article

Preemptive Priority Queues

Author:

Wei ChangAuthors Info & Claims

Operations Research, Volume 13, Issue 5

Pages 820 - 827

https://doi.org/10.1287/opre.13.5.820

Published: 01 October 1965 Publication History

Abstract

Customers of different priorities arrive at a counter in accordance with a Poisson process. The customers are served by a single server in order of priority and for each priority in order of arrival. Preemptive discipline is assumed. Three service policies are considered: i preemptive-resume, ii preemptive-repeat-identical, and iii preemptive-repeat-different. The time-dependent solutions for these priority systems are very complicated. However, the problem can be simplified in case of stationary solutions. In this paper, a step-by-step method is proposed to find the stationary distributions of the queue sizes, the waiting times, and the busy periods of each priority class.

References

[1]

LAJOS TAKACS, "Priority Queues," Opns. Res. 12, 63-74 (1964).

Digital Library

Google Scholar

[2]

D. P. GAVER, JR., "A Waiting Line with Interrupted Service, Including Priorities," J. Roy. Stat. Doc. Ser. B, 24, 73-96 (1962).

Crossref

Google Scholar

[3]

A. COBHAM, "Priority Assignment in Waiting Lines," Opns. Res. 2, 70-76 (1954).

Google Scholar

[4]

D. P. GAVER, JR., "Imbedded Markov Chain Analysis of a Waiting-Line Process in Continuous Time," Ann Math Stat. 31, 86-103 (1959).

Google Scholar

[5]

H. KESTEN AND J. TH. RUNNENBERG, "Priority in Waiting-Line Problems," Proc. Akad. Wet. Amst. A 60, 161-200 (1957).

Google Scholar

[6]

R. G. MILLER, JR., "Priority Queues," Ann Math Stat. 31, 86-103 (1960).

Crossref

Google Scholar

[7]

P. M. MORSE, Queues, Inventories and Maintenance, Wiley, New York, 1958.

Google Scholar

[8]

F. F. STEPHAN, "TWO Queues under Preemptive Priority with Poisson Arrival and Service Rates," Opns. Res. 4, 213-220 (1956).

Digital Library

Google Scholar

[9]

H. WHITE AND L. CHRISTIE, "Queuing with Preemptive Priorities or with Breakdown," Opns. Res. 6, 79-95 (1958).

Digital Library

Google Scholar

[10]

B. AVI-ITZHAK AND P. NOAR, "Multi-Purpose Service Stations in Queuing Theory," Proc. Third IFORS Conf., Oslo, 1963.

Google Scholar

Cited By

View all

Raj RJain V(2023)Resource and traffic control optimization in MMAP[c]/PH[c]/S queueing system with PH retrial times and catastrophe phenomenonTelecommunications Systems10.1007/s11235-023-01053-x84:3(341-362)Online publication date: 2-Sep-2023
https://dl.acm.org/doi/10.1007/s11235-023-01053-x
Bouloukakis GGeorgantas NKattepur AIssarny VBinder WCortellessa VKoziolek ASmirni EPoess M(2017)Timeliness Evaluation of Intermittent Mobile Connectivity over Pub/Sub SystemsProceedings of the 8th ACM/SPEC on International Conference on Performance Engineering10.1145/3030207.3030220(275-286)Online publication date: 17-Apr-2017
https://dl.acm.org/doi/10.1145/3030207.3030220
Drekic S(2003)A preemptive resume queue with an expiry time for retained servicePerformance Evaluation10.1016/S0166-5316(02)00232-854:1(59-74)Online publication date: 1-Sep-2003
https://dl.acm.org/doi/10.1016/S0166-5316%2802%2900232-8
Show More Cited By

Recommendations

Priority Queues

Customers of different priorities are arriving at a counter in accordance with a Poisson process. The customers are served by a single server in order of priority and for each priority in order of arrival. Two cases are considered: i service with ...
(N,n)-preemptive priority queues

In this paper, we propose a new priority discipline, called the (N,n)-preemptive priority discipline. Under this discipline, the preemption of the service of a low-class customer is determined by two thresholds N and n of the queue length of high-class ...
From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times
Abstract
We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

Operations Research Volume 13, Issue 5

October 1965

204 pages

ISSN:0030-364X

Issue’s Table of Contents

Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 October 1965

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

10
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Raj RJain V(2023)Resource and traffic control optimization in MMAP[c]/PH[c]/S queueing system with PH retrial times and catastrophe phenomenonTelecommunications Systems10.1007/s11235-023-01053-x84:3(341-362)Online publication date: 2-Sep-2023
https://dl.acm.org/doi/10.1007/s11235-023-01053-x
Bouloukakis GGeorgantas NKattepur AIssarny VBinder WCortellessa VKoziolek ASmirni EPoess M(2017)Timeliness Evaluation of Intermittent Mobile Connectivity over Pub/Sub SystemsProceedings of the 8th ACM/SPEC on International Conference on Performance Engineering10.1145/3030207.3030220(275-286)Online publication date: 17-Apr-2017
https://dl.acm.org/doi/10.1145/3030207.3030220
Drekic S(2003)A preemptive resume queue with an expiry time for retained servicePerformance Evaluation10.1016/S0166-5316(02)00232-854:1(59-74)Online publication date: 1-Sep-2003
https://dl.acm.org/doi/10.1016/S0166-5316%2802%2900232-8
Stanford DDrekic S(2000)Interdeparture time distributions in ΣiMi/Gi/1 priority queuesQueueing Systems: Theory and Applications10.1023/A:101911880051636:1/3(1-21)Online publication date: 14-Nov-2000
https://dl.acm.org/doi/10.1023/A%3A1019118800516
Drekic SStanford D(2000)Threshold-based interventions to optimize performance in preemptive priority queuesQueueing Systems: Theory and Applications10.1023/A:101910653055835:1/4(289-315)Online publication date: 14-Jan-2000
https://dl.acm.org/doi/10.1023/A%3A1019106530558
Chang W(1975)Sequential server queues for computer communication system analysisIBM Journal of Research and Development10.1147/rd.195.047619:5(476-485)Online publication date: 1-Sep-1975
https://dl.acm.org/doi/10.1147/rd.195.0476
Chang W(1970)Single-server queuing processes in computing systemsIBM Systems Journal10.1147/sj.91.00369:1(36-71)Online publication date: 1-Mar-1970
https://dl.acm.org/doi/10.1147/sj.91.0036
Schrage L(1969)A Mixed-Priority Queue with Applications to the Analysis of Real-Time SystemsOperations Research10.1287/opre.17.4.72817:4(728-742)Online publication date: 1-Aug-1969
https://dl.acm.org/doi/10.1287/opre.17.4.728
Chang W(1969)Queuing Analysis of Real-Time Computer ProcessingManagement Science10.1287/mnsc.15.11.65815:11(658-671)Online publication date: 1-Jul-1969
https://dl.acm.org/doi/10.1287/mnsc.15.11.658
Jaiswal N Thiruvengadam K(1967)Finite-Source Priority QueuesSIAM Journal on Applied Mathematics10.1137/011511115:5(1278-1293)Online publication date: 1-Sep-1967
https://dl.acm.org/doi/10.1137/0115111

View Options

View options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Recommendations

Priority Queues

(N,n)-preemptive priority queues

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations