The Study On Reliability Problems In Network System

Network reliability encompasses a range of issues related to the design, analysis and calculate, maintenance of network, one of the most basic is network reliability analysis, which is devoted to research how to calculate the reliability of a network subject to their components reliability parameter.Because of widely presenting of Computer network, Communication network, transmission network and traffic network etc. in realistic world, whether they can operate stability or not influence not only the life of common population but also safety and stabilize of community, economic development etc of a country. So Network reliability problems much more than only concern of network developer and operator, especially is a hot topic paid close attention by researchers. At the same time network reliability problems have the definite trouble, therefore there are a lot of issues include the methods of analysis, theory models etc. need to be studied deeply.From analysis methods and theory models this paper studied some network reliability issues exist in network systems. The research is comprised mainly of four aspects: bounds of network reliability; performability of network reliability; lumpability problems of network reliability models; fuzzy analysis methods of network reliability. The main results are listed in the following:· The background, status, significance and mathematic methods of involving of network reliability are introduced briefly.· An algorithm of network cutest number with certain edges is given and numerical examples demonstrated the feasible and efficiency of the algorithm.· After studied the relation between connected subnet numbers and the cutest numbers of the network, a formula for computing the coefficient bounds of all-terminal reliability polynomial is obtained, then obtain the bounds of all-terminal reliability. The good performance of the bounds is illustrated by comparing the accurate value and bounds value of a SDH network.· Another bound of all-terminate reliability based on most probable strategy is given in the case of network components with same reliability. Numerical exampledemonstrates the bound is superior to Jacobos, BBST, Kruskal-Katona, Ball-Provan.·Bound of k-terminate reliability is presented by using the edges variable to obtain the algebraic represent of network, then convert k-terminate reliability problem into another problem. An example of Red Arpanet is given to comparison the results.· Proposed a method by using components' steady availability to generate most probable state space of network and merging-vertex algorithm to judge whether a state connected or not. Then Markov theory is used successfully and some important reliability indexes of network system are obtained including steady availability, mean time to first failure, steady fault-frequency.· Established a performability model of network system under the performance criterion, and used Markov theory obtained some performance indexes. An example cf performability analysis of a common channel signaling network (CGSN) under delay constraint demonstrated the feasible and efficiency.· Presented a reduction axiom of capacity related network and matrix reduction method for obtaining path function of the network. A new method for calculating the capacity reliability is given by means of ordered binary decision diagram of Boolean function.· Investigated the lumpability problems of continuous time Markov model of network system, analysis the relationships between lumpable, nearly lumpable and generator matrix and the conduction satisfied by generator matrix under which Markovian process is lumpable, nearly lumpable is given.· In the field of profust theory, profust availability of repairable network system is present; profust reliability indexes of Markov model is given; The relationships between two kind of definition of fuzzy reliability existed in literatures is analysied. Profust reliability analysis of Consecutive-k-out of-n:F system and a emit system are given.