Otherwise coherent networks become incoherent when capacity is concerned

See the network in Figure 1 below. Source node 1 fails, which from a pure availability perspective disrupts only traffic originating or terminating at node 1 because all other nodes can still communicate. So a coherent network (as is the one in the figure) continues to be coherent after this failure, as it must due to the definition of coherent.

But now consider performance. Say the traffic from node 1 (for our example, between nodes 1 and 4, but not necessarily) was significant enough to constrain the traffic traversing the network between nodes 2 and 3. For example, the node in the center of the figure may be insufficient for the demand on the network. Traffic between nodes 2 and 3 cannot be adequately carried when all resources in the network are working.  From their perspective, the service fails when the network is fully working. But when node 1 fails, suddenly resources are free, and the network can now carry all the traffic between nodes 2 and 3. When the network fails in this way, the network suddenly works from the perspective of nodes 2 and 3.

This situation demonstrates incoherent behavior in a network when capacity constraints are considered. The example network is simple, but clearly extends to the more complex, realistic case. This case, which we may all reference, resulted from a conversation with a colleague where we concluded that this type of incoherent behavior was often forgotten.

incoherent network illustration

Fig. 1. A simple network to illustrate incoherent behavior under capacity constraints.

NOTE: Special thanks to Troy Houston from SevOne for pointing out an error in an earlier version of this post.

About Rupe

Dr. Jason Rupe wants to make the world more reliable, even though he likes to break things. He received his BS (1989), and MS (1991) degrees in Industrial Engineering from Iowa State University; and his Ph.D. (1995) from Texas A&M University. He worked on research contracts at Iowa State University for CECOM on the Command & Control Communication and Information Network Analysis Tool, and conducted research on large scale systems and network modeling for Reliability, Availability, Maintainability, and Survivability (RAMS) at Texas A&M University. He has taught quality and reliability at these universities, published several papers in respected technical journals, reviewed books, and refereed publications and conference proceedings. He is a Senior Member of IEEE and of IIE. He has served as Associate Editor for IEEE Transactions on Reliability, and currently works as its Managing Editor. He has served as Vice-Chair'n for RAMS, on the program committee for DRCN, and on the committees of several other reliability conferences because free labor is always welcome. He has also served on the advisory board for IIE Solutions magazine, as an officer for IIE Quality and Reliability division, and various local chapter positions for IEEE and IIE. Jason has worked at USWEST Advanced Technologies, and has held various titles at Qwest Communications Intl., Inc, most recently as Director of the Technology Modeling Team, Qwest's Network Modeling and Operations Research group for the CTO. He has always been those companies' reliability lead. Occasionally, he can be found teaching as an Adjunct Professor at Metro State College of Denver. Jason is the Director of Operational Modeling (DOM) at Polar Star Consulting where he helps government and private industry to plan and build highly performing and reliable networks and services. He holds two patents. If you read this far, congratulations for making it to the end!
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