Abstract
This paper presents the performance analysis of a discrete-time finite-buffer queue with batch input, general interarrival and geometric service times. It is assumed that a batch arriving with size larger than the available buffer is partially accepted and the rest is rejected. The queue is analyzed for early arrival system as well as for late-arrival system with delayed access using both the supplementary variable and imbedded Markov chain techniques. Besides obtaining state probabilities at various epochs and loss probability of a batch as well as of a customer, other performance measures have also been discussed. The waiting time analysis of an arbitrary customer of a batch is also carried out.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bruneel, H., and Kim, B.G. 1993. Discrete Time Models for Communication Systems Including ATM. Boston: Kluwer Academic Publishers.
Chaudhry, M.L., and Gupta, U.C. 1996. Performance analysis of the discrete–time GI/Geom/1/N queue. Journal of Applied Probability 33: 239–255.
Chaudhry, M.L. and Gupta, U.C. 1997. Queue–length and waiting–time distributions of discrete–time GIX/Geom/1 queueing–systems with early and late arrivals. Queueing Systems: 25: 307–334.
Chaudhry, M.L., and Templeton, J.G.C. 1983. A First Course in Bulk Queues. New York: Wiley.
Gallager, R.B. 1996. Discrete Stochastic Processes. New York: Kluwer Academic Publishers.
Gravey, A., and Hébuterne G. 1992. Simultaneity in discrete time single server queues with Bernoulli inputs, Performance Evaluation 14: 123–131.
Hunter, J.J. 1983. Mathematical Techniques of Applied Probability, Volume II, Discrete Time Models: Techniques and Applications. New York: Academic Press.
Kouvatsos, D.D., and Fretwell B. 1996. Closed form performance distributions of a discrete time GIG/D/1/Nqueue with correlated traffic. In Data Communications and Their Performance (S. Fdida and R.O. Onvural Eds.), pp.141–163. New York: Chapman Hall.
Maple 1995. Maple V Release 4. Waterloo Maple Software, 450 Philip Street, Waterloo, Ontario, N2L 5J2 Canada.
Special issue on Advances in Discrete Time Queues 1994. Queueing Systems Volume 18, Nos. 1–2. Miyazawa, M. and Takagi, H. (editors).
Takagi, H. 1993. Queueing Analysis– A Foundation of Performance Evaluation: Volume 3, Discrete–Time Systems. Amsterdam: Elsevier.
Special Issue on Discrete–Time Models and Analysis Methods 1995. Performance Evaluation Volume 21, Nos. 1–2. Tran–Gia, P., Blondia, C. and Towsley, D. (editors).
Vinck, B., and Bruneel, H. 1994. Analyzing the discrete–time G (G)/Geo/1 queue using complex integration. Queueing Systems 18: 47–68.
Woodward, M.E. 1994. Communication and Computer Networks: Modelling with Discrete–Time Queues. Los Alamitos, California: IEEE Computer Society Press.
Rights and permissions
About this article
Cite this article
Chaudhry, M., Gupta, U. Performance Analysis of Discrete-Time Finite-Buffer Batch-Arrival GIX/Geom/1/N Queues. Discrete Event Dynamic Systems 8, 55–70 (1998). https://doi.org/10.1023/A:1008208526758
Issue Date:
DOI: https://doi.org/10.1023/A:1008208526758