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References
Karlin, H., Taylor, S.J.: A First Course in Stochastic Processes. New York: Academic Press 1975
Kingman, J.F.C.: On Queues in Heavy Traffic. J. Roy. Statist. Soc., ser. B, 24, 383–392 (1962)
Kingman, J.F.C.: The Heavy Traffic Approximation in the Theory of Queues. Proc. Sympos. Congestion Theory. Chapel Hill: University of North Carolina Press, pp. 137–169, 1965
Komlos, J., Major, P., Tusnady, G.: An approximation of partial sums of independent random variables and the sample DF. II. Z. Wahrscheinlichkeitstheorie verw. Gebiete 34, 33–58 (1976)
Prohorov, Y.: Convergence of random Processes and limit theorems in Probability. Theor. Probability Appl. 1, 157–214 (1956)
Rosenkrantz, W.: On rates of convergence for the invariance principle. Trans. Amer. Math. Soc. 129, 542–552 (1967)
Rosenkrantz, W.: A rate of convergence for the Von Mises Statistic. Trans. Amer. Math. Soc. 139, 329–337 (1969)
Shepp, L.: Radon-Nikodym Derivatives of Gaussian Measures. Ann. Math. Statist. 37, 321–354 (1966)
Major, P.: The Approximation of Partial Sums of Independent RV's. Z. Wahrscheinlichkeitstheorie verw. Gebiete 35, 213–220 (1976)
Csörgö, S.: (Private communication, 5/24/79).
Dudley, R.M.: Speeds of Metric Probability Convergence. Z. Wahrscheinlichkeitstheorie 22, 323–332 (1972)
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This research was supported by the Air Force office of scientific research contract F 49620-79-C-0209
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Rosenkrantz, W.A. On the accuracy of Kingman's heavy traffic approximation in the theory of queues. Z. Wahrscheinlichkeitstheorie verw Gebiete 51, 115–121 (1980). https://doi.org/10.1007/BF00533822
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DOI: https://doi.org/10.1007/BF00533822