Analysis of a Multiserver Queue with Setup Times
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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.
Keywordsqueueing performance multiserver queue setup times continuous time Markov chain difference equations matrix geometric solutions numerical inversion
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- I. Adan and J. van der Wal, Difference and Differential Equations in Stochastic Operations Research (1998).Google Scholar
- 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).Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- S.N. Elaydi, An Introduction to Difference Equations, Mathematics. (Springer-Verlag, New York, 1999).Google Scholar
- 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.Google Scholar
- Y. Levy and U. Yechiali, An M/M/s queue with servers' vacations, INFOR 14 (1976) 153–163.Google Scholar
- 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.Google Scholar
- 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).Google Scholar
- R.F. Serfozo, Extreme values of birth and death processes and queues, Stochastic Processes and their Applications 27 (1988) 291–306.Google Scholar
- 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.Google Scholar