Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T06:46:51.995Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffusion limits for congestion models

Published online by Cambridge University Press:  14 July 2016

Donald R. Mcneil
Donald R. Mcneil*
Affiliation:
Princeton University
Get access Rights & Permissions [Opens in a new window]

Abstract

Heuristic methods yield simple limiting results for the behaviour of input-output systems under conditions of heavy traffic. It is assumed that the input is time-dependent, while the output rate depends entirely on the content of the system. It is shown that the content, when suitably normalized and scaled, behaves like a (non-stationary) Ornstein-Uhlenbeck process.

Keywords

HEAVY TRAFFICASYMPTOTICDIFFUSION PROCESSCONGESTION MODEL
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 368 - 376
Copyright
Copyright © Applied Probability Trust 1973 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ashton, W. D. (1966) The Theory of Road Traffic Flow. Methuen, London.Google Scholar
Cox, D. R. and Miller, H. D. (1965) The Theory of Stochastic Processes. Wiley, New York.Google Scholar
Clarke, A. B. (1956) A waiting time process of Markov type. Ann. Math. Statist. 27, 452–459.Google Scholar
Hasofer, A. M. (1964) On the single-server queue with non-homogeneous Poisson input and general service time. J. Appl. Prob. 1, 369–384.Google Scholar
Kendall, D. G. (1948) On the generalized “Birth and Death” process. Ann. Math. Statist. 19, 1–15.Google Scholar
Kingman, J. F. C. (1962) On queues in heavy traffic. J. R. Statist. Soc. B 24, 383–392.Google Scholar
Iglehart, D. L. (1965) Limiting diffusion approximations for the many server queue and the repairman problem. J. Appl. Prob. 2, 429–441.Google Scholar
Newell, G. F. (1968) Queues with time-dependent arrival rates. I, II and III. J. Appl. Prob. 5, 439–451, 579–590, 591–606.Google Scholar