Hostname: page-component-7dd5485656-j7khd Total loading time: 0 Render date: 2025-10-30T17:04:32.839Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterization of the departure process from an ME/ME/1 queue

Published online by Cambridge University Press:  15 April 2004

Jayesh Kumaran ,
Kenneth Mitchell  and
Appie van de Liefvoort
Jayesh Kumaran
Affiliation:
Division of Computer Science and Electrical Engineering, School of Computing and Engineering, University of Missouri-Kansas City, Missouri 64110, USA; mitchellke@umkc.edu.
Kenneth Mitchell
Affiliation:
Division of Computer Science and Electrical Engineering, School of Computing and Engineering, University of Missouri-Kansas City, Missouri 64110, USA; mitchellke@umkc.edu.
Appie van de Liefvoort
Affiliation:
Division of Computer Science and Electrical Engineering, School of Computing and Engineering, University of Missouri-Kansas City, Missouri 64110, USA; mitchellke@umkc.edu.
Get access

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).

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 2: Advances in modelling of complex systems , April 2004 , pp. 173 - 191
Copyright
© EDP Sciences, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Akar, N., Oguz, N. and Sohraby, K., A novel computational method for solving finite QBD processes. Commun. Stat. Stochastic Models 16 (2000) 273-311. CrossRef
Asmussen, S. and Møller, J., 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. CrossRef
Asmussen, S. and O'Cinneide, C., Representations for matrix-geometric and matrix exponential steady-state distributions with applications to many-server queues. Commun. Statist. Stochastic Models 14 (1998) 369-387. CrossRef
Beran, J., Sherman, R., Taqqu, M. and Willinger, W., Long-range dependence in variable bit rate video traffic. IEEE Trans. Commun. 43 (1995) 1566-1579. CrossRef
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).
Burke, P., The output of queueing systems. Oper. Res. 699 (1956) 699-704. CrossRef
Daley, D., The correlation structure of the output process of some single server queueing systems. Ann. Math. Stat. 39 (1968) 1007-1019. CrossRef
Disney, R. and deMorais, P., Covariance properties for the departure process of M/E k /1//N queues. AIIE Transactions 8 (1976) 169-175. CrossRef
Gelenbe, E., On approximate computer system models. J. ACM 22 (1975) 261-269. CrossRef
Gelenbe, E., Mang, X. and Feng, Y., 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 Informatica 7 (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
Girish, M. and Approximations, J.-Q. Hu for the departure process of a GI/GI/1 queue with Markov-modulated arrivals. Eur. J. Oper. Res. 134 (2001) 540-556. CrossRef
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).
The de, J.-Q. Huparture process of a GI/GI/1 queue and its MacLaurin series. Oper. Res. 44 (1996) 810-815.
Ishikawa, A., On the joint distribution of the departure intervals in an M/G/1//N queue. J. Oper. Res. Soc. Japan 34 (1991) 422-435.
King, R., 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.
Latouche, G. and Ramaswami, V., A logarithmic reduction algorithm for quasi-birth-death process. J. Appl. Probab. 30 (1993) 650-674. CrossRef
Lee, Y., van de Liefvoort, A. and Wallace, V., Modeling correlated traffic with a generalized IPP. Perform. Eval. 40 (2000) 99-114. CrossRef
van de Liefvoort, A., The waiting time distribution and its moments of the PH/PH/1 queue. Oper. Res. Lett. 9 (1990) 261-269. CrossRef
Linvy, M., Melamed, B. and Tsiolis, A., 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).
Mitchell, K. and van de Liefvoort, A., Approximation models of feed-forward queueing networks with correlated arrivals. Perform. Eval. 51 (2003) 137-152. CrossRef
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.
Pancha, P. and Zarki, M., Variable bit rate video transmission. IEEE Communications 32 (1994) 54-66. CrossRef
Patuwo, B., Disney, R. and McNickle, D., The effect of correlated arrivals on queues. IIE Transactions 25 (1993) 105-110. CrossRef
D. Reininger, B. Melamed and D. Raychaudhuri, Variable bit rate MPEG video: Characteristics, modeling and multiplexing, in Proc. of the Fourteenth International Teletraffic Congress 1 (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.
Whitt, W., Approximating a point process by a renewal process I: Two basic methods. Oper. Res. 30 (1982) 125-147. CrossRef
Whitt, W., The queueing network analyzer. Bell System Technical J. 62 (1983) 2799-2815.
Whitt, W., Approximations for departure processes and queues in series. Naval Research Logistics Quarterly 31 (1984) 499-521. CrossRef