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The aim of the present article is to give a historical survey of some important research works related to queues in machining system since 2010. Queues of failed machines in machine repairing problem occur due to the failure of machines at random in the manufacturing industries, where different jobs are performed on machining stations. Machines are subject to failure what may result in significant loss of production, revenue, or goodwill. In addition to the references on queues in machining system, which is also called 'Machine Repair Problem' (MRP) or 'Machine Interference Problem' (MIP), a meticulous list of books and survey papers is also prepared so as to provide a detailed catalog for understanding the research in queueing domain. We have classified the relevant literature according to a year of publishing, methodological, and modeling aspects. The author(s) hope that this survey paper could be of help to learners contemplating research on queueing domain.

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Survivability of a node vulnerable network is often assessed in terms of the (node) connectivity of the graph that represents the logical topology of the network. When the damage causing events have widespread impact then, owing to the physical layout of the network facilities, each event can destroy several nodes. As a survivability measure. therefore. we define the generalized connectivity as the miriimurn number of eiwrt.s (rather than the minimum number of node removals) required to disconnect the network. To model the possible effects of damage causing events. we introduce the notion of a ctepenitence ~rcrph on the nodes of the network and a set of ndmissible cliques in this graph. Nodes that are nonadjacent in the dependence graph are independent. i.e.. they cannot bc damaged by the same event, and each event destroys an admissible clique of nodes. We present techniques for calculating o r bounding the generalized connectivity of given network graphs. and for synthesizing minimum link networks with prescribed generalized connectivity.