Classical network reliability problems assume both net- works and components have only binary states, fully working or fully failed states. But many actual networks are multi-state, such as communication networks and ...Classical network reliability problems assume both net- works and components have only binary states, fully working or fully failed states. But many actual networks are multi-state, such as communication networks and transportation networks. The nodes and arcs in the networks may be in intermediate states which are not fully working either fully failed. A simulation ap- proach for computing the two-terminal reliability of a multi-state network is described. Two-terminal reliability is defined as the probability that d units of demand can be supplied from the source to sink nodes under the time threshold T. The capacities of arcs may be in a stochastic state following any discrete or continuous distribution. The transmission time of each arc is also not a fixed number but stochastic according to its current capacity and de- mand. To solve this problem, a capacitated stochastic coloured Petri net is proposed for modelling the system behaviour. Places and transitions respectively stand for the nodes and arcs of a net- work. Capacitated transition and self-modified token colour with route information are defined to describe the multi-state network. By the simulation, the two-terminal reliability and node importance can be estimated and the optimal route whose reliability is highest can also be given. Finally, two examples of different kinds of multi- state networks are given.展开更多
基金supported by the National Natural Science Foundation of China (70971132)
文摘Classical network reliability problems assume both net- works and components have only binary states, fully working or fully failed states. But many actual networks are multi-state, such as communication networks and transportation networks. The nodes and arcs in the networks may be in intermediate states which are not fully working either fully failed. A simulation ap- proach for computing the two-terminal reliability of a multi-state network is described. Two-terminal reliability is defined as the probability that d units of demand can be supplied from the source to sink nodes under the time threshold T. The capacities of arcs may be in a stochastic state following any discrete or continuous distribution. The transmission time of each arc is also not a fixed number but stochastic according to its current capacity and de- mand. To solve this problem, a capacitated stochastic coloured Petri net is proposed for modelling the system behaviour. Places and transitions respectively stand for the nodes and arcs of a net- work. Capacitated transition and self-modified token colour with route information are defined to describe the multi-state network. By the simulation, the two-terminal reliability and node importance can be estimated and the optimal route whose reliability is highest can also be given. Finally, two examples of different kinds of multi- state networks are given.
