[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
article

Approximations for the waiting-time distribution in an $$M/PH/c$$M/PH/c priority queue

Published: 01 March 2015 Publication History

Abstract

We investigate the use of priority mechanisms when assigning service engineers to customers as a tool for service differentiation. To this end, we analyze a non-preemptive $$M/PH/c$$M/PH/c priority queue with various customer classes. For this queue, we present various accurate and fast methods to estimate the first two moments of the waiting time per class given that all servers are occupied. These waiting time moments allow us to approximate the overall waiting time distribution per class. We subsequently apply these methods to real-life data in a case study.

References

[1]
Al Hanbali A (2011) Busy period analysis of the level dependent PH/PH/1/K queue. Queueing Syst 67(3):221-249.
[2]
Al Hanbali A, de Haan R, Boucherie R, van Ommeren J-K (2012) Time-limited polling systems with batch arrivals and phase-type service times. Ann Oper Res 198(1):57-82.
[3]
Al Hanbali A, Alvarez EM, van der Heijden MC (2013) Approximations for the waiting time distribution in an M/G/c priority queue. Beta Working Paper, 411. http://beta.ieis.tue.nl/node/2084.
[4]
Altinkemer K, Bose I, Pal R (1998) Average waiting time of customers in an M/D/k queue with nonpreemptive priorities. Comput Oper Res 25(4):317-328.
[5]
Bertsimas D, Nakazato D (1995) The distributional Little's lawand its applications.OperRes 43(2):298-310.
[6]
Buzen J, Bondi A (1983) Response times of priority classes under preemptive resume in M/M/m queues. Oper Res 31(3):456-465.
[7]
Cohen JW (1969) The single server queue, Section III. 3.8(i). North-Holland, Amsterdam.
[8]
Cohen M, Agrawal N, Agrawal V (2006) Winning the aftermarket. Harv Bus Rev 84(5):129-138.
[9]
Harchol-Balter M, Osogami T, Scheller-Wolf A, Wierman A (2005) Multi-server queueing systems with multiple priority classes. Queueing Syst 51(3):331-360.
[10]
Jagerman DL, Melamed B (2003) Models and approximations for call center design. Methodol Comput Appl Probab 5(2):159-181.
[11]
Janssen A, Van Leeuwaarden J (2008) Back to the roots of the M/D/s queue and the works of erlang, crommelin and pollaczek. Statistica Neerlandica 62(3):299-313.
[12]
Jardine AKS, Tsang AHC (2006) Maintenance, replacement, and reliability: theory and applications. CRC Press, Boca Raton.
[13]
Kella O, Yechiali U (1985) Waiting times in the non-preemptive priority M/M/c queue. Stoch Models 1(2):257-262.
[14]
Kimura T (1983) Diffusion approximation for an M/G/m queue. Oper Res 31(2):304-321 Law A (2007) Simulation modeling and analysis. McGraw-Hill, New York.
[15]
Marie R (1980) Calculating equilibrium probabilities for ¿(n)/ck/1/n queues. In: Proceedings of performance '80. Canada, Toronto, pp 117-125.
[16]
Munnik M (2011) Service level agreements at Océ development of a queuing model which can predict the waiting time of corrective maintenance jobs at the Planning Department. MSc Thesis, University of Twente.
[17]
Neuts M F (1981) Matrix-geometric solutions in stochastic models: an algorithmic approach. Johns Hopkins University Press, Baltimore.
[18]
Nojo S, Watanabe H (1987) A new stage method getting arbitrary coefficient of variation by two stages. IEICE Trans E 70(1):33-36.
[19]
Riordan J (1962) Stochastic service systems. Wiley, New York.
[20]
Sleptchenko A, van Harten A, van der Heijden MC (2005) An exact solution for the state probabilities of the multi-class, multi-server queue with preemptive priorities. Queueing Syst 50(1):81-108.
[21]
Tijms H (1988) A quick and practical approximation to the waiting time distribution in the multiserver queue with priorities. In: Iazeolla G et al (eds) Computer performance and reliability. North-Holland, Amsterdam, pp 161-169.
[22]
Tijms H (2003) A first course in stochastic models. Wiley, New York.
[23]
van der Heijden MC (1993) Performance analysis for reliability and inventory models. PhD thesis, Free University Amsterdam.
[24]
Wagner D (1997) Analysis of mean values of a multi-server model with non-preemptive priorities and non-renewal input. Stoch Models 13(1):67-84.
[25]
Williams T (1980) Nonpreemptive multi-server priority queues. J Oper Res Soc 31(2):1105-1107.
[26]
Whitt W (1992) Understanding the efficiency of multi-server service systems. Manag Sci 38(5):708-723.
[27]
Zeltyn S, Feldman Z, Wasserkrug S (2009) Waiting and sojourn times in a multi-server queue with mixed priorities. Queueing Syst 61(4):305-328

Cited By

View all
  • (2022)Medical QoS provisioning for multi-class data in coexisting wireless body area networksTelecommunications Systems10.1007/s11235-021-00857-z79:1(151-161)Online publication date: 1-Jan-2022
  • (2019)Multi-server preemptive priority queue with general arrivals and service timesPerformance Evaluation10.1016/j.peva.2017.08.003115:C(150-164)Online publication date: 1-Jan-2019

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image OR Spectrum
OR Spectrum  Volume 37, Issue 2
March 2015
250 pages

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 March 2015

Author Tags

  1. $$M/PH/c$$M/PH/c queue
  2. Priority queues
  3. Service differentiation
  4. Service-level agreements
  5. Waiting time moments

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 17 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2022)Medical QoS provisioning for multi-class data in coexisting wireless body area networksTelecommunications Systems10.1007/s11235-021-00857-z79:1(151-161)Online publication date: 1-Jan-2022
  • (2019)Multi-server preemptive priority queue with general arrivals and service timesPerformance Evaluation10.1016/j.peva.2017.08.003115:C(150-164)Online publication date: 1-Jan-2019

View Options

View options

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media