The Tree Cut and Merge Algorithm for Estimation of Network Reliability

Abstract

This article presents Monte Carlo techniques for estimating network reliability+ For highly reliable networks, techniques based on graph evolution models provide very good performance+ However, they are known to have significant simulation cost+ An existing hybrid scheme~based on partitioning the time space! is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme+ To overcome these difficulties, a new hybrid scheme~based on partitioning the edge set! is proposed in this article+ The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network+ It also provides reliability bounds with little overhead+

Applications of the Cross-Entropy Method in Reliability

“…Elperin, Gertsbakh and Lomonosov proposed Evolution Models for estimating the reliability of highly reliable networks [11,12,22]. Hui et al [18] proposed a hybrid scheme that provides bounds and can provide a speed-up by several orders of magnitude in certain classes of networks. They also proposed another scheme [19] which employs the Cross-Entropy technique to speed-up the estimation in general classes of networks.…”

“…We now construct a sequence of pairs {(v t ,γ t )} such that v t converges to a reference vector close to the optimal CE reference parameter and γ t eventually reaches one. Starting with v 0 = u = (u 1 ,…,u m ), at each iteration t we draw a random sample Y (1) ,…,Y (N) from the pdf f(⋅;v t-1 }) of Y and update the level parameter γ t using equation (18) and the reference parameter v t using equation (19), which in this case has the analytical solution …”

“…A result of simulations is given in Table 2. The following CE parameters were used: (initial) sample size N=2000 and rarity parameter ρ=0.01 in equation (18). In both CMC and CMC-CE, a final sample size of one million was used to estimate r .…”

The Cross-Entropy Method for Network Reliability Estimation

“…Elperin, Gertsbakh, and Lomonosov proposed Evolution Models for estimating reliability of highly reliable networks Lomonosov, 1991, 1992). Hui et al proposed a hybrid scheme that provides bounds and can provide speed-up by several orders of magnitude in a certain class of networks (Hui et al, 2003).…”

Designing an Optimal Network Using the Cross-Entropy Method

“…In Section 3 we present the CE approach to the problem. In Section 4 we consider a noisy version of the CE method [5,6], where the network reliability is estimated (rather than evaluated) using graph evolution techniques [7][8][9]. We conclude with a numerical experiment in Section 5 that illustrates the effectiveness of our approach.…”