Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-06T02:31:33.439Z Has data issue: false hasContentIssue false
  • English
  • Français

Queueing with alternating priorities, treated as random walk on the lattice in the plane

Published online by Cambridge University Press:  14 July 2016

Micha Yadin
Micha Yadin*
Affiliation:
Technion—Israel Institute of Technology and Kansas State University
Get access Rights & Permissions [Opens in a new window]

Extract

The queueing system with alternating priorities has been discussed recently in numerous articles (Maxwell [1], Avi Itzhak, Maxwell, Miller [2], Neuts, Yadin [3], and others). Consider a system which consists of several queueing units. Each unit is independent in the sense that it has its own waiting line which is generated by an independent Poisson stream of customers. However, all of the units are served by a single server who allocates his time between the units.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 1 , April 1970 , pp. 196 - 218
Copyright
Copyright © Applied Probability Trust 

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

[1] Maxwell, W. L. (1963) Investigation of Multi-Product, Single Machine Scheduling and Inventory Problem. Ph.D. Thesis, Cornell University, Ithaca, N.Y. Google Scholar
[2] Avi Itzhak, B., Maxwell, W. L. and Miller, L. W. (1965) Queueing with alternating priorities, Operat. Res. 13, 306–318.CrossRefGoogle Scholar
[3] Neuts, M. F. and Yadin, M. (1968) The transient behaviour of the queue with alternating priorities, with special reference to the waiting times. Mimeo Series No. 136, Dept. of Stat., Purdue Univ. Google Scholar
[4] Yadin, M. (1965) On a Random Walk in the Positive Orthant of the Plane and a Study of Queueing System with Alternating Priorities, D.Sc. Thesis, Technion, I.I.T., Haifa, Israel.Google Scholar
[5] Van Danzig, D. (1947) Sur la méthode des functions génératrices. Colloq. Internat. du C.N.R.S. 13, 29–45.Google Scholar
[6] Runnenberg, J. T. (1965) On the use of the method of collective marks in queueing theory. Proc. Symp. Congestion Theory. Univ. N. Carolina, Monograph series in Prob. and Stat. No. 2, 399–438.Google Scholar
[7] Feller, W. (1960) An Introduction to Probability Theory and its Applications, Vol. 1, 2nd. ed. John Wiley and Sons Inc., New York.Google Scholar
[8] Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. 2, John Wiley and Sons Inc., New York.Google Scholar
[9] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[10] Saaty, T. L. (1961) Elements of Queueing Theory. McGraw-Hill Inc., New York.Google Scholar