Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Queueing Systems
Published in: Queueing Systems 3-4/2016

01-10-2016

Optimality of the fastest available server policy

Authors: William P. Millhiser, Charu Sinha, Matthew J. Sobel

Published in: Queueing Systems | Issue 3-4/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We give sufficient conditions under which a policy that assigns customers to the Fastest Available Server, labeled FAS, is optimal among nonidling policies in queueing models with multiple independent Markov-modulated Poisson arrival processes and heterogeneous parallel exponential servers with server-dependent service rates. The criteria are to minimize the long-run average cost per unit time and the expected present value of the costs. We obtain results for loss and delay queueing models with finite- or infinite-capacity buffers under a first-come-first-served priority scheme. We analyze the robustness of the cost structure assumptions that are invoked in the proof of FAS optimality.
previous article Dominant poles and tail asymptotics in the critical Gaussian many-sources regime
next article On the non-Markovian multiclass queue under risk-sensitive cost

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Appendix
Available only for authorised users
Literature
1.
Ahn, H.-S., Lewis, M.E.: Flexible server allocation and customer routing policies for two parallel queues when service rates are not additive. Oper. Res. 61(2), 344–358 (2011)CrossRef
2.
Akşin, Z., Armony, M., Mehrotra, V.: The modern call center: a multi-disciplinary perspective on operations management research. Prod. Oper. Manag. 16(6), 665–688 (2007)
3.
Andradóttir, S., Ayhan, H., Down, D.G.: Queueing systems with synergistic servers. Oper. Res. 59(3), 772–780 (2011)CrossRef
4.
Armony, M.: Dynamic routing in large-scale service systems with heterogeneous servers. Queueing Syst. 51(3–4), 287–329 (2005)CrossRef
5.
Cooper, R.B., Palakurthi, S.: Heterogeneous-server loss systems with ordered entry: an anomaly. Oper. Res. Lett. 8(6), 347–349 (1989)CrossRef
6.
Cox, D.R., Smith, W.L.: Queues. Chapman and Hall, London (1961)
7.
Denardo, E.V.: Contraction mappings in the theory underlying dynamic programming. SIAM Rev. 9(2), 165–177 (1967)CrossRef
8.
Derman, C., Lieberman, G.J., Ross, S.M.: On the optimal assignment of servers and a repairman. J. Appl. Probab. 17(2), 577–581 (1980)CrossRef
9.
de Véricourt, F., Zhou, Y.P.: On the incomplete results for the heterogeneous server problem. Queueing Syst. 52(3), 189–191 (2006)CrossRef
10.
Green, L.: A multiple dispatch queueing model of police patrol operations. Manag. Sci. 30(6), 653–664 (1984)CrossRef
11.
Green, L.V., Kolesar, P.J.: The lagged PSA for estimating peak congestion in multiserver Markovian queueds with periodic arrival rates. Manag. Sci. 43(1), 80–87 (1997)CrossRef
12.
Harrison, J.M., López, M.J.: Heavy traffic resource pooling in parallel-server systems. Queueing Syst. 33(4), 339–368 (1999)CrossRef
13.
Heyman, D.P.: Numerical methods in queueing theory, Ch. 11. In: Rao, C., Shanbhag, D. (eds.) Handbook of Statistics, vol. 21 (Stochastic Processes: Modelling and Simulation), pp. 407–429. Elsevier, Amsterdam (2003)
14.
Heyman, D.P., Lucantoni, D.: Modeling multiple IP traffic streams with rate limits. IEEE/ACM Trans. Netw. 11(6), 948–958 (2003)CrossRef
15.
Heyman, D.P., Sobel, M.J.: Stochastic models in operations research, vol II. Stochastic Optimization. Dover, Garden City (2004)
16.
Hopp, W.J., VanOyen, M.P.: Agile workforce evaluation: a framework for cross-training and coordination. IIE Trans. 36(10), 919–940 (2004)CrossRef
17.
Jensen, A.: Markov chains as an aid in the study of Markov processes. Skandinavisk Aktuarietidskrift. 36, 87–91 (1953)
18.
Katehakis, M.N.: A note on the hypercube model. Oper. Res. Lett. 3(6), 319–322 (1985)CrossRef
19.
Koole, G.: Stochastic scheduling and dynamic programming. CWI Tract 113, CWI, Amsterdam (1992)
20.
Lin, W., Kumar, P.: Optimal control of a queueing system with two heterogeneous servers. IEEE Trans. Autom. Control. 29(8), 696–703 (1984)CrossRef
21.
Mandelbaum, A., Stolyar, A.L.: Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized \(c\mu \)-rule. Oper. Res. 52(6), 836–855 (2004)CrossRef
22.
Sennott, L.: Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley, New York (1999)
23.
Shanthikumar, J.G., Yao, D.D.: Comparing ordered-entry queues with heterogeneous servers. Queueing Syst. 2(3), 235–244 (1987)CrossRef
24.
Serfozo, R.: An equivalence between continuous and discrete time Markov decision processes. Oper. Res. 27(3), 616–620 (1979)CrossRef
25.
Seth, K.: Optimal service policies, just after idle periods, in two-server heterogeneous queuing systems. Oper. Res. 25(2), 356–360 (1977)CrossRef
26.
Sobel, M.J.: The optimality of full service policies. Oper. Res. 30(4), 636–649 (1982)CrossRef
27.
Sobel, M.J.: Throughput maximization in a loss queueing system with heterogeneous servers. J. Appl. Probab. 27(3), 693–700 (1990)CrossRef
28.
Williams, R.J.: On dynamic scheduling of a parallel server system with complete resource pooling. In: McDonald, D.R., Turner, S.R.E. (eds.) Analysis of Communication Networks: Call Centres, Traffic and Performance, pp. 49–71. American Mathematical Society, Providence, RI (2000)CrossRef
Metadata
Title
Optimality of the fastest available server policy
Authors
William P. Millhiser
Charu Sinha
Matthew J. Sobel
Publication date
01-10-2016
Publisher
Springer US
Published in
Queueing Systems / Issue 3-4/2016
Print ISSN: 0257-0130
Electronic ISSN: 1572-9443
DOI
https://doi.org/10.1007/s11134-016-9502-1

Other articles of this Issue 3-4/2016

Queueing Systems 3-4/2016 Go to the issue

OriginalPaper

Steady-state analysis of shortest expected delay routing

OriginalPaper

A functional central limit theorem for Markov additive arrival processes and its applications to queueing systems

OriginalPaper

Dominant poles and tail asymptotics in the critical Gaussian many-sources regime

OriginalPaper

Waiting times in classical priority queues via elementary lattice path counting

OriginalPaper

Dynamic control of a tandem system with abandonments

OriginalPaper

On the non-Markovian multiclass queue under risk-sensitive cost

Premium Partner

    Image Credits