Abstract
The aim of the present paper is to treat the inhomogeneous machine interference model by the Markov Renewal Theory. This approach enables one to find the steady-state characteristics of the model without getting involved in analytical questions like smoothness of stationary distribution (cf. theorem 2.1. in [1]). The formulae (2.2) for expected sojourn times in a subset of state space allows an elegant treatment of expected waiting times and busy period length.
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References
Sztrik, J., Tomkó, J. (1982). Multiprogramozás inhomogén programokkal. Alk. Matematikai Lapok, 8, 285–296.
Takács, L. (1962). Introduction to the Theory of Queues. Oxford University Press.
Tomkó, J. (1986). Renewal method in the Theory of Semi-Markov Processes on arbitrary spaces. To appear in the Proc. of the fourth Vilnius Conf. on Probab. and Math. Stat. VNU Science Press, Netherlands.
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© 1986 Springer-Verlag
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Tomkó, J. (1986). Semi-Markov analysis of the inhomogeneous machine interference model. In: Prékopa, A., Szelezsáan, J., Strazicky, B. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043928
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DOI: https://doi.org/10.1007/BFb0043928
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