Abstract
Priority queueing systems come natural when customers with diversified delay requirements have to wait to get service. The customers that cannot tolerate but small delays get service priority over customers which are less delay-sensitive. In this contribution, we analyze a discrete-time two-class preemptive repeat identical priority queue with infinite buffer space and generally distributed service times. Newly arriving high-priority customers interrupt the on-going service of a low-priority customer. After all high-priority customers have left the system, the interrupted service of the low-priority customer has to be repeated completely. By means of a probability generating functions approach, we analyze the system content and the delay of both types of customers. Performance measures (such as means and variances) are calculated and the impact of the priority scheduling is discussed by means of some numerical examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Walraevens, B. Steyaert and H. Bruneel. Analysis of a preemptive repeat priority buffer with resampling. In Proceedings of the International Network Optimization Conference (INOC 2003), pages 581–586, Evry, October 2003.
H. White and L. Christie. Queuing with preemptive priorities or with breakdown. Operations Research, 6(1)(1958) 79–95.
R. Miller. Priority queues. Annals of Mathematical Statistics, 31(1960) 86–103.
L. Kleinrock. Queueing systems volume II: Computer applications. John Wiley & Sons (1976).
U. Sumita and O. Sheng. Analysis of query processing in distributed database systems with fully replicated files: a hierarchical approach. Performance Evaluation, 8(3)(1988) 223–238.
C. Yoon and C. Un. Unslotted 1- and pi-persistent CSMA-CD protocols for fiber optic bus networks. IEEE Transactions on Communications, 42(2–4)(1994) 458–465.
A. Krinik, D. Marcus, R. Shiflett, and L. Chu. Transient probabilities of a single server priority queueing system. Journal of Statistical Planning and Inference, 101(1–2)(2002) 185–190.
H. Castel and G. Hebuterne. Performance analysis of an optical MAN ring for asynchronous variable length packets, pages 214–220. LNCS 3124 (Proceedings of ICT 2004). Springer Verlag, 2004.
S. Mukherjee, D. Saha, and S. Tripathi. A preemptive protocol for voice-data integration in ring-based LAN: performance analysis and comparison. Performance Evaluation, 11(3)(1995) 339–354.
D. Fiems, B. Steyaert, and H. Bruneel. Discrete-time queues with generally distributed service times and renewal-type server interruptions. Performance Evaluation, 55(3–4)(2004) 277–298.
D. Cox. The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables. Proceedings of the Cambridge Philosophical Society, 51(1955) 433–441.
J. Walraevens, B. Steyaert, and H. Bruneel. Performance analysis of a GI-G-1 preemptive resume priority buffer, pages 745–756. LNCS 2345 (Proceedings of the Networking 2002 Conference, Pisa). Springer Verlag, 2002.
H. Bruneel and B. Kim. Discrete-time models for communication systems including ATM. Kluwer Academic Publisher, Boston, (1993).
D. Fiems and H. Bruneel. A note on the discretization of Little’s result. Operations Research Letters, 30(1)(2002) 17–18.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Walraevens, J., Fiems, D. & Bruneel, H. The discrete-time preemptive repeat identical priority queue. Queueing Syst 53, 231–243 (2006). https://doi.org/10.1007/s11134-006-7770-x
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11134-006-7770-x