Publication: Entropy maximization and the busy period of some single-server vacation models
Loading...
Full text at PDC
Publication Date
2004-07
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
EDP Sciences
Citations
Exportar
Abstract
In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in M/G/1 vacation models operating under the N-, T- and D-policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biased probability density function satisfying the system's constraints. The analysis of the three controllable M/G/1 queueing models provides a parallel numerical study of the solution obtained via the maximum entropy approach versus “classical” solutions. The maximum entropy analysis of a continuous system descriptor (like the busy period) enriches the current body of literature which, in most cases, reduces to discrete queueing measures (such as the number of customers in the system).
Description
This research was supported by the project BFM2002-02189.
UCM subjects
Unesco subjects
Keywords
Citation
J. Abate and W. Whitt, Numerical inversion of Laplace transforms of probability distributions. ORSA J. Comput. 7 (1995) 36–43.
J.R. Artalejo, G-networks: A versatile approach for work removal in queueing networks. Eur. J. Oper. Res. 126 (2000) 233–249.
J.R. Artalejo, On the M/G/1 queue with D-policy. Appl. Math. Modelling 25 (2001) 1055–1069.
K.R. Balachandran and H. Tijms, On the D-policy for the M/G/1 queue. Manage. Sci. 21 (1975) 1073–1076.
B.D. Bunday, Basic Optimization Methods. Edward Arnold, London (1984).
B.T. Doshi, Queueing systems with vacations - A survey. Queue. Syst. 1 (1986) 29–66.
M.A. El-Affendi and D.D. Kouvatsos, A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium. Acta Inform. 19 (1983) 339–355.
G.I. Falin, M. Martin and J.R. Artalejo, Information theoretic approximations for the M/G/1 retrial queue. Acta Inform. 31 (1994) 559–571.
K.G. Gakis, H.K. Rhee and B.D. Sivazlian, Distributions and first moments of the busy period and idle periods in controllable M/G/1 queueing models with simple and dyadic policies. Stoch. Anal. Appl. 13 (1995) 47–81.
E. Gelenbe, Product-form queueing networks with negative and positive customers. J. Appl. Prob. 28 (1991) 656–663.
E. Gelenbe, G-networks: A unifying model for neural and queueing networks. Ann. Oper. Res. 48 (1994) 433–461.
E. Gelenbe and R. Iasnogorodski, A queue with server of walking type (autonomous service). Annales de l’Institut Henry Poincaré, Series B 16 (1980) 63–73.
S. Guiasu, Maximum entropy condition in queueing theory. J. Opl. Res. Soc. 37 (1986) 293–301.
D. Heyman, The T-policy for the M/G/1 queue. Manage. Sci. 23 (1977) 775–778.
L. Kleinrock, Queueing Systems, Volume 1: Theory. John Wiley & Sons, Inc., New York (1975).
D.D. Kouvatsos, Entropy maximisation and queueing networks models. Ann. Oper. Res. 48 (1994) 63–126.
Y. Levy and U. Yechiali, Utilization of idle time in an M/G/1 queueing system. Manage. Sci. 22 (1975) 202–211.
J.A. Nelder and R. Mead, A simplex method for function minimization. Comput. J. 7 (1964) 308–313.
W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical Recipes in Fortran, The Art of Scientific Computing. Cambridge University Press (1992).
J.E. Shore, Information theoretic approximations for M/G/1 and G/G/1 queuing systems. Acta Inform. 17 (1982) 43–61.
L. Tadj and A. Hamdi, Maximum entropy solution to a quorum queueing system. Math. Comput. Modelling 34 (2001) 19–27.
H. Takagi, Queueing Analysis. Vol. 1–3, North-Holland, Amsterdam (1991).
J. Teghem Jr., Control of the service process in a queueing system. Eur. J. Oper. Res. 23 (1986) 141–158.
U. Wagner and A.L.J. Geyer, A maximum entropy method for inverting Laplace transforms of probability density functions. Biometrika 82 (1995) 887–892.
K.H. Wang, S.L. Chuang and W.L. Pearn, Maximum entropy analysis to the N policy M/G/1 queueing systems with a removable server. Appl. Math. Modelling 26 (2002) 1151–1162.
M. Yadin and P. Naor, Queueing systems with a removable server station. Oper. Res. Quar. 14 (1963) 393–405.