Applying the shortest-path-counting problem to evaluate the importance of city road segments and the connectedness of the network-structured system

2004 ◽  
Vol 11 (5) ◽  
pp. 555-573 ◽  
Author(s):  
Tatsuo Oyama ◽  
Hozumi Morohosi
Keyword(s):  
Shortest Path ◽  
Counting Problem ◽  
Structured System ◽  
Path Counting ◽  
Road Segments

scholarly journals Quasi-Birth-and-Death Processes, Lattice Path Counting, and Hypergeometric Functions

2009 ◽  
Vol 46 (02) ◽  
pp. 507-520 ◽  
Author(s):  
Johan S. H. van Leeuwaarden ◽  
Mark S. Squillante ◽  
Erik M. M. Winands
Keyword(s):  
Hypergeometric Functions ◽  
Lattice Path ◽  
Explicit Solutions ◽  
Rate Matrix ◽  
Birth And Death Processes ◽  
Counting Problem ◽  
Classical Models ◽  
Associated Matrix ◽  
Path Counting ◽  
Lattice Path Counting

In this paper we consider a class of quasi-birth-and-death processes for which explicit solutions can be obtained for the rate matrix R and the associated matrix G . The probabilistic interpretations of these matrices allow us to describe their elements in terms of paths on the two-dimensional lattice. Then determining explicit expressions for the matrices becomes equivalent to solving a lattice path counting problem, the solution of which is derived using path decomposition, Bernoulli excursions, and hypergeometric functions. A few applications are provided, including classical models for which we obtain some new results.

scholarly journals Quasi-Birth-and-Death Processes, Lattice Path Counting, and Hypergeometric Functions

2009 ◽  
Vol 46 (2) ◽  
pp. 507-520 ◽  
Author(s):  
Johan S. H. van Leeuwaarden ◽  
Mark S. Squillante ◽  
Erik M. M. Winands
Keyword(s):  
Hypergeometric Functions ◽  
Lattice Path ◽  
Explicit Solutions ◽  
Rate Matrix ◽  
Birth And Death Processes ◽  
Counting Problem ◽  
Classical Models ◽  
Associated Matrix ◽  
Path Counting ◽  
Lattice Path Counting

In this paper we consider a class of quasi-birth-and-death processes for which explicit solutions can be obtained for the rate matrix R and the associated matrix G. The probabilistic interpretations of these matrices allow us to describe their elements in terms of paths on the two-dimensional lattice. Then determining explicit expressions for the matrices becomes equivalent to solving a lattice path counting problem, the solution of which is derived using path decomposition, Bernoulli excursions, and hypergeometric functions. A few applications are provided, including classical models for which we obtain some new results.

scholarly journals Shortest path counting in probabilistic biological networks

2018 ◽  
Vol 19 (1) ◽  
Author(s):  
Yuanfang Ren ◽  
Ahmet Ay ◽  
Tamer Kahveci
Keyword(s):  
Shortest Path ◽  
Biological Networks ◽  
Path Counting
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