Open Access
Issue |
RAIRO-Oper. Res.
Volume 58, Number 4, July-August 2024
|
|
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Page(s) | 2767 - 2782 | |
DOI | https://doi.org/10.1051/ro/2024107 | |
Published online | 02 July 2024 |
- J. Abate and W. Whitt, Transient behavior of the M/M/1 queue via Laplace transforms. Adv. Appl. Probab. 20 (1988) 145–178. [CrossRef] [MathSciNet] [Google Scholar]
- N. Akar and E. Arikan, A numerically efficient method for the MAP/D/1/K queue via rational approximations. Queueing syst. 22 (1996) 97–120. [CrossRef] [Google Scholar]
- R.O. Al-Seedy, A.A. El-Sherbiny, S.A. El-Shehawy and S.I. Ammar, Transient solution of the M/M/c queue with balking and reneging. Comput. Math. Appl. 57 (2009) 1280–1285. [CrossRef] [MathSciNet] [Google Scholar]
- G. Ayyappan and S. Shyamala, Time dependent solution of MX/G/1 queuing model with bernoulli vacation and balking. Int. J. Comput. Appl. 61 (2013). [Google Scholar]
- F.P. Barbhuiya and U.C. Gupta, A difference equation approach for analysing a batch service queue with the batch renewal arrival process. J. Differ. Equ. Appl. 25 (2019) 233–242. [CrossRef] [Google Scholar]
- F.P. Barbhuiya and U.C. Gupta, Analytical and computational aspects of the infinite buffer single server n policy queue with batch renewal input. Comput. Oper. Res. 118 (2020) 104916. [CrossRef] [MathSciNet] [Google Scholar]
- V.E. Benes, On queues with Poisson arrivals. Ann. Math. Stat. (1957) 670–677. [CrossRef] [Google Scholar]
- M.S. Bratiychuk and W. Kempa, Application of the superposition of renewal processes to the study of batch arrival queues. Queueing Syst. 44 (2003) 51–67. [CrossRef] [MathSciNet] [Google Scholar]
- M.S. Bratiychuk and W. Kempa, Explicit Formulae for the Queue Length Distribution of Batch Arrival Systems (2004). [Google Scholar]
- G. Brière and M.L. Chaudhry, Computational analysis of single-server bulk-arrival queues: GIX/M/1. Queueing Syst. 2 (1987) 173–185. [CrossRef] [Google Scholar]
- J.W. Brown and R.V. Churchill, Complex Variables and Applications. McGraw-Hill (2009). [Google Scholar]
- D.G. Champernowne, An elementary method of solution of the queueing problem with a single server and constant parameters. J. R. Stat. Soc. Ser. B 18 (1956) 125–128. [CrossRef] [Google Scholar]
- R.H. Chan, K.-C. Ma and W.-K. Ching, Boundary value methods for solving transient solutions of markovian queueing networks. Appl. Math. Comput. 172 (2006) 690–700. [MathSciNet] [Google Scholar]
- B.W. Conolly, A difference equation technique applied to the simple queue. J. R. Stat. Soc. Ser. B 20 (1958) 165–167. [CrossRef] [Google Scholar]
- S. Dharmaraja and R. Kumar, Transient solution of a Markovian queuing model with heterogeneous servers and catastrophes. Opsearch 52 (2015) 810–826. [CrossRef] [MathSciNet] [Google Scholar]
- G. Easton, M.L. Chaudhry and M.J.M. Posner, Some corrected results for the queue GIX/M/1. Eur. J. Oper. Res. 18 (1984) 131–132. [CrossRef] [Google Scholar]
- G. Easton, M.L. Chaudhry and M.J.M. Posner, Some numerical results for the queuing system GIX/M/1. Eur. J. Oper. Res. 18 (1984) 133–135. [CrossRef] [Google Scholar]
- S.N. Elaydi, An Introduction to Difference Equations. Springer, New York (2005). [Google Scholar]
- W.K. Grassmann, Transient solutions in Markovian queueing systems. Comput. Oper. Res. 4 (1977) 47–53. [CrossRef] [Google Scholar]
- U.C. Gupta, N. Kumar and F.P. Barbhuiya, A queueing system with batch renewal input and negative arrivals. Appl. Probab. Stoch. Proc. (2020) 143–157. [CrossRef] [Google Scholar]
- W.H. Kaczynski, L.M. Leemis and J.H. Drew, Transient queueing analysis. INFORMS J. Comput. 24 (2012) 10–28. [CrossRef] [MathSciNet] [Google Scholar]
- B.R.K. Kashyap and M.L. Chaudhry, An Introduction to Queueing Theory. Kingston, Ont.: A&A Publications (1988). [Google Scholar]
- W.D. Kelton, Transient exponential-Erlang queues and steady-state simulation. Commun. ACM 28 (1985) 741–749. [CrossRef] [Google Scholar]
- W.M. Kempa, A comprehensive study on the queue-size distribution in a finite-buffer system with a general independent input flow. Perform. Eval. 108 (2017) 1–15. [CrossRef] [Google Scholar]
- W.M. Kempa and M. Kobielnik, Transient solution for the queue-size distribution in a finite-buffer model with general independent input stream and single working vacation policy. Appl. Math. Model. 59 (2018) 614–628. [Google Scholar]
- A. Kuznetsov, On the convergence of the Gaver–Stehfest algorithm. SIAM J. Numer. Anal. 51 (2013) 2984–2998. [CrossRef] [MathSciNet] [Google Scholar]
- W. Ledermann and G.E.H. Reuter, Spectral theory for the differential equations of simple birth and death processes. Phil. Trans. R. Soc. London Ser. A Math. Phys. Sci. 246 (1954) 321–369. [Google Scholar]
- P. Leguesdron, J. Pellaumail, G. Rubino and B. Sericola, Transient analysis of the M/M/1 queue. Adv. Appl. Probab. 25 (1993) 702–713. [Google Scholar]
- P.R. Parthasarathy, A transient solution to an M/M/1 queue: a simple approach. Adv. Appl. Probab. 19 (1987) 997–998. [CrossRef] [MathSciNet] [Google Scholar]
- P.R. Parthasarathy and M. Sharafali, Transient solution to the many-server Poisson queue: A simple approach. J. Appl. Probab. 26 (1989) 584–594. [CrossRef] [MathSciNet] [Google Scholar]
- G. Rubino, Transient analysis of Markovian queueing systems: A survey with focus on closed forms and uniformization. Queueing Theory 2 Adv. Trends (2021) 269–307. [CrossRef] [Google Scholar]
- J.T. Runnenburg, Probabilistic Interpretation of Some Formulae in Queueing Theory. Stichting Mathematisch Centrum, Zuivere Wiskunde (1958). [Google Scholar]
- O.P. Sharma and U.C. Gupta, Transient behaviour of an M/M/1/N queue. Stoch. Process. Appl. 13 (1982) 327–331. [CrossRef] [Google Scholar]
- O.P. Sharma and B.D. Bunday, A simple formula for the transient state probabilities of an M/M/1/∞ queue. Optimization 40 (1997) 79–84. [CrossRef] [MathSciNet] [Google Scholar]
- O.P. Sharma and A.M.K. Tarabia, On the busy period of a multichannel Markovian queue. Stoch. Anal. Appl. 18 (2000) 859–869. [CrossRef] [Google Scholar]
- R. Sudhesh, A. Azhagappan and S. Dharmaraja, Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience. RAIRO:RO 51 (2017) 591–606. [CrossRef] [EDP Sciences] [Google Scholar]
- L. Takács, Investigation of waiting time problems by reduction to Markov processes. Acta Math. Hung. 6 (1955) 101–129. [CrossRef] [Google Scholar]
- L. Takács, Transient behavior of single-server queuing processes with recurrent input and exponentially distributed service times. Oper. Res. 8 (1960) 231–245. [CrossRef] [Google Scholar]
- H. Takagi and D.-A. Wu, Multiserver queue with semi-markovian batch arrivals. Comput. Commun. 27 (2004) 549–556. [CrossRef] [Google Scholar]
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