scholarly journals Product form solution for g-networks with dependent service

2004 ◽  
Vol 38 (2) ◽  
pp. 105-119 ◽  
Author(s):  
Pavel Bocharov ◽  
Ciro D'Apice ◽  
Evgeny Gavrilov ◽  
Alexandre Pechinkin
Keyword(s):  
Form Solution ◽  
Product Form

Matrix product-form solutions for Markov chains with a tree structure

1994 ◽  
Vol 26 (04) ◽  
pp. 965-987 ◽  
Author(s):  
Raymond W. Yeung ◽  
Bhaskar Sengupta
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Closed Form Solution ◽  
Steady State Solution ◽  
Form Solution ◽  
Product Form ◽  
Matrix Product ◽  
Preemptive Resume ◽  
Finite Set ◽  
Markov Modulated

We have two aims in this paper. First, we generalize the well-known theory of matrix-geometric methods of Neuts to more complicated Markov chains. Second, we use the theory to solve a last-come-first-served queue with a generalized preemptive resume (LCFS-GPR) discipline. The structure of the Markov chain considered in this paper is one in which one of the variables can take values in a countable set, which is arranged in the form of a tree. The other variable takes values from a finite set. Each node of the tree can branch out into d other nodes. The steady-state solution of this Markov chain has a matrix product-form, which can be expressed as a function of d matrices Rl,· ··, Rd. We then use this theory to solve a multiclass LCFS-GPR queue, in which the service times have PH-distributions and arrivals are according to the Markov modulated Poisson process. In this discipline, when a customer's service is preempted in phase j (due to a new arrival), the resumption of service at a later time could take place in a phase which depends on j. We also obtain a closed form solution for the stationary distribution of an LCFS-GPR queue when the arrivals are Poisson. This result generalizes the known result on a LCFS preemptive resume queue, which can be obtained from Kelly's symmetric queue.

On the product-form solution of a class of multiple-bus multiprocessor system models

1986 ◽  
Vol 6 (1-2) ◽  
pp. 117-124 ◽  
Author(s):  
Marco Ajmone Marsan ◽  
Gianfranco Balbo ◽  
Giovanni Chiola ◽  
Susanna Donatelli
Keyword(s):  
Form Solution ◽  
Product Form ◽  
Multiprocessor System ◽  
System Models

scholarly journals Product-Form Solution for Cascade Networks With Intermittent Energy

2019 ◽  
Vol 13 (1) ◽  
pp. 918-927 ◽  
Author(s):  
Yasin Murat Kadioglu ◽  
Erol Gelenbe
Keyword(s):  
Form Solution ◽  
Product Form
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