Analysis of a discrete-time queueing system with time-limited service

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.

[1]  Kin K. Leung,et al.  A single-server queue with vacations and gated time-limited service , 1990, IEEE Trans. Commun..

[2]  Marjory J. Johnson,et al.  Cycle Time Properties Of The FDDI Token Ring Protocol , 1987, IEEE Trans. Software Eng..

[3]  Mandyam M. Srinivasan,et al.  The M/G/1 queueing system with vacations and timer-controlled service , 1994, IEEE Trans. Commun..

[4]  Hideaki Takagi,et al.  Queuing analysis of polling models , 1988, CSUR.

[5]  Charles A. Brooks,et al.  Performance of the timed token scheme in MAP , 1990, IEEE Trans. Commun..

[6]  Fouad A. Tobagi,et al.  Throughput analysis of a timer controlled token passing protocol under heavy load , 1989, IEEE Trans. Commun..

[7]  Kin K. Leung,et al.  An execution/sleep scheduling policy for serving an additional job in priority queueing systems , 1993, JACM.

[8]  Richard O. LaMaire.  An M/G/1 Vacation Model of an FDDI Station , 1991, IEEE J. Sel. Areas Commun..

[9]  Marjory J. Johnson,et al.  Cycle Time Properties Of The FDDI Token Ring Protocol , 1986, IEEE Transactions on Software Engineering.

[10]  Kin K. Leung,et al.  Two Vacation Models for Token-Ring Networks where Service is Controlled by Timers , 1994, Perform. Evaluation.

[11]  Kin K. Leung,et al.  A Single-Server Queue with Vacations and Non-Gated Time-Limited Service , 1991, Perform. Evaluation.

[12]  Onno J. Boxma,et al.  Waiting times in discrete-time cyclic-service systems , 1988, IEEE Trans. Commun..

[13]  Hideaki Takagi,et al.  Analysis of polling systems , 1986 .

[14]  Hideaki Takagi,et al.  Queueing analysis: a foundation of performance evaluation , 1993 .

[15]  W. Bux.  Token-ring local-area networks and their performance , 1989 .

[16]  Hideaki Takagi,et al.  Application of Polling Models to Computer Networks , 1991, Comput. Networks ISDN Syst..

[17]  Yutaka Takahashi,et al.  Queueing analysis: A foundation of performance evaluation, volume 1: Vacation and priority systems, Part 1: by H. Takagi. Elsevier Science Publishers, Amsterdam, The Netherlands, April 1991. ISBN: 0-444-88910-8 , 1993 .

[18]  Kin K. Leung,et al.  Cyclic-Service Systems with Probabilistically-Limited Service , 1991, IEEE J. Sel. Areas Commun..

[19]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..