Abstract
This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length.
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References
I. Adan and J. van der Wal, Combining make to order and make to stock, OR Spektrum 20 (1998) 73–81.
I. Adan and J. van der Wal, Difference and Differential Equations in Stochastic Operations Research (1998).
J.R. Artalejo and A. Economou, Markovian controllable queueing systems with hysteretic policies: Analysis of the busy period and the waiting time distributions, Methodology and Computing in Applied Probability (to appear).
J.R. Artalejo and M.J. Lopez-Herrero, On the M/M/m queue with removable servers, in: Stochastic Point Processes, S.K. Srinivasan and A. Vijayakumar eds. (Narosa Publishing House, 2003) pp. 124–143.
D. Bertsimas, An exact FCFS waiting time analysis for a general class of G/G/s queueing systems, Queueing Systems 3 (1988) 305–320.
W. Bischof, Analysis of M/G/1-queues with setup times and vacations under six different service disciplines, Queueing Systems 39 (2001) 265–301.
A. Borthakur and G. Choudhury, A multiserver Poisson queue with a general startup time under N-Policy, Calcutta Statistical Association Bulletin 49 (1999) 199–213.
G. Choudhury, On a batch arrival Poisson queue with a random setup and vacation period, Computers and Operations Research 25 (1998) 1013–1026.
G. Choudhury, An MX/G/1 queueing system with a setup period and a vacation period, Queueing Systems 36 (2000) 23–38.
S.N. Elaydi, An Introduction to Difference Equations, Mathematics. (Springer-Verlag, New York, 1999).
Q.M. He and E. Jewkes, Flow time in the MAP/G/1 queue with customer batching and setup times, Stochastic Models 11 (1995) 691–711.
G.V. Krishna Reddy, R. Nadarajan, and R. Arumuganathan, Analysis of a bulk queue with N-policy multiple vacations and setup times, Computers and Operations Research 25 (1998) 957–967.
Y. Levy and U. Yechiali, An M/M/s queue with servers' vacations, INFOR 14 (1976) 153–163.
M.J. Lopez-Herrero and M.F. Neuts, The distribution of the maximum orbit size of an M/G/1 retrial queue during the busy period, in: Advances in Stochastic Modelling, eds. J.R. Artalejo and A. Krishnamoorthy (Notable Publications Inc., 2002) pp. 219–231.
M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (Johns Hopkins University Press, Baltimore, 1981, reprinted by Dover Publications, New York, 1994).
J. Resing and R. Rietman, The M/M/1 queue with gated random order of service, Statistica Neerlandica 58 (2004) 97–110.
R.F. Serfozo, Extreme values of birth and death processes and queues, Stochastic Processes and their Applications 27 (1988) 291–306.
N. Tian, Q.L. Li and J. Cao, Conditional stochastic decompositions in the M/M/c queue with server vacations, Stochastic Models 15 (1999) 367–377.
Z.G. Zhang and N. Tian, Analysis of queueing systems with synchronous single vacation for some servers, Queueing Systems 45 (2003) 161–175.
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AMS subject classification: 90B22, 60K25
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Artalejo, J.R., Economou, A. & Lopez-Herrero, M.J. Analysis of a Multiserver Queue with Setup Times. Queueing Syst 51, 53–76 (2005). https://doi.org/10.1007/s11134-005-1740-6
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DOI: https://doi.org/10.1007/s11134-005-1740-6