Product Form Approximations for Communicating Markov Processes

2008 ◽  
Author(s):  
Peter Buchholz
Keyword(s):  
Markov Processes ◽  
Product Form

Online Network Optimization Using Product-Form Markov Processes

2016 ◽  
Vol 61 (7) ◽  
pp. 1838-1853 ◽  
Author(s):  
Jaron Sanders ◽  
Sem C. Borst ◽  
Johan S. H. van Leeuwaarden
Keyword(s):  
Markov Processes ◽  
Network Optimization ◽  
Product Form

scholarly journals Product-Form Solutions for a Class of Structured Multidimensional Markov Processes

2014 ◽  
Vol 74 (3) ◽  
pp. 844-863 ◽  
Author(s):  
Jori Selen ◽  
Ivo J.B.F. Adan ◽  
Johan S.H. van Leeuwaarden
Keyword(s):  
Markov Processes ◽  
Product Form

Connecting reversible Markov processes

1986 ◽  
Vol 18 (4) ◽  
pp. 880-900 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Random Walks ◽  
Markov Processes ◽  
Product Form ◽  
Migration Process ◽  
Reversible Markov Processes

We provide a framework for interconnecting a collection of reversible Markov processes in such a way that the resulting process has a product-form invariant measure with respect to which the process is reversible. A number of examples are discussed including Kingman&s reversible migration process, interconnected random walks and stratified clustering processes.

Connecting internally balanced quasi-reversible Markov processes

1992 ◽  
Vol 24 (04) ◽  
pp. 934-959 ◽  
Author(s):  
W. Henderson ◽  
C. E. M. Pearce ◽  
P. K. Pollett ◽  
P. G. Taylor
Keyword(s):  
Invariant Measure ◽  
Markov Processes ◽  
General Framework ◽  
Feedback Mechanism ◽  
Product Form ◽  
Reversible Markov Processes ◽  
The Individual ◽  
Internal Balance ◽  
Feedback Queues ◽  
Individual Nodes

We provide a general framework for interconnecting a collection of quasi-reversible nodes in such a way that the resulting process exhibits a product-form invariant measure. The individual nodes can be quite general, although some degree of internal balance will be assumed. Any of the nodes may possess a feedback mechanism. Indeed, we pay particular attention to a class of feedback queues, characterized by the fact that their state description allows one to maintain a record of the order in which events occur. We also examine in some detail the problem of determining for which values of the arrival rates a node does exhibit quasi-reversibility.

Connecting reversible Markov processes

1986 ◽  
Vol 18 (04) ◽  
pp. 880-900 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Random Walks ◽  
Markov Processes ◽  
Product Form ◽  
Migration Process ◽  
Reversible Markov Processes

We provide a framework for interconnecting a collection of reversible Markov processes in such a way that the resulting process has a product-form invariant measure with respect to which the process is reversible. A number of examples are discussed including Kingman&s reversible migration process, interconnected random walks and stratified clustering processes.

Connecting internally balanced quasi-reversible Markov processes

1992 ◽  
Vol 24 (4) ◽  
pp. 934-959 ◽  
Author(s):  
W. Henderson ◽  
C. E. M. Pearce ◽  
P. K. Pollett ◽  
P. G. Taylor
Keyword(s):  
Invariant Measure ◽  
Markov Processes ◽  
General Framework ◽  
Feedback Mechanism ◽  
Product Form ◽  
Reversible Markov Processes ◽  
The Individual ◽  
Internal Balance ◽  
Feedback Queues ◽  
Individual Nodes

We provide a general framework for interconnecting a collection of quasi-reversible nodes in such a way that the resulting process exhibits a product-form invariant measure. The individual nodes can be quite general, although some degree of internal balance will be assumed. Any of the nodes may possess a feedback mechanism. Indeed, we pay particular attention to a class of feedback queues, characterized by the fact that their state description allows one to maintain a record of the order in which events occur. We also examine in some detail the problem of determining for which values of the arrival rates a node does exhibit quasi-reversibility.

Replacement of train wheels: an application of dynamic reversal of a Markov process

1994 ◽  
Vol 31 (01) ◽  
pp. 1-8
Author(s):  
David Gates ◽  
Mark Westcott
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Time Reversal ◽  
Equilibrium Distribution ◽  
Natural Extension ◽  
Product Form ◽  
Simple Derivation ◽  
Original Process ◽  
Population Process ◽  
Ordinary Time

A problem of regrinding and recycling worn train wheels leads to a Markov population process with distinctive properties, including a product-form equilibrium distribution. A convenient framework for analyzing this process is via the notion of dynamic reversal, a natural extension of ordinary (time) reversal. The dynamically reversed process is of the same type as the original process, which allows a simple derivation of some important properties. The process seems not to belong to any class of Markov processes for which stationary distributions are known.

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