Free Access
Issue
RAIRO-Oper. Res.
Volume 54, Number 3, May-June 2020
Page(s) 675 - 691
DOI https://doi.org/10.1051/ro/2019020
Published online 10 March 2020
  • A.S. Alfa, A discrete MAP/PH/1 queue with vacations and exhaustive time-limited Service. Oper. Res. Lett. 18 (1995) 31–44. [CrossRef] [Google Scholar]
  • A.S. Alfa, Discrete time analysis of MAP/PH/1 vacation queue with gated time service. Queueing. Syst. 29 (1998) 35–54. [Google Scholar]
  • A.S. Alfa, Some decomposition results for a class of vacation queue. Oper. Res. Lett. 42 (2014) 140–144. [CrossRef] [Google Scholar]
  • N. Akar, N.C. Oğuz and K. Sohraby, A novel computational method for solving finite QBD processes. Stoch. Models. 16 (2000) 273–311. [CrossRef] [Google Scholar]
  • J.R. Artalejo, A. Gómez-Corral and Q.M. He, Markovian arrivals in stochastic modelling: a survey and some new results. Sort 34 (2000) 101–156. [Google Scholar]
  • Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations. Oper. Res. Lett. 33 (2005) 654–681. [CrossRef] [MathSciNet] [Google Scholar]
  • R.H. Bartel and G.W. Stewart, Solution of the equation AX+XB=C. Commun. ACM. 15 (1972) 820–826. [Google Scholar]
  • H. Bruneel and B.G. Kim, Discrete-Time Models for Communication Systems Including ATM. Kluwer Academic Publishers, Boston (1993). [CrossRef] [Google Scholar]
  • S.R. Chakravarthy, Markovian Arrival Processes. Wiley Encyclopedia of Operations Research and Management Science (2010). [Google Scholar]
  • S. Chakravarthy, Analysis of the MAP/PH/1/K queue with service control. Appl. Stochastic. Models. Data. Anal. 12 (1996) 179–191. [CrossRef] [Google Scholar]
  • S. Chakravarthy and S. Ozkar, MAP/PH/1 queueing model with working vacation and crowdsourcing. Math. Appl. 44 (2016) 263–294. [Google Scholar]
  • V. Chandrasekaran, K. Indhira, M. Saravanarajan and P. Rajadurai, A survey on working vacation queueing models. Int. J. Pure Appl. Math. 106 (2016) 33–41. [Google Scholar]
  • B.T. Doshi, Queueing systems with vacations—A survey. Queueing. Syst. 1 (1986) 29–66. [Google Scholar]
  • A.N. Dudin, A.V. Kazimirsky, V.I. Klimenok, L. Breuer and U. Krieger, The queueing model MAP/PH/1//N with feedback operating in a Markovian random environment. Aust. J. Stat. 34 (2005) 101–110. [Google Scholar]
  • H.R. Gail, S.L. Hantler and B.A. Taylor, Solutions of the basic matrix equation for M/G/1 and G/M/1 type Markov chain. Stoch. Models. 10 (1994) 1–43. [CrossRef] [Google Scholar]
  • S. Gao, J. Wang and W. Li, An M/G/1 retrial queue with general retrial times, working vacations and vacation interruption. Asia-Pac. J. Oper. Res. 31 (2014) 6–31. [Google Scholar]
  • A. Graham, Kronecker Products and Matrix Calculus: With Applications. John-Wiley, New York (1981). [Google Scholar]
  • A. Heindl, M. Telek, Output models of MAP/PH/1(/K) queues for an efficient network decomposition. Perform. Eval. 49 (2002) 321–339. [CrossRef] [Google Scholar]
  • J.D. Kim, D.W. Choi and K.C. Chae, Analysis of queue-length distribution of the M/G/1 queue with Working Vacation. Hawaii Int. Conf. Stat. Related Fields 2003 (2003) 1191–1200. [Google Scholar]
  • C. Kim, S. Dudin and V. Klimenok, The MAP/PH/1/N queue with flows of customers as a model for traffic control in telecommunication networks. Perform. Eval. 66 (2009) 564–579. [CrossRef] [Google Scholar]
  • G. Latouche and G. Ramaswami, In: Vol. 5 of ASA-SIAM Series on Statistics and Applied Probability. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1999). [Google Scholar]
  • J. Li and N. Tian, Performance analysis of a G/M/1 Queue with single working vacation. Appl. Math. Comput. 217 (2009) 4960–4971. [Google Scholar]
  • J. Li, N. Tian and W. Liu, Discrete-time GI/Geom/1 queue with multiple working vacations. Queueing. Syst. 56 (2007) 53–63. [Google Scholar]
  • J. Li, N. Tian, Z.G. Zhang and H.P. Luh, Analysis of the M/G/1 Queue with exponentially working vacations—a matrix analytic approach. Queueing. Syst. 61 (2011) 139–166. [Google Scholar]
  • D.M. Lucantoni, New results on the single server queue with a batch Markovian arrival process. Stoch. Models. 7 (1991) 1–46. [CrossRef] [Google Scholar]
  • C. Luo, W. Li, K. Yu and C. Ding, The matrix-form solution for GeoX/G/1/N working vacation queue and its application to state-dependent cost control. Comput. Oper. Res. 67 (2016) 63–74. [Google Scholar]
  • M.F. Neuts, Probability distributions of phase type. In: Liber Amicorum Prof. Emeritus H. Florin, University of Louvain, Belgium, 1975, 173–206. [Google Scholar]
  • M.F. Neuts, A versatile Markovian point process. J. Appl. Probab. 16 (1979) 764–779. [Google Scholar]
  • M.F. Neuts, Matrix-geometric Solution in Stochastic Model. Johns Hopkins University Press, Baltimore, MD (1981). [Google Scholar]
  • M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications. Marcel Dekker, NY (1989). [Google Scholar]
  • M.F. Neuts, Models based on the Markovian arrival process. IEICE. T. Commun. E75B (1992) 1255–1265. [Google Scholar]
  • L.D. Servi and S.G. Finn, M/M/1 queues with working vacation (M/M/1/WV). Perform. Eval. 50 (2002) 41–52. [CrossRef] [Google Scholar]
  • N. Tian and Z.G. Zhang, Vacation Queueing Models-Theory and Application. Springer-Verlag, New York (2006). [CrossRef] [Google Scholar]
  • N. Tian, Z. Ma and M. Liu, The discrete time Geom/Geom/1 queue with multiple working vacations. Appl. Math. Model. 32 (2007) 2941–2953. [Google Scholar]
  • N. Tian, J. Li and Z.G. Zhang, Matrix-analytic method and working vacation queues-survey. Int. J. Inform. Manage. Sci. 20 (2009) 603–633. [Google Scholar]
  • D. Wu and H. Takagi, M/G/1 queue with multiple working vacations. Perform. Eval. 63 (2006) 654–681. [CrossRef] [Google Scholar]
  • D. Yang and D. Wu, Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns. Comput. Ind. Eng. 82 (2015) 151–158. [Google Scholar]

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