Transient Analysis of a Single-Server Queue with Batch Arrivals Using Modeling and Functions Akin to the Modified Bessel Functions
The paper considers a single-server queue with fixedsize
batch Poisson arrivals and exponential service times, a model
that is useful for a buffer that accepts messages arriving as fixed size
batches of packets and releases them one packet at time. Transient
performance measures for queues have long been recognized as
being complementary to the steady-state analysis. The focus of the
paper is on the use of the functions that arise in the analysis of the
transient behaviour of the queuing system. The paper exploits
practical modelling to obtain a solution to the integral equation
encountered in the analysis. Results obtained indicate that under
heavy load conditions, there is significant disparity in the statistics
between the transient and steady state values.
[1] G. N. Higginbottom, Performance Evaluation of Communication
Networks, Artech House 1998
[2] H. P. Schwefel, L. Lipsky, M. Jobmann, "On the Necessity of Transient
Performance Analysis in Telecommunication Networks," 17th International Teletraffic Congress (ITC17), Salvador da Bahia, Brazil,
September 24-28 2001
[3] B. van Holt, C. Blondia, "Approximated Transient Queue Length and
Waiting Time Distribution via Steady State Analysis", Stochastic
Models 21, pp.725-744, 2005
[4] T. Hofkens, K. Spacy, C. Blondia, "Transient Analysis of the DBMAP/
G/1 Queue with an Applications to the Dimensioning of Video
Playout Buffer for VBR Traffic", Proceedings of Networking, Athens
Greece, 2004
[5] D. M. Lucantoni, G. L. Choudhury, W. Witt, "The Transient
BMAP/PH/1 Queue", Stochastic Models 10, pp.461-478, 1994
[6] W. Böhm. S. G. Mohanty, "Transient Analysis of Queues with
Heterogeneous Arrivals" , Queuing Systems, Vol.18, pp.27-45, 1994
[7] G. L. Choudhury, D. M. Lucantoni, W. Witt, "Multidimensional
Transform Inversion with Application to the Transient M/G/1 Queue",
Annals of Applied Probability, 4, 1994, pp.719-740.
[8] J. Abate, G. L. Choudhury, W. Whitt, "An Introduction to Numerical
Transform Inversion and its Application to Probability Models" In: W.
Grassman, (ed.) Computational Probability, pp. 257-323. Kluwer,
Boston , 1999.
[9] L. Kelinrock, R. Gail, Queuing Systems: Problems and Solutions, John
Wiley & Sons, 1996.
[10] R. G. Hohlfeld, J. I. F. King, T. W. Drueding, G. v. H. Sandri, "Solution
of convolution integral equations by the method of differential
inversion", SIAM Journal on Applied Mathematics, Vol. 53 , No.1
(February 1993), Pages: 154 - 167
[11] A. S. Vasudeva Murthy, "A note on the differential inversion method of
Hohlfeld et al.",SIAM Journal on Applied Mathematics, Vol. 55 , No.3
(June 1995), pp. 719 - 722
[12] P. L. Bharatiya , "The Inversion of a Convolution Transform Whose
Kernel is a Bessel Function", The American Mathematical Monthly, Vol.
72, No. 4. (Apr., 1965), pp. 393-397
[1] G. N. Higginbottom, Performance Evaluation of Communication
Networks, Artech House 1998
[2] H. P. Schwefel, L. Lipsky, M. Jobmann, "On the Necessity of Transient
Performance Analysis in Telecommunication Networks," 17th International Teletraffic Congress (ITC17), Salvador da Bahia, Brazil,
September 24-28 2001
[3] B. van Holt, C. Blondia, "Approximated Transient Queue Length and
Waiting Time Distribution via Steady State Analysis", Stochastic
Models 21, pp.725-744, 2005
[4] T. Hofkens, K. Spacy, C. Blondia, "Transient Analysis of the DBMAP/
G/1 Queue with an Applications to the Dimensioning of Video
Playout Buffer for VBR Traffic", Proceedings of Networking, Athens
Greece, 2004
[5] D. M. Lucantoni, G. L. Choudhury, W. Witt, "The Transient
BMAP/PH/1 Queue", Stochastic Models 10, pp.461-478, 1994
[6] W. Böhm. S. G. Mohanty, "Transient Analysis of Queues with
Heterogeneous Arrivals" , Queuing Systems, Vol.18, pp.27-45, 1994
[7] G. L. Choudhury, D. M. Lucantoni, W. Witt, "Multidimensional
Transform Inversion with Application to the Transient M/G/1 Queue",
Annals of Applied Probability, 4, 1994, pp.719-740.
[8] J. Abate, G. L. Choudhury, W. Whitt, "An Introduction to Numerical
Transform Inversion and its Application to Probability Models" In: W.
Grassman, (ed.) Computational Probability, pp. 257-323. Kluwer,
Boston , 1999.
[9] L. Kelinrock, R. Gail, Queuing Systems: Problems and Solutions, John
Wiley & Sons, 1996.
[10] R. G. Hohlfeld, J. I. F. King, T. W. Drueding, G. v. H. Sandri, "Solution
of convolution integral equations by the method of differential
inversion", SIAM Journal on Applied Mathematics, Vol. 53 , No.1
(February 1993), Pages: 154 - 167
[11] A. S. Vasudeva Murthy, "A note on the differential inversion method of
Hohlfeld et al.",SIAM Journal on Applied Mathematics, Vol. 55 , No.3
(June 1995), pp. 719 - 722
[12] P. L. Bharatiya , "The Inversion of a Convolution Transform Whose
Kernel is a Bessel Function", The American Mathematical Monthly, Vol.
72, No. 4. (Apr., 1965), pp. 393-397
@article{"International Journal of Electrical, Electronic and Communication Sciences:54097", author = "Vitalice K. Oduol", title = "Transient Analysis of a Single-Server Queue with Batch Arrivals Using Modeling and Functions Akin to the Modified Bessel Functions", abstract = "The paper considers a single-server queue with fixedsize
batch Poisson arrivals and exponential service times, a model
that is useful for a buffer that accepts messages arriving as fixed size
batches of packets and releases them one packet at time. Transient
performance measures for queues have long been recognized as
being complementary to the steady-state analysis. The focus of the
paper is on the use of the functions that arise in the analysis of the
transient behaviour of the queuing system. The paper exploits
practical modelling to obtain a solution to the integral equation
encountered in the analysis. Results obtained indicate that under
heavy load conditions, there is significant disparity in the statistics
between the transient and steady state values.", keywords = "batch arrivals, modelling, single-server queue,time-varying probabilities, transient analysis.", volume = "3", number = "9", pages = "1670-6", }