A coherent model for reliability of multiprocessor networks

Boesch, Francis T.; Gross, David R.; Suffel, Charles L.

doi:10.1109/24.556593

Cited by 3 publications

(5 citation statements)

References 12 publications

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“…In [5–7] BGS introduced

{R}_{\alpha}^{(k)}\left(G,p\right)

and studied several properties of it. Since any

i

‐node induced subgraph of

G

that contains a connected component of order at least

k+1

contains a connected component of order at least

k

, it follows that

{A}_i^{\left(k+1\right)}(G)\le {A}_i^{(k)}(G)

for every

i

, thus

{R}_{\alpha}^{\left(k+1\right)}\left(G,p\right)\le {R}_{\alpha}^{(k)}\left(G,p\right)

.…”

Section: Suffel's Researchmentioning

confidence: 99%

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Dr. Charles L. Suffel: Scholar, teacher, mentor, friend

et al. 2022

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Dr. Charles L. Suffel (1941Suffel ( -2021 was an influential mathematics educator and scholar at Stevens Institute of Technology for more than half a century. Managing Editor of Networks for 20 years, Suffel's reach extended far beyond the Stevens campus. He coauthored dozens of graph theory papers and mentored more than a dozen Ph.D. thesis students. In this article, we discuss his contributions to the field of network reliability theory and his legacy as a teacher and mentor. KEYWORDSAll-terminal reliability, component order connectivity, component order edge connectivity, component order reliability, compression, neighbor-component order connectivity, spanning trees, weighted component edge connectivity SUFFEL'S RESEARCHCharlie Suffel received his Ph.D. from Brooklyn Polytechnical University in 1969 under the direction of the functional analyst George Bachmann. He also worked for a stint at Bell Labs before joining Stevens Institute of Technology as an assistant professor. The first half dozen publications of his academic career were in the area of functional analysis and topological vector spaces. Promoted to full professor in 1979, Suffel would go on to co-author more than more than 50 papers in the areas of graph theory and network reliability theory. The first of these studied subgraphs of Eulerian graphs [14]; coauthored with Boesch and Ralph Tindell, it appeared in the first edition of Journal of Graph Theory. In fact, his most frequent collaborators were Boesch (27 co-authored papers), Dan Gross (23), John T. Saccoman (13) and Bill Kazmierczak (12), the latter two being among Suffel's 15 completed Ph.D. students. What should be noted is that Suffel continued to be an active researcher during his 20 years as the Dean of Graduate Studies at Stevens; in fact, 30 of his papers were published during that time, and more

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“…In [5–7] BGS introduced

{R}_{\alpha}^{(k)}\left(G,p\right)

and studied several properties of it. Since any

i

‐node induced subgraph of

G

that contains a connected component of order at least

k+1

contains a connected component of order at least

k

, it follows that

{A}_i^{\left(k+1\right)}(G)\le {A}_i^{(k)}(G)

for every

i

, thus

{R}_{\alpha}^{\left(k+1\right)}\left(G,p\right)\le {R}_{\alpha}^{(k)}\left(G,p\right)

.…”

Section: Suffel's Researchmentioning

confidence: 99%

“…In [5][6][7] BGS introduced R (k) 𝛼 (G, p) and studied several properties of it. Since any i-node induced subgraph of G that contains a connected component of order at least k + 1 contains a connected component of order at least k, it follows that…”

Section: Component Order Reliabilitymentioning

confidence: 99%

Dr. Charles L. Suffel: Scholar, teacher, mentor, friend

et al. 2022

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“…Connectivity of generic deterministic graphs under independent node failure has also received significant attention in the literature [5], [16], [21]. In this line of work, is called residual node connectivity and can be expressed as [5]: (4) where is the failure probability of each node and is the number of connected induced subgraphs of with exactly nodes.…”

Section: Deterministic Graphsmentioning

confidence: 99%

“…In this line of work, is called residual node connectivity and can be expressed as [5]: (4) where is the failure probability of each node and is the number of connected induced subgraphs of with exactly nodes. While this closed-form expansion is beneficial for simple graphs (such as trees), computation of for a generic graph requires the knowledge of an NP-complete metric , whose expression is unknown even for the basic hypercube [39].…”

Section: Deterministic Graphsmentioning

confidence: 99%

“…This led to the following approximate model for the probability that an -node, -regular graph partitions under -percent node failure [31]: (5) where (6) Other approaches that study disconnection of hypercubes include [11], [14], [18], [24]; however, none of them provide a practically usable model that is both accurate and simple to evaluate.…”

Section: Deterministic Graphsmentioning

confidence: 99%

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On Static and Dynamic Partitioning Behavior of Large-Scale P2P Networks

Leonard

Yao

Wang

et al. 2008

IEEE/ACM Trans. Networking

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Abstract-In this paper, we analyze the problem of network disconnection in the context of large-scale P2P networks and understand how both static and dynamic patterns of node failure affect the resilience of such graphs. We start by applying classical results from random graph theory to show that a large variety of deterministic and random P2P graphs almost surely (i.e., with probability 1(1)) remain connected under random failure if and only if they have no isolated nodes. This simple, yet powerful, result subsequently allows us to derive in closed-form the probability that a P2P network develops isolated nodes, and therefore partitions, under both types of node failure. We finish the paper by demonstrating that our models match simulations very well and that dynamic P2P systems are extremely resilient under node churn as long as the neighbor replacement delay is much smaller than the average user lifetime.

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