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Computing Conditional Distributions of Queuing Network Matrices
| Content Provider | Scilit |
|---|---|
| Author | Semal, Pierre Courtois, Pierre-Jacques |
| Copyright Year | 2021 |
| Description | This paper addresses the problem of computing conditional steady-state distributions in large Markovian queuing networks. An algebraic framework is introduced to describe and analyze decomposition techniques which yield these distributions. First, this yields a new proof that the so-called short-cut or Norton's method [1][5] gives exact results under conditions of local balance. As opposed to previous work, this proof is constructive in the sense that the Norton's method is directly derived from the global and the local balance equations. A by-product of the proof is to generalize the class of network routing schemes to which the theorem applies. Besides, it is shown that the exact conditional distributions can also be obtained by decomposition under conditions that are weaker than local balance. These conditions are called here “subsystem balance” and the corresponding exact decomposition “bounded population range” (BPR). In the second part of the paper, properties of polyhedra of Perron-Frobenius eigenvectors are used to analyze the accuracy of these methods 330when they are applied to more general queuing networks that do not satisfy any type of balance. We show, then, how the accuracy depends on the structure of the entire network and can thereby be arbitrary poor in the absence of any special network property. On the other hand, the methods are guaranteed to be accurate when the network is “nearly completely decomposable.” Finally, for networks without any specific property, the BPR method provides better guarantees than the Norton's method; another advantage of the BPR method is that it always converges as the amount of computation involved is increased. Book Name: Numerical Solution of Markov Chains |
| Related Links | https://api.taylorfrancis.com/content/chapters/edit/download?identifierName=doi&identifierValue=10.1201/9781003210160-17&type=chapterpdf |
| Ending Page | 356 |
| Page Count | 28 |
| Starting Page | 329 |
| DOI | 10.1201/9781003210160-17 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2021-06-16 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Numerical Solution of Markov Chains Operations Research and Management Science Transportation Norton Queuing Networks Distributions Computing Structure Decomposition |
| Content Type | Text |
| Resource Type | Chapter |
