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

1974 ◽  
Vol 11 (01) ◽  
pp. 94-101 ◽  
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.

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

1974 ◽  
Vol 11 (1) ◽  
pp. 94-101 ◽  
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.

scholarly journals Optimum Flows in Directed Bipartite Dynamic Network. The Static Approach

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Combinatorial Optimization ◽  
Network Flow ◽  
Dynamic Network ◽  
Time Varying ◽  
Flow Models ◽  
Dynamic Network Flow ◽  
Static Approach ◽  
Network Flow Models ◽  
Discrete Values ◽  
Time Expanded Network

The theory of flows is one of the most important parts of Combinatorial Optimization and it has various applications. In this paper we study optimum (maximum or minimum) flows in directed bipartite dynamic network and is an extension of article [9]. In practical situations, it is easy to see many time-varying optimum problems. In these instances, to account properly for the evolution of the underlying system overtime, we need to use dynamic network flow models. When the time is considered as a variable discrete values, these problems can be solved by constructing an equivalent, static time expanded network. This is a static approach.

Networks

2013 ◽  
pp. 150-178
Author(s):  
Alireza Boloori ◽  
Monirehalsadat Mahmoudi
Keyword(s):  
Network Theory ◽  
Network Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Network Problems

This chapter sheds light on various aspects of network theory and relevant concepts including basic definitions, the most common types of network flow problems that have been studied by literature, and the main algorithms and solution approaches proposed for solving network problems.

scholarly journals On self-tuning networks-on-chip for dynamic network-flow dominance adaptation

2014 ◽  
Vol 13 (2s) ◽  
pp. 1-21 ◽  
Author(s):  
Xiaohang Wang ◽  
Mei Yang ◽  
Yingtao Jiang ◽  
Peng Liu ◽  
Masoud Daneshtalab ◽  
...  
Keyword(s):  
Network Flow ◽  
Dynamic Network ◽  
Networks On Chip ◽  
Dynamic Network Flow ◽  
Self Tuning ◽  
On Chip
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