Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-23T09:54:12.422Z Has data issue: false hasContentIssue false
  • English
  • Français

Single-Server with Delay-Dependent Arrival Streams

Published online by Cambridge University Press:  27 July 2009

P. H. Brill
P. H. Brill
Affiliation:
University of Windor, Windsor, Ontario, Canada N9B 3P4
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper derives the steady-state distribution of the virtual wait in GI/M1 queues in which the interarrival times depend on the virtual wait. Applications are queues in which the time it will take for the system to start servicing a new arrival (virtual wait) affects the generation of new arrivals. Such queues arise in airport or large-city freeway traffic control systems. Related state-dependent situations occur in production-inventory systems, cash flow in banking or in insurance systems, dam control systems, and in natural sciences. The method of analysis is by means of system-point level crossing theory.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 2 , April 1988 , pp. 231 - 247
Copyright
Copyright © Cambridge University Press 1988

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

Brill, P.H. (1975). System-point theory in exponential queues. Ph.D. Dissertation. University of Toronto, Toronto, Canada.Google Scholar
Brill, P.H. (1979). An embedded level crossing technique for dams and queues. Journal of Applied Probability 16:174–186.Google Scholar
Bril, P.H. (1983). System-point Monte-Carlo simulation of stationary distributions of waiting times in single-server queues. University of Waterloo, Technical Report STAT-83−1 1.Google Scholar
Brill, P.H. (1987). System-point computation of distributions in queues, dams, and inventories. University of Windsor, Faculty of Business Administration, Working Paper No. W87−12 (1987). (submitted for publication).Google Scholar
Brill, P.H. (1987). Queues with delay-dependent arrival streams. University of Windsor, Faculty of Business Administration, Working Paper No. 87−16.Google Scholar
Brill, P.H. & Hornik, J. (1984). A system-point approach to nonuniform advertising insertions. Operations Research 32:7–22.CrossRefGoogle Scholar
Brill, P.H. & Posner, M.J.M. (1981). The system-point method in exponential queues: a level crossing approach. Mathematics of Operations Research 6(1):31–49.Google Scholar
Gross, D. & Harris, C.M. (1974). Fundamentals of Queuing Theory. New York: John Wiley & Sons.Google Scholar
Prabhu, N.U. (1965). Queues and Inventories, A Study of Their Basic Stochastic Processes. New York: Wiley & Sons.Google Scholar
Posner, M.J.M. (1973). Single-server queues with service time depending on waiting time. Operations Research 21:610–616.CrossRefGoogle Scholar
Ross, S.M. (1983). Stochastic Processes. New York: John Wiley & Sons.Google Scholar
Takacs, L. (1962). Introduction to the Theory of Queues. New York: Oxford University Press.Google Scholar
Tricomi, F.G. (1985). Integral Equations. New York: Dover Publications, Inc.Google Scholar