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.

In the k-splittable flow problem, each commodity can only use at most k paths and the key point is to find the suitable transmitting paths for each commodity. To guarantee the efficiency of the network, minimizing congestion is important, but it is not enough, the cost consumed by the network is also needed to minimize. Most researches restrict to congestion or cost, but not the both. In this paper, we consider the bi-objective (minimize congestion, minimize cost) k-splittable problem. We propose three different heuristic algorithms for this problem, 1 A , 2A and 3 A . Each algorithm finds paths for each commodity in a feasible splittable flow, and the only difference between these algorithms is the initial feasible flow. We compare the three algorithms by testing instances, showing that choosing suitable initial feasible flow is important for obtaining good results.

No abstract

In this paper, we propose a new online scheduling model with linear lookahead intervals, which has the character that at any time [Formula: see text], one can foresee the jobs that will coming in the time interval [Formula: see text] in which [Formula: see text]. In this new lookahead model, the length of the lookahead intervals are variable as the time going on and the number of jobs increasing, and has the tend of steady growth. In this paper, we consider online scheduling of unit length jobs on [Formula: see text] identical parallel-batch machines under this new lookahead model to minimize makespan. The batch capacity is unbounded, that is [Formula: see text]. We present an optimal online algorithm for [Formula: see text], and provide a best possible online algorithm of competitive ratio [Formula: see text] for [Formula: see text], where [Formula: see text] is the positive root of [Formula: see text].

In the multiple protocol label-switched (MPLS) networks, the commodities are transmitted by the label-switched 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 in the network may be too much loaded, affecting the performance of the whole network drastically. For this problem, in [1], we proposed two mathematical models to describe it and a heuristic algorithm which quickly finds transmitting paths for each commodity are also presented. In this paper, we propose a new heuristic algorithm which finds a feasible path set for each commodity, and then select some paths from the path set through a mixed integer linear programming to transmit the demand of each commodity. This strategy reduces the scale of the original problem to a large extent. We test 50 instances and the results show the effectiveness of the new heuristic algorithm.