A new algorithm is given to find product-form solutions for the joint equilibrium probabilities in a class of synchronized Markov processes. This is based on, and proved by, multiple applications of the Reversed Compound Agent Theorem (RCAT) and can describe multi-way synchronizations (seen as chains of pairwise synchronizations) that occur in a prescribed order. The length of the sequence is unbounded but finite with probability 1. Several applications are given to illustrate the methodology, which include various modes of resets in queueing networks with negative customers. In particular, it is shown that there is a type of reset that can propagate further transitions in a chain actively. Furthermore, a number of completely new product-form models, for example, where the transitions in a chain are non-homogeneous, are given.

Product-Forms in Multi-Way Synchronizations

MARIN, Andrea
2014-01-01

Abstract

A new algorithm is given to find product-form solutions for the joint equilibrium probabilities in a class of synchronized Markov processes. This is based on, and proved by, multiple applications of the Reversed Compound Agent Theorem (RCAT) and can describe multi-way synchronizations (seen as chains of pairwise synchronizations) that occur in a prescribed order. The length of the sequence is unbounded but finite with probability 1. Several applications are given to illustrate the methodology, which include various modes of resets in queueing networks with negative customers. In particular, it is shown that there is a type of reset that can propagate further transitions in a chain actively. Furthermore, a number of completely new product-form models, for example, where the transitions in a chain are non-homogeneous, are given.
2014
57
File in questo prodotto:
File Dimensione Formato  
cj13.pdf

non disponibili

Tipologia: Documento in Post-print
Licenza: Accesso chiuso-personale
Dimensione 981.99 kB
Formato Adobe PDF
981.99 kB Adobe PDF   Visualizza/Apri

I documenti in ARCA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/39336
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 21
  • ???jsp.display-item.citation.isi??? 14
social impact