Gelenbe, Erol Probabilistic models of computer systems. II: Diffusion approximations, waiting times and batch arrivals. (English) Zbl 0419.60086 Acta Inf. 12, 283-303 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 Documents MSC: 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.) 60J60 Diffusion processes Keywords:diffusion approximations; waiting times and batch arrivals; exponential holding times Citations:Zbl 0343.60066 PDF BibTeX XML Cite \textit{E. Gelenbe}, Acta Inf. 12, 283--303 (1979; Zbl 0419.60086) Full Text: DOI References: [1] Gaver, D.P.: Diffusion approximations and models for certain congestion problems, J. Appl. Prob. 5, 607-623 (1968) · Zbl 0194.20801 [2] Newell, G.F.: Applications of queueing theory, London: Chapman and Hall 1971 · Zbl 0258.60004 [3] Gaver, D.P., Shedler, G.S.: Processor utilization in multiprogramming systems via diffusion approximations, Operations Research 21, 569-576 (1963) [4] Kobayashi, H.: Application of the diffusion approximation to queueing networks: Part I ? Equilibrium queue distributions, JACM 21, 2, 316-328 (1974) · Zbl 0278.60074 [5] Reiser, H., Kobayashi, H.: Accuracy of a diffusion approximation for some queueing networks, IBM J. Res. Dev. 18, 110-124 (1974) · Zbl 0275.68014 [6] Gelenbe, E.: On approximate computer system models, JACM 22, 261-269 (1975) · Zbl 0322.68035 [7] Feller, W.: Diffusion processes in one dimension, Trans. Am. Math. Soc., 77, 1-31 (1954) · Zbl 0059.11601 [8] Cox, D.R.: A use of complex probabilities in the theory of stochastic processes, Proc. Cambridge Philosophical Society, 51, 313-319 (1955) · Zbl 0066.37703 [9] Gelenbe, E., Muntz, R.R.: Probabilistic models of computer systems Part I (Exact results), Acta Informatica. 7, 35-60 (1976) · Zbl 0343.60066 [10] Gelenbe, E.: A diffusion model for drum input-output operations with general interarrivai distribution, unpublished note [11] Cox, D.R.: Renewal Theory, Methuen and Co Ltd., Science Paperbacks (Methuen’s Monographs on Applied Probability and Statistics), 1970 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.