Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T18:45:41.287Z Has data issue: false hasContentIssue false
  • English
  • Français

The single-server queue with random service output

Published online by Cambridge University Press:  14 July 2016

O. J. Boxma
O. J. Boxma*
Affiliation:
Mathematical Institute, University of Utrecht
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper a problem arising in queueing and dam theory is studied. We shall consider a G/G*/1 queueing model, i.e., a G/G/1 queueing model of which the service process is a separable centered process with stationary independent increments. This is a generalisation of the well-known G/G/1 model with constant service rate.

Several results concerning the amount of work done by the server, the busy cycles etc., are derived, mainly using the well-known method of Pollaczek. Emphasis is laid on the similarities and dissimilarities between the results of the ‘classical’ G/G/1 model and the G/G*/1 model.

Keywords

QUEUEINGPROCESSES WITH STATIONARY INDEPENDENT INCREMENTSINFINITE DAMSPOLLACZEK INTEGRAL EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 763 - 778
Copyright
Copyright © Applied Probability Trust 1975 

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] Boxma, O. J. (1974) The single-server queue with varying service intensity. Master's Thesis, Delft University of Technology, Delft (In Dutch).Google Scholar
[2] Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
[3] Cohen, J. W. (1974) Regenerative processes and stationary distributions in queueing theory. Report, Mathematical Institute, Utrecht.Google Scholar
[4] Feller, W. (1966) An Introduction to Probability Theory and its Applications , Vol. II. Wiley, New York.Google Scholar
[5] Gani, J. and Pyke, R. (1960) The content of a dam as the supremum of an infinitely divisible process. J. Math. Mech. 9, 639–651.Google Scholar
[6] Grinstein, J. and Rubinovitch, M. (1974) Queues with random output — the case of Poisson arrivals. J. Appl. Prob. 11, 771–784.CrossRefGoogle Scholar
[7] Prabhu, N. U. and Rubinovitch, M. (1971) On a continuous time extension of Feller's lemma. Z. Wahrscheinlichkeitsth. 17, 220–226.Google Scholar
[8] Stidham, S. (1972) Regenerative processes in the theory of queues, with applications to the alternating-priority queue. Adv. Appl. Prob. 4, 542–577.CrossRefGoogle Scholar
[9] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.Google Scholar