×

zbMATH — the first resource for mathematics

Stochastic theory of a fluid model of producers and consumers coupled by a buffer. (English) Zbl 0656.60079
The paper analyzes a fluid model which is of interest in manufacture and communications: m producing machines supply a buffer, n consuming machines feed from it. No attempt is made to preserve the identity of individual jobs. Each machine alternates between exponentially distributed random periods called “in service” and “failed” states. The producers and consumers have their own failure and repair rates and working capacities. If the buffer is either full or empty the machines are not utilized to capacity.
This system is considered during statistical equilibrium; the state distribution is obtained in the form of spectral expansion of solution of a system of differential equations. Some results are formulated for a more general fluid model, the reversible Markov drift processes, for which the corresponding eigenvalue problem is solved. To complete the spectral expansion, a system of linear equations is obtained from the boundary conditions. Some interesting features of computations are presented, too.
Reviewer: L.Lakatos

MSC:
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
PDF BibTeX XML Cite
Full Text: DOI