Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T20:00:31.513Z Has data issue: false hasContentIssue false
  • English
  • Français

Analyzing discrete-time bulk-service Geo/Geob/m queue

Published online by Cambridge University Press:  08 November 2006

Veena Goswami ,
Umesh C. Gupta  and
Sujit K. Samanta
Veena Goswami
Affiliation:
Department of Computer Science, Kalinga Institute of Industrial Technology, Bhubaneswar-751024, India; veena_goswami@yahoo.com
Umesh C. Gupta
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India; umesh@maths.iitkgp.ernet.in; sujit.samanta@rediffmail.com
Sujit K. Samanta
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India; umesh@maths.iitkgp.ernet.in; sujit.samanta@rediffmail.com
Get access

Abstract

This paper analyzes adiscrete-time multi-server queue in which service capacity of eachserver is a minimum of one and a maximum of b customers. Theinterarrival- and service-times are assumed to be independent andgeometrically distributed. The queue is analyzed under theassumptions of early arrival system and late arrival system withdelayed access. Besides, obtaining state probabilities atarbitrary and outside observer's observation epochs, someperformance measures and waiting-time distribution in the queuehave also been discussed. Finally, it is shown that in limitingcase the results obtained in thispaper tend to the continuous-time counterpart.

Keywords

Bulk-servicediscrete-timemulti-serverqueueingwaiting-time.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 3 , July 2006 , pp. 267 - 284
Copyright
© EDP Sciences, 2006

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.)

References

Artalejo, J.R. and Hern, O.ández-Lerma, Performance analysis and optimal control of the Geo/Geo/c queue. Perform. Evaluation 1013 (2002) 1–25.
H. Bruneel and B.G. Kim, Discrete-Time Models for Communication Systems Including ATM. Kluwer Academic Publishers, Boston (1983).
W.C. Chan and D.Y. Maa, The GI/Geom/N queue in discrete-time. INFOR 16 (3) (1978) 232–252.
Chaudhry, M.L. and Chang, S.H., Analysis of the discrete-time bulk-service queue Geo/GY/1/N + B. Oper. Res. Lett. 32 (2004) 355–363. CrossRef
M.L. Chaudhry and U.C. Gupta, Transient behaviour of the discrete-time Geom/Geom/m/m Erlang loss model, in Proc. of Probability Models and Statistics, edited by A.C. Borthakur and H. Choudhury. A J. Medhi Festschrift, New age international limited, publishers, New Delhi (1996) 133–145.
Chaudhry, M.L. and Gupta, U.C., Algorithmic discussions of distributions of numbers of busy channels for GI/Geom/m/m queues. INFOR. 38 (2000) 51–63.
M.L. Chaudhry and U.C. Gupta, Numerical evaluation of state probabilities at different epochs in multiserver GI/Geom/m queue, in Proc. of Advances on Methodological and Applied Aspects of Probability and Statistics, edited by N. Balakrishnan. Gordon and Breach Science Publishers (2001) 31–46.
Chaudhry, M.L. and Kim, N.M., A complete and simple solution for a discrete-time multi-server queue with bulk arrivals and deterministic service times. Oper. Res. Lett. 31 (2003) 101–107. CrossRef
M.L. Chaudhry, U.C. Gupta and V. Goswami, Modelling and analysis of discrete-time multiserver queues with batch arrivals: GIX/Geom/m. Inform. J. Comput. 13 (3) (2001) 172–180.
M.L. Chaudhry, U.C. Gupta and V. Goswami, On discrete-time multiserver queue with finite buffer: GI/Geom/m/N. Comput. Oper. Res. 31 (2004) 2137–2150. CrossRef
P. Gao, S. Wittevrongel and H. Bruneel, Discrete-time multiserver queues with geometric service times. Comput. Oper. Res. 31 (2004) 81–99.
Gravey, A. and G. Hébuterne, Simultaneity in discrete time single server queues with Bernoulli inputs. Perform. Evaluation 14 (1992) 123–131. CrossRef
U.C. Gupta and V. Goswami, Performance analysis of finite buffer discrete-time queue with bulk service. Comput. Oper. Res. 29 (2002) 1331–1341.
Gupta, U.C., Samanta, S.K. and Sharma, R.K., Computing queueing length and waiting time distributions in finite-buffer discrete-time multi-server queues with late and early arrivals. Comput. Math. Appl. 48 (2004) 1557–1573. CrossRef
J.J. Hunter, Mathematical Techniques of Applied Probability, Vol-II, Discrete Time Models: Techniques and Applications. New York, Academic Press (1983).
J. Medhi, Stochastic Models in Queueing Theory. Academic Press, Inc. (1991).
Rubin, I. and Zhang, Z., Message delay and queue size analysis for circuit-switched TDMA systems. IEEE Trans. Comm. 39 (1991) 905–913. CrossRef
R.M. Spiegel, Schaum's outline of theory and problems of calculus of finite differences and difference equations. Mcgraw Hill Inc. (1971).
S. Wittevrongel, H. Bruneel and B. Vinck, Analysis of the Discrete-Time G(G)/Geom/c Queueing Model, in Proc. of Networking 2002-Lecture Notes in Computer Science 2345, edited by E. Gregori, M. Conti, A.T. Campbell, G. Omidyar and M. Zukerman. Pisa, Italy (2002) 757–768.
M.E. Woodward, Communication and Computer Networks: Modelling with Discrete-Time Queues. Los Alamitos, CA: California IEEE Computer Society Press (1994).