protocol, requiring a high cost for path maintenance in the network devices and to reconstruct the original information at destination [8,9]. All the above mentioned examples show how imposing a realistic number of paths represents an essential modeling need, which is not yet captured neither by the basic variant of the Quickest Flow Problem [10], nor by the Quickest Path Problem [11].…”

A randomized rounding approach to a k-splittable multicommodity flow problem with lower path flow bounds affording solution quality guarantees

“…The authors achieve run time O(K κ 2 · m log(m) · log(ρ)) under the balance condition, with ρ being the ratio of the sum of demands an the minimum link capacity. Another polynomial-time algorithm for the maximum-flow problem is given in [13], although the authors do not calculate the rank of this time explicitly. They build an initial feasible-solution in terms of link flows and reinterpret it as a superposition of path flows, with a possibility of having several different paths for a commodity.…”