Probabilistic models of computer systems
Tóm tắt
In this paper we examine certain problems related to the use of diffusion approximations for the approximate modelling of computer systems. In particular we develop a model which allows us to handle waiting times and batch arrivals: these results are a new approach to the use of diffusion approximations. We also examine the effect of the distribution of holding times at boundaries: this question had remained open in earlier studies. We show that the stationary distributions associated with these diffusion models depend only on the average residence time of the process on the boundaries and not on the complete distribution function. This result justifies the use of exponential holding times as had been done in an earlier study.
Tài liệu tham khảo
Gaver, D.P.: Diffusion approximations and models for certain congestion problems, J. Appl. Prob. 5, 607–623 (1968)
Newell, G.F.: Applications of queueing theory, London: Chapman and Hall 1971
Gaver, D.P., Shedler, G.S.: Processor utilization in multiprogramming systems via diffusion approximations, Operations Research 21, 569–576 (1963)
Kobayashi, H.: Application of the diffusion approximation to queueing networks: Part I — Equilibrium queue distributions, JACM 21, 2, 316–328 (1974)
Reiser, H., Kobayashi, H.: Accuracy of a diffusion approximation for some queueing networks, IBM J. Res. Dev. 18, 110–124 (1974)
Gelenbe, E.: On approximate computer system models, JACM 22, 261–269 (1975)
Feller, W.: Diffusion processes in one dimension, Trans. Am. Math. Soc., 77, 1–31 (1954)
Cox, D.R.: A use of complex probabilities in the theory of stochastic processes, Proc. Cambridge Philosophical Society, 51, 313–319 (1955)
Gelenbe, E., Muntz, R.R.: Probabilistic models of computer systems Part I (Exact results), Acta Informatica. 7, 35–60 (1976)
Gelenbe, E.: A diffusion model for drum input-output operations with general interarrivai distribution, unpublished note
Cox, D.R.: Renewal Theory, Methuen and Co Ltd., Science Paperbacks (Methuen's Monographs on Applied Probability and Statistics), 1970