Uncertain Dynamic Network Flow Problems

This paper is concerned with a class of dynamic network flow problems in which the amount of flow leaving node i in one time period for node j is the fraction pij of the total amount of flow which arrived at node i during the previous time period. The fraction pij whose sum over j equals unity may be interpreted as the transition probability of a finite Markov chain in that the unit flow in state i will move to state j with probability pij during the next period of time. The conservation equations for this class of flows are derived, and the limiting behavior of the flows in the network as related to the properties of the fractions Pij are discussed.

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Some limit theorems for a class of network problems as related to finite Markov chains

Journal of Applied Probability ◽

10.2307/3212586 ◽

1974 ◽

Vol 11 (1) ◽

pp. 94-101 ◽

Cited By ~ 1

Author(s):

Masao Nakamura

Keyword(s):

Network Flow ◽

Limit Theorems ◽

Transition Probability ◽

Dynamic Network ◽

Limiting Behavior ◽

Flow Problems ◽

Dynamic Network Flow ◽

Time Period ◽

Network Problems ◽

Finite Markov Chains

This paper is concerned with a class of dynamic network flow problems in which the amount of flow leaving node i in one time period for node j is the fraction pij of the total amount of flow which arrived at node i during the previous time period. The fraction pij whose sum over j equals unity may be interpreted as the transition probability of a finite Markov chain in that the unit flow in state i will move to state j with probability pij during the next period of time. The conservation equations for this class of flows are derived, and the limiting behavior of the flows in the network as related to the properties of the fractions Pij are discussed.

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Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽

10.3390/math9151716 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1716

Author(s):

Adrian Marius Deaconu ◽

Delia Spridon

Keyword(s):

Network Flow ◽

Large Scale ◽

Random Network ◽

Minimum Cost ◽

Maximum Flow ◽

Network Flow Problems ◽

Commodity Flow ◽

Vast Number ◽

Flow Problems ◽

Execution Speed

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

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Review of Network Flow Algorithms David P. Williamson

ACM SIGACT News ◽

10.1145/3457588.3457592 ◽

2021 ◽

Vol 52 (1) ◽

pp. 12-15

Author(s):

S.V. Nagaraj

Keyword(s):

Graduate Students ◽

Real World ◽

Network Flow ◽

Network Flows ◽

Optimization Problems ◽

Capacity Constraints ◽

Incoming Flow ◽

Network Flow Problems ◽

Flow Problems ◽

Real World Problems

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

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