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Some remarks on a result of Blomqvist

Published online by Cambridge University Press:  14 July 2016

T. P. Speed
T. P. Speed*
Affiliation:
University of Sheffield
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Abstract

An alternative proof of a result of Blomqvist on the “heavy-traffic” problem for the two-barrier random walks using weak convergence methods is indicated.

Keywords

FINITE DAMDISCRETE TIMESTEADY STATEHEAVY TRAFFIC
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 1 , March 1973 , pp. 229 - 232
Copyright
Copyright © Applied Probability Trust 1973 

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References

Billingsley, P. (1968) Convergence of Probability Measures. John Wiley, New York.Google Scholar
Blomqvist, N. (1973) A heavy traffic result for the finite dam. J. Appl. Prob. 10, 223–228.CrossRefGoogle Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Methuen, London.Google Scholar
Phatarfod, R. M., Speed, T. P. and Walker, A. M. (1971) A note on random walks. J . Appl. Prob. 8, 198–201.CrossRefGoogle Scholar
Pyke, R. (1969) Applications of almost surely convergent constructions of weakly convergent processes. In Probability and Information Theory. Lecture Notes in Mathematics, 89. Springer-Verlag, Berlin.Google Scholar
Speed, T. P. (1973) A note on random walks. II. J. Appl. Prob. 10, 218–222.CrossRefGoogle Scholar
Whitt, W. (1968) Weak convergence theorems for queues in heavy traffic. Technical Report No. 2. Department of Operations Research, Stanford University, Stanford, California.Google Scholar