Skip to main content Accessibility help
×
Home

Nonparametric Inference for Queueing Networks of Geom X /G/∞ Queues in Discrete Time

  • Dominic Edelmann (a1) and Cornelia Wichelhaus (a1)

Abstract

We study nonparametric estimation problems for discrete-time stochastic networks of Geom X /G/∞ queues. We assume that we are only able to observe the external arrival and external departure processes at the nodes over a stretch of time. Based on such incomplete information of the system, we aim to construct estimators for the unknown general service time distributions at the nodes without imposing any parametric condition. We propose two different estimation approaches. The first approach is based on the construction of a so-called sequence of differences, and a crucial relation between the expected number of external departures at a node and specific sojourn time distributions in the network. The second approach directly utilizes the structure of the cross-covariance functions between external arrival and departure processes at the nodes. Both methods lead to deconvolution problems which we solve explicitly. A detailed simulation study illustrates the numerical performances of our estimators and shows their advantages and disadvantages.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Nonparametric Inference for Queueing Networks of Geom X /G/∞ Queues in Discrete Time
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Nonparametric Inference for Queueing Networks of Geom X /G/∞ Queues in Discrete Time
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Nonparametric Inference for Queueing Networks of Geom X /G/∞ Queues in Discrete Time
      Available formats
      ×

Copyright

Corresponding author

Postal address: Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany.
∗∗ Email address: dominic.edelmann@googlemail.com
∗∗∗ Email address: wichelhaus@statlab.uni-heidelberg.de

References

Hide All
Bhat, U. N. and Subba Rao, S. (1986/87). Statistical analysis of queueing systems. Queueing Systems 1, 217247.
Bingham, N. H. and Pitts, S. M. (1999). Non-parametric estimation for the M/G/∞ queue. Ann. Inst. Statist. Math. 51, 7197.
Brown, M. (1970). An M/G/∞ estimation problem. Ann. Math. Statist. 41, 651654.
Conti, P. L. (1999). Large sample Bayesian analysis for Geo/G/1 discrete-time queueing models. Ann. Statist. 27, 17851807.
Conti, P. L. (2002). Nonparametric statistical analysis of discrete-time queues, with applications to ATM teletraffic data. Stoch. Models 18, 497527.
Daley, D. J. (1976). Queueing output processes. Adv. Appl. Prob. 8, 395415.
Hall, P. and Park, J. (2004). Nonparametric inference about service time distribution from indirect measurements. J. R. Statist. Soc. B 66, 861875.
Hansen, M. B. and Pitts, S. M. (2006). Nonparametric inference from the M/G/1 workload. Bernoulli 12, 737759.
Ke, J.-C. and Chu, Y.-K. (2006). Nonparametric and simulated analysis of intensity for a queueing system. Appl. Math. Comput. 183, 12801291.
Liu, Z., Wynter, L., Xia, C. H. and Zhang, F. (2006). Parameter inference of queueing models for IT systems using end-to-end measurements. Performance Evaluation 63, 3660.
Pickands, J., III and Stine, R. A. (1997). Estimation for an M/G/∞ queue with incomplete information. Biometrika 84, 295308.
Pitts, S. M. (1994). Nonparametric estimation of the stationary waiting time distribution function for the GI/G/1 queue. Ann. Statist. 22, 14281446.
Proakis, J. G. and Manolakis, D. G. (1992). Digital Signal Processing: Principles, Algorithms, and Applications. Macmillan, New York.
Ross, S. M. (1970). Identifiability in GI/G/k queues. J. Appl. Prob. 7, 776780.
Wichelhaus, C. and Langrock, R. (2012). Nonparametric inference for stochastic feedforward networks based on cross-spectral analysis of point processes. Electron. J. Statist. 6, 16701714.

Keywords

MSC classification

Related content

Powered by UNSILO

Nonparametric Inference for Queueing Networks of Geom X /G/∞ Queues in Discrete Time

  • Dominic Edelmann (a1) and Cornelia Wichelhaus (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.