Characterization of the departure process from an ME/ME/1 queue
Jayesh Kumaran; Kenneth Mitchell; Appie van de Liefvoort
RAIRO - Operations Research (2010)
- Volume: 38, Issue: 2, page 173-191
- ISSN: 0399-0559
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topKumaran, Jayesh, Mitchell, Kenneth, and Appie van de Liefvoort. "Characterization of the departure process from an ME/ME/1 queue." RAIRO - Operations Research 38.2 (2010): 173-191. <http://eudml.org/doc/105307>.
@article{Kumaran2010,
abstract = {
In this paper we propose a family of finite approximations for the departure process of an ME/ME/1 queue indexed by a
parameter k defined as the system size of the finite approximation. The approximations capture the
interdeparture times from an ME/ME/1 queue exactly and preserve the lag correlations of inter-event times of
the departures from an ME/ME/1 queue up to lag (k - 1).
},
author = {Kumaran, Jayesh, Mitchell, Kenneth, Appie van de Liefvoort},
journal = {RAIRO - Operations Research},
language = {eng},
month = {3},
number = {2},
pages = {173-191},
publisher = {EDP Sciences},
title = {Characterization of the departure process from an ME/ME/1 queue},
url = {http://eudml.org/doc/105307},
volume = {38},
year = {2010},
}
TY - JOUR
AU - Kumaran, Jayesh
AU - Mitchell, Kenneth
AU - Appie van de Liefvoort
TI - Characterization of the departure process from an ME/ME/1 queue
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 2
SP - 173
EP - 191
AB -
In this paper we propose a family of finite approximations for the departure process of an ME/ME/1 queue indexed by a
parameter k defined as the system size of the finite approximation. The approximations capture the
interdeparture times from an ME/ME/1 queue exactly and preserve the lag correlations of inter-event times of
the departures from an ME/ME/1 queue up to lag (k - 1).
LA - eng
UR - http://eudml.org/doc/105307
ER -
References
top- N. Akar, N. Oguz and K. Sohraby, A novel computational method for solving finite QBD processes. Commun. Stat. Stochastic Models16 (2000) 273-311.
- S. Asmussen and J. Møller, Calculation of the steady state waiting time distribution in GI/PH/c and MAP/PH/c queues. Queue. Syst. Theory Appl.37 (2001) 9-29.
- S. Asmussen and C. O'Cinneide, Representations for matrix-geometric and matrix exponential steady-state distributions with applications to many-server queues. Commun. Statist. Stochastic Models14 (1998) 369-387.
- J. Beran, R. Sherman, M. Taqqu and W. Willinger, Long-range dependence in variable bit rate video traffic. IEEE Trans. Commun.43 (1995) 1566-1579.
- D. Berstimas and D. Nakazato, The departure process from a GI/GI/1 queue and its applications to the analysis of tandem queues. Tech. Rep. 3725–91, Sloan School of Management (1990). Working paper.
- G. Bolch, S. Greiner, H. de Meer and K. Trivedi, Queuing Networks and Markov Chains. A Wiley-Interscience Publication, New York, John Wiley & Sons (1998).
- P. Burke, The output of queueing systems. Oper. Res.699 (1956) 699-704.
- D. Daley, The correlation structure of the output process of some single server queueing systems. Ann. Math. Stat.39 (1968) 1007-1019.
- R. Disney and P. deMorais, Covariance properties for the departure process of M/Ek/1//N queues. AIIE Transactions8 (1976) 169-175.
- E. Gelenbe, On approximate computer system models. J. ACM22 (1975) 261-269.
- E. Gelenbe, X. Mang and Y. Feng, Diffusion cell loss estimate for ATM with multiclass bursty traffic. Int. J. Comput. Syst. Sci. Engin.11 (1996) 325-333.
- E. Gelenbe and I. Mitrani, Analysis and Synthesis of Computer Systems. Academic press, London, New York (1980).
- E. Gelenbe and G. Pujolle, The behaviour of a single queue in a general queueing network. Acta Informatica7 (1976/77) 123-136.
- E. Gelenbe and G. Pujolle, A diffusion model for multiple class queueing networks, in Measuring, Modelling and Evaluating Computer Systems, Proc. of the Third International Symposium, Bonn – Bad Godesberg, Germany, edited by H. Beilner and H. Gelenbe. North-Holland (1977) 189-199
- M. Girish and J.-Q. Hu, Approximations for the departure process of a GI/GI/1 queue with Markov-modulated arrivals. Eur. J. Oper. Res.134 (2001) 540-556.
- D. Green, Departure Process from MAP/PH/1 Queues. Ph.D. Thesis, The University of Adelaide, Department of Applied Mathematics (1999).
- A. Heindl, Traffic-Based Decomposition of General Queueing Networks with Correlated Input Processes. Ph.D. Thesis, Technical University, Berlin (2001).
- J.-Q. Hu, The departure process of a GI/GI/1 queue and its MacLaurin series. Oper. Res.44 (1996) 810-815.
- A. Ishikawa, On the joint distribution of the departure intervals in an M/G/1//N queue. J. Oper. Res. Soc. Japan34 (1991) 422-435.
- R. King, The covariance structure of the departure process from M/G/1 queues with finite waiting lines. J. R. Stat. Soc.33 (1982) 401-405.
- P. Kühn, Approximation analysis of general queueing networks by decomposition. IEEE Trans. Commun.COM-27 (1979) 113-126.
- J. Kumaran, Ph.D. Thesis, University of Missouri-Kansas city, School of Computing Engineering. Forthcoming.
- G. Latouche and V. Ramaswami, A logarithmic reduction algorithm for quasi-birth-death process. J. Appl. Probab.30 (1993) 650-674.
- Y. Lee, A. van de Liefvoort and V. Wallace, Modeling correlated traffic with a generalized IPP. Perform. Eval.40 (2000) 99-114.
- A. van de Liefvoort, The waiting time distribution and its moments of the PH/PH/1 queue. Oper. Res. Lett.9 (1990) 261-269.
- M. Linvy, B. Melamed and A. Tsiolis, The impact of autocorrelation on queueing systems. Manage. Sci.39 (1993) 332-339.
- L. Lipsky, Queueing Theory: A Linear Algebraic Approach. New York, MacMillan (1992).
- L. Lipsky, P. Fiorini, W. Hsin and A. van de Liefvoort, Auto-correlation of lag-k for customers departing from semi-Markov processes. Tech. Rep. TUM-19506, Technical University Munich (1995).
- K. Mitchell and A. van de Liefvoort, Approximation models of feed-forward queueing networks with correlated arrivals. Perform. Eval.51 (2003) 137-152.
- K. Mitchell, A. van de Liefvoort and J. Place, Second-order statistics of an isolated departure stream from a shared buffer with correlated sources, in Proc. of the Eighth International Conference on Telecommunication Systems Modeling and Analysis, March (2000) 565-574.
- P. Pancha and M. Zarki, Variable bit rate video transmission. IEEE Communications32 (1994) 54-66.
- B. Patuwo, R. Disney and D. McNickle, The effect of correlated arrivals on queues. IIE Transactions25 (1993) 105-110.
- D. Reininger, B. Melamed and D. Raychaudhuri, Variable bit rate MPEG video: Characteristics, modeling and multiplexing, in Proc. of the Fourteenth International Teletraffic Congress1 (1994) 295-306.
- R. Sadre and B. Haverkort, Characterising traffic streams in networks of MAP/MAP/1 queues, in Proc. of the Eleventh GI/ITG, Conference on Measuring Modelling and Evaluation of Computer Communication Systems (2001) 195-208.
- W. Whitt, Approximating a point process by a renewal process I: Two basic methods. Oper. Res.30 (1982) 125-147.
- W. Whitt, The queueing network analyzer. Bell System Technical J.62 (1983) 2799-2815.
- W. Whitt, Approximations for departure processes and queues in series. Naval Research Logistics Quarterly31 (1984) 499-521.
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