PH-graphs for analyzing shortest path problems with correlated traveling times

Buchholz, Peter; Felko, Iryna

doi:10.1016/j.cor.2015.01.001

Cited by 6 publications

(6 citation statements)

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“…We present PHGs formally and by a simple example. Further details about the model and algorithms to fit the parameters of the included PHDs can be found in Buchholz and Felko (2015) and Dohndorf (2017). After introduction of the basic model, the shortest path problem and the basics for solving the problem are introduced.…”

Section: Ph-graphsmentioning

confidence: 99%

“…Furthermore, an approach is introduced to approximate the convex hull of Pareto optimal policies, if several goal functions are combined. The problem will be solved in the context of PH-graphs (PHGs) (Buchholz and Felko 2015), a recently published class of stochastic graphs that allows one to include generally distributed edge costs and correlation between adjacent edges. Edge costs are modeled by phase-type distributions (PHDs) (Buchholz et al 2014;Neuts 1981).…”

Section: Introductionmentioning

confidence: 99%

“…We analyze the problems in the context of PHGs which have been defined in Buchholz and Felko (2015) and Dohndorf (2017). Distributions in this model class are described by PHDs (Neuts 1981) and correlations between edge costs are introduced using concepts from Markovian arrival processes (MAPs) (Neuts 1979) which have been adopted to adjacent distributions in a graph (Buchholz and Felko 2015;Dohndorf 2017). PHDs and MAPs are commonly used in performance and reliability analysis and methods to determine their parameters from measurements are available (Buchholz et al 2014).…”

Section: Introductionmentioning

confidence: 99%

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A multi-objective approach for PH-graphs with applications to stochastic shortest paths

Buchholz

Dohndorf

2020

Math Meth Oper Res

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Stochastic shortest path problems (SSPPs) have many applications in practice and are subject of ongoing research for many years. This paper considers a variant of SSPPs where times or costs to pass an edge in a graph are, possibly correlated, random variables. There are two general goals one can aim for, the minimization of the expected costs to reach the destination or the maximization of the probability to reach the destination within a given budget. Often one is interested in policies that build a compromise between different goals which results in multi-objective problems. In this paper, an algorithm to compute the convex hull of Pareto optimal policies that consider expected costs and probabilities of falling below given budgets is developed. The approach uses the recently published class of PH-graphs that allow one to map SSPPs, even with generally distributed and correlated costs associated to edges, on Markov decision processes (MDPs) and apply the available techniques for MDPs to compute optimal policies.

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Section: Ph-graphsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A multi-objective approach for PH-graphs with applications to stochastic shortest paths

Buchholz

Dohndorf

2020

Math Meth Oper Res

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“…See Liggett [1985] for a background of this area and other examples. An exception is Buchholz and Felko [2015], where link traversal times are modeled by correlated random variables with phase-type distributions (if the traversal time of link u ends in phase x it will begin at link v in phase y with probability P u,v (x, y) if the path (u, v) is followed). This Markovian setting differs from our setting, which need not be Markovian and also does not account for different transmission models.…”

Section: Related Workmentioning

confidence: 99%

Untitled

Towsley¹,

Williamson²

2016

ACM Trans. Model. Perform. Eval. Comput. Syst.

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In this article, we investigate the traversal time of a file across N communication links subject to stochastic changes in the sending rate of each link. Each link's sending rate is modeled by a finite-state Markov process. Two cases, one where links evolve independently of one another (N mutually independent Markov processes) and the second where their behaviors are dependent (these N Markov processes are not mutually independent), are considered. A particular instance where the above is encountered is ad hoc delay/tolerant networks where links are subject to intermittent unavailability.

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“…Buchholz and Felko presented a new approach to model weighted graphs with correlated weights at the edges. Such models are meaningful in describing many real world problems like routing in computer networks or finding shortest paths in traffic models under realistic assumptions [15]. Sommer has solved the shortest path queries in static networks [16].…”

Section: Introductionmentioning

confidence: 99%

Research on Optimal Path of Data Migration among Multisupercomputer Centers

Zhang

Feng

2016

Scientific Programming

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Data collaboration between supercomputer centers requires a lot of data migration. In order to increase the efficiency of data migration, it is necessary to design optimal path of data transmission among multisupercomputer centers. Based on the situation that the target center which finished receiving data can be regarded as the new source center to migrate data to others, we present a parallel scheme for the data migration among multisupercomputer centers with different interconnection topologies using graph theory analysis and calculations. Finally, we verify that this method is effective via numeric simulation.

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PH-graphs for analyzing shortest path problems with correlated traveling times

Cited by 6 publications

References 34 publications

A multi-objective approach for PH-graphs with applications to stochastic shortest paths

A multi-objective approach for PH-graphs with applications to stochastic shortest paths

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Research on Optimal Path of Data Migration among Multisupercomputer Centers

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