Analysis of a Multiserver Queue with Setup Times
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- I. Adan and J. van der Wal, Combining make to order and make to stock, OR Spektrum 20 (1998) 73–81. CrossRef
- 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. CrossRef
- W. Bischof, Analysis of M/G/1-queues with setup times and vacations under six different service disciplines, Queueing Systems 39 (2001) 265–301. CrossRef
- 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. CrossRef
- G. Choudhury, An M X /G/1 queueing system with a setup period and a vacation period, Queueing Systems 36 (2000) 23–38. CrossRef
- 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. CrossRef
- 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. CrossRef
- 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. CrossRef
- Analysis of a Multiserver Queue with Setup Times
Volume 51, Issue 1-2 , pp 53-76
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- queueing performance
- multiserver queue
- setup times
- continuous time Markov chain
- difference equations
- matrix geometric solutions
- numerical inversion
- Industry Sectors
- Author Affiliations
- 1. Department of Statistics and O.R., Faculty of Mathematics, Complutense University of Madrid, Madrid, 28040, Spain
- 2. Department of Mathematics, University of Athens, Panepistemioupolis, Athens, 15784, Greece
- 3. School of Statistics, Complutense University of Madrid, Madrid, 28040, Spain