Equilibrium joining strategies in the M n /G/1 queue with server breakdowns and repairs

Equilibrium joining strategies in the M n /G/1 queue with server breakdowns and repairs Oper Res Int J https://doi.org/10.1007/s12351-018-0407-0 ORIGINAL PAPER Equilibrium joining strategies in the M ∕G∕1 queue with server breakdowns and repairs 1,2 1 3 Sheng Zhu  · Jinting Wang  · Bin Liu Received: 11 October 2017 / Revised: 10 March 2018 / Accepted: 19 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract This paper considers an almost observable unreliable M ∕G∕1 queue- ing system in which the arriving customers can observe the queue length upon their arrivals but not the state of the server. The arrival rates are state-dependent and the server is subject to breakdowns when it works. The lifetime of the server and the repair time are independent, and they follow two different general distribu - tions. To obtain the steady-state queue length distribution, we present an auxiliary system called modified M ∕G∕1 queueing system. Comparing the unreliable system with the modified system, we derive the steady-state queue length distributions at the arrival instant of a tagged customer. Moreover, we study customers’ equilibrium joining strategies based on a nonlinear waiting cost function. These results provide managerial insights into strategic behaviors of customers. Keywords Queueing system · Nash equilibrium · Equilibrium strategies · Breakdowns · Repairs Mathematics Subject Classification Primary 60K25; Secondary 90B22 Supported by the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Operational Research Springer Journals

Equilibrium joining strategies in the M n /G/1 queue with server breakdowns and repairs

25 pages
Read Article

Loading next page...
 
/lp/springer_journal/equilibrium-joining-strategies-in-the-m-n-g-1-queue-with-server-dj6T7JTYkA
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Business and Management; Operations Research/Decision Theory; Operations Research, Management Science; Computational Intelligence
ISSN
1109-2858
eISSN
1866-1505
D.O.I.
10.1007/s12351-018-0407-0
Publisher site
See Article on Publisher Site

Abstract

Oper Res Int J https://doi.org/10.1007/s12351-018-0407-0 ORIGINAL PAPER Equilibrium joining strategies in the M ∕G∕1 queue with server breakdowns and repairs 1,2 1 3 Sheng Zhu  · Jinting Wang  · Bin Liu Received: 11 October 2017 / Revised: 10 March 2018 / Accepted: 19 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract This paper considers an almost observable unreliable M ∕G∕1 queue- ing system in which the arriving customers can observe the queue length upon their arrivals but not the state of the server. The arrival rates are state-dependent and the server is subject to breakdowns when it works. The lifetime of the server and the repair time are independent, and they follow two different general distribu - tions. To obtain the steady-state queue length distribution, we present an auxiliary system called modified M ∕G∕1 queueing system. Comparing the unreliable system with the modified system, we derive the steady-state queue length distributions at the arrival instant of a tagged customer. Moreover, we study customers’ equilibrium joining strategies based on a nonlinear waiting cost function. These results provide managerial insights into strategic behaviors of customers. Keywords Queueing system · Nash equilibrium · Equilibrium strategies · Breakdowns · Repairs Mathematics Subject Classification Primary 60K25; Secondary 90B22 Supported by the

Journal

Operational Research – Springer Journals

Published: May 29, 2018

References

  • Individual equilibrium dynamic routing in a multiple server retrial queue
    Anthony, C
  • A discrete-time queueing system with server breakdowns and changes in the repair times
    Atencia, I
  • A discrete-time Geo/G/1 retrial queue with server breakdowns
    Atencia, I; Moreno, P
  • An $$M^{[X]}/G/1$$ M [ X ] / G / 1 retrial queue with server breakdowns and constant rate of repeated attempts
    Atencia, I; Bouza, G; Moreno, P
  • Some queueing problems with the service station subject to breakdown
    Avi-Itzhak, B; Naor, P
  • Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes
    Boudali, O; Economou, A
  • Equilibrium customer strategies in a single server Markovian queue with setup times
    Burnetas, A; Economou, A
  • An $$M{/}G{/}1$$ M / G / 1 queue with two phases of service subject to the server breakdown and delayed repair
    Choudhury, G; Tadj, L
  • Equilibrium balking strategies in the observable single server queue with breakdowns and repairs
    Economou, A; Kanta, S
  • Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue
    Economou, A; Kanta, S
  • A probability approach for the analysis of the $$M_n/G/1$$ M n / G / 1 queue
    Economou, A; Manou, A
  • Optimal customer return rate for an $$M/M/1$$ M / M / 1 queueing system with retrials
    Elcan, A
  • An introduction to probability theory and its applications
    Feller, W
  • A primer in game theory
    Gibbons, R
  • A vacation queueing model with service breakdowns
    Gray, WJ; Wang, P; Scott, M
  • Strategic behavior and social optimization in Markovian vacation queues
    Guo, P; Hassin, R
  • Analysis and comparision of queues with different levels of delay information
    Guo, P; Zipkin, P
  • Nash equilibrium and subgame perfection in observable queues
    Hassin, R; Haviv, M
  • To queue or not to queue
    Hassin, R; Haviv, M
  • Working vacations queueing model with multiple types of server breakdowns
    Jain, M; Jain, A
  • A general bulk service queue with arrival rate dependent on server breakdowns
    Jayaraman, D; Nadarajan, R; Sitrarasu, MR
  • On $$M{/}G{/}1$$ M / G / 1 system under NT policies with breakdowns, startup and closedown
    Ke, JC
  • Batch arrival queues under vacation policies with server breakdowns and startup/closedown times
    Ke, JC
  • The conditional distribution of the residual service time in the $$M_n/G/1$$ M n / G / 1 queue
    Kerner, Y
  • Equilibrium joining probabilities for an $$M{/}G{/}1$$ M / G / 1 queue
    Kerner, Y
  • The $$M{/}G{/}1$$ M / G / 1 queue with disasters and working breakdowns
    Kim, BK; Lee, DH
  • Queues with interruptions: a survey
    Krishnamoorthy, A; Pramod, PK; Chakravarthy, SR
  • A game theoretic model for two types of customers competing for service
    Kulkarni, VG
  • Retrial queues with server subject to breakdowns and repairs
    Kulkarni, VG; Choi, BD
  • $$Geo/G/1$$ G e o / G / 1 queues with disasters and general repair times
    Lee, DH; Yang, Ws; Park, HM
  • A $$BMAP/G/1$$ B M A P / G / 1 retrial queue with a server subject to breakdowns and repairs
    Li, Q; Ying, Y; Zhao, YQ
  • On the discrete-time system with server breakdowns: computational algorithm and optimization algorithm
    Lin, CH; Ke, JC
  • The service encounter
    Maister, DH
  • A many server queue with server interruptions
    Mitrany, JL; Avi-Itzhak, B
  • The regulation of queue size by levying tolls
    Naor, P
  • Combining a maintenance center $$M/M/c/m$$ M / M / c / m queue into the economic production quantity model with stochastic machine breakdowns and repair
    Sabri-Laghaie, K; Mansouri, M; Motaghedi-Larijani, A; Jalali-Naini, G
  • Queueing with breakdown
    Thiruvenydan, K
  • System delay versus system content for discrete-time queueing systems subject to server interruptions
    Vinck, B; Bruneela, H
  • A single-server discrete-time retrial G-queue with server breakdowns and repairs
    Wang, J; Zhang, P
  • Equilibrium analysis of the observable queues with balking and delayed repairs
    Wang, J; Zhang, F
  • Strategic joining in $$M/M/1$$ M / M / 1 retrial queues
    Wang, J; Zhang, F
  • Reliability analysis of the retrial queue with server breakdowns and repairs
    Wang, J; Cao, J; Li, Q
  • Maximum entropy analysis of the $$M^{[x]}/M/1$$ M [ x ] / M / 1 queueing system with multiple vacations and server breakdowns
    Wang, KH; Chan, MC; Ke, JC
  • Optimal control of the $$N$$ N policy $$M{/}G{/}1$$ M / G / 1 queueing system with server breakdowns and general startup times
    Wang, KH; Wang, TY; Pearn, WL
  • Queuing with preemptive priorities or with breakdown
    White, H; Christie, L
  • On the optimal and equilibrium retrial rates in an unreliable retrial queue with vacations
    Zhang, F; Wang, J; Liu, B

You’re reading a free preview. Subscribe to read the entire article.

Try 2 weeks free now

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

or browse the journals available

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off

Sign up
for free
Start 14 day
Free Trial