TY - JOUR
T1 - Analysis of exponential reliable production lines using Kronecker descriptors
AU - Fernandes, P.
AU - Okelly, M. E J
AU - Papadopoulos, C. T.
AU - Sales, A.
N1 - Funding Information:
The order of authors is merely alphabetical. Paulo Fernandes is funded by CNPq Brazil (PQ 307284/2010-7). Afonso Sales receives grants from CAPES Brazil (PNPD 02388/09-0). Chrissoleon Papadopoulos for this research was co-financed by the European Union (European Social Fund -– ESF) and Greek national funds through the Operational Program ‘Education and Lifelong Learning’ of the National Strategic Reference Framework (NSRF) – Research Funding Program: THALES. Investing in knowledge society through the European Social Fund.
PY - 2013/7/1
Y1 - 2013/7/1
N2 - This paper presents a solution procedure for reliable production lines with service times distributed according to an exponential distribution, based on a Markovian formulation with a Kronecker structured representation (sum of tensor products). Specifically, structured Markovian formalisms are used to reduce the impact of the well-known state explosion problem associated with other methods of solution. Such formalisms combined with the Kronecker representation deliver memory efficiency in storing very large models, i.e. models with more than states. The exact steady-state solutions of these models may be obtained using efficient existing software packages. The proposed solution procedure is illustrated with two detailed examples, and generalised with a model construction algorithm. The computed throughput for several examples of production lines with perfectly reliable machines, as well as the computational costs in terms of CPU time to solve them with PEPS2007 and GTAexpress software packages, are also presented. In effect the paper demonstrates the power of the use of the Kronecker descriptor analysis applied to the derivation of the exact solution of the particular class of production lines considered. The Kronecker descriptor methodology is well-known to analysts concerned with computer and communication systems.
AB - This paper presents a solution procedure for reliable production lines with service times distributed according to an exponential distribution, based on a Markovian formulation with a Kronecker structured representation (sum of tensor products). Specifically, structured Markovian formalisms are used to reduce the impact of the well-known state explosion problem associated with other methods of solution. Such formalisms combined with the Kronecker representation deliver memory efficiency in storing very large models, i.e. models with more than states. The exact steady-state solutions of these models may be obtained using efficient existing software packages. The proposed solution procedure is illustrated with two detailed examples, and generalised with a model construction algorithm. The computed throughput for several examples of production lines with perfectly reliable machines, as well as the computational costs in terms of CPU time to solve them with PEPS2007 and GTAexpress software packages, are also presented. In effect the paper demonstrates the power of the use of the Kronecker descriptor analysis applied to the derivation of the exact solution of the particular class of production lines considered. The Kronecker descriptor methodology is well-known to analysts concerned with computer and communication systems.
KW - Markov modelling
KW - manufacturing systems engineering
KW - performance analysis
KW - production modelling
KW - queueing networks
KW - stochastic automata networks
KW - stochastic models
KW - tensor (Kronecker) algebra
KW - throughput
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U2 - 10.1080/00207543.2012.754550
DO - 10.1080/00207543.2012.754550
M3 - Article
AN - SCOPUS:84880572625
VL - 51
SP - 4240
EP - 4257
JO - International Journal of Production Research
JF - International Journal of Production Research
SN - 0020-7543
IS - 14
ER -