Abstract
We analyze a discrete-time, single-server queueing system in which the length of each service period is limited. The server takes a vacation when the limit expires or the queue empties, whichever occurs first. In the former case, the preempted service is resumed after the vacation without loss or creation of any work. This system models the transmission of message frames from a station on timed-token local-area networks (for example, FDDI and IEEE 802.4 token bus). We study the process of the unfinished work and the joint process of the queue size and the remaining service time. By using the technique of discrete Fourier transforms to determine some unknown functions in the governing equations, we numerically obtain exact mean waiting times.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ANSI Standard,FDDI Token Ring — Media Access Control (ANSI X3.139-1987, Nov. 5, 1986).
ANSI/IEEE Standard 802.4,Token-Passing Bus Access Method (IEEE Press, New York, 1985).
O.J. Boxma and W.P. Groenendijk, Waiting times in discrete time cyclic-service systems, IEEE Trans. Commun. COM-36 (1988) 164–170.
W. Bux, Token-ring local-area networks and their performance, Proc. IEEE 77 (1989) 238–256.
J. Chiarawongse, M.M. Srinivasan and T.J. Teorey, TheM/G/1 queueing system with vacations and timer-controlled service, IEEE Trans. Commun. COM-42 (1994) 1846–1855.
B.T. Doshi, Queueing systems with vacations — a survey, Queueing Syst. 1 (1986) 29–66.
R.O. LaMaire, AnM/G/1 vacation model of an FDDI station, IEEE J. Sel. Areas Commun. SAC-9 (1991) 257–264.
K.K. Leung, Cyclic-service systems with probabilistically-limited service, IEEE J. Sel. Areas Commun. SAC-9 (1991) 185–193.
K.K. Leung, An execution/sleep scheduling policy for serving an additional job in priority queueing systems, J. ACM 40 (1993) 394–417.
K.K. Leung and M. Eisenberg, A single-server queue with vacations and gated time-limited service, IEEE Trans. Commun. COM-38 (1990) 1454–1462.
K.K. Leung and M. Eisenberg, A single-server queue with vacations and non-gated time-limited service, Perf. Eval. 12 (1991) 115–125.
K.K. Leung and D.M. Lucantoni, Two vacation models for token-ring networks where service is controlled by timers, in:Performance '93, eds. G. Lazeolla and S.S. Lavenberg (Elsevier, Amsterdam, 1993) pp. 163–182.
A.V. Oppenheim and R. Schafer,Signal Processing (Prentice-Hall, Englewood Cliffs, New Jersey, 1975).
J.W. Pang and F.A. Tobagi, Throughput analysis of a timer controlled token passing protocol under heavy load, IEEE Trans. Commun. COM-37 (1989) 694–702.
K.C. Sevcik and M.J. Johnson, Cycle time properties of the FDDI token ring protocol, IEEE Trans. Software Eng. SE-13 (1987) 376–385.
H. Takagi,Analysis of Polling Systems (The MIT Press, Cambridge, MA, 1986).
H. Takagi, Queuing analysis of polling models, ACM Comp. Surveys 20 (1988) 5–28.
H. Takagi,Queueing Analysis: A Foundation of Performance Evaluation, Vol. 1:Vacation and Priority Systems, Part 1 (Elsevier, Amsterdam, 1991).
H. Takagi, Application of polling models to computer networks, Comp. Networks ISDN Syst. 22 (1991) 193–211.
H. Takagi,Queueing Analysis: A Foundation of Performance Evaluation, Vol. 3:Discrete-Time Systems (Elsevier, Amsterdam, 1993).
O.-C. Yue and C.A. Brooks, Performance of the timed token scheme in MAP, IEEE Trans. Commun. COM-38 (1990) 1006–1012.
Author information
Authors and Affiliations
Additional information
A part of the work of H. Takagi was done while he was with IBM Research, Tokyo Research Laboratory.
Rights and permissions
About this article
Cite this article
Takagi, H., Leung, K.K. Analysis of a discrete-time queueing system with time-limited service. Queueing Syst 18, 183–197 (1994). https://doi.org/10.1007/BF01158781
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01158781