I am willing to work on queuing models but in classical queuing models, it is assumed the probability distributions of arrival and service are known or at least the rate is known. However, I am willing to work on the case when there is not complete information about parameters and they are learned over time. Can I know if it is possible to model this problem? Moreover, how is it possible to use machine learning algorithms in queuing models?


1 Answer 1


Certainly, and to take the problem's structure into account, one could model the queue knowing - or guessing - prior information about the queue's structure and/or parameter distribution and use Bayesian inference. See for example the following sources and their references:

  • Armero, C., & Bayarri, M. J. (1994). Bayesian prediction in M/M/1 queues. Queueing Systems, 15(1-4), 401-417.

  • Ausın, M. C., Wiper, M. P., & Lillo, R. E. (2004). Bayesian estimation for the M/G/1 queue using a phase-type approximation. Journal of Statistical Planning and Inference, 118(1-2), 83-101.

  • Bingham, N. H., & Pitts, S. M. (1999). Nonparametric inference from M/G/l busy periods. Stochastic Models, 15(2), 247-272.

  • Hansen, M. B., & Pitts, S. M. (2006). Nonparametric inference from the M/G/1 workload. Bernoulli, 12(4), 737-759.

  • Muddapur, M. V. (1972). Bayesian estimates of parameters in some queueing models. Annals of the Institute of Statistical Mathematics, 24(1), 327-331.

  • Rohrscheidt, F. M. V. (2017). Bayesian Nonparametric Inference for Queueing Systems (Doctoral dissertation). Available online here

  • Shestopaloff, A. Y., & Neal, R. M. (2014). On Bayesian inference for the M/G/1 queue with efficient MCMC sampling. arXiv preprint arXiv:1401.5548.

  • Sutton, C. A., & Jordan, M. I. (2008, December). Probabilistic inference in queueing networks. In SysML.

I know you mentioned Machine Learning, but as you want to pay attention to incomplete information regarding the parameters and learning over time, I think classic Bayesian Modelling should to be given a try. Moreover:

  1. The above publication by Hansen & Pitts studies sufficient conditions for the empirical process to converge weakly to a Gaussian Process (Gaussian Processes are considered a probabilistic approach to learning in kernel machines - like a probabilistic counterpart to Support Vector Machines). In the final sections they provide experimental results for different service time distributions.
  2. The one by Sutton & Jordan considers Gibbs sampling and Expectation Maximization, which are again related to Machine Learning (its authors are also quite renowned in the Machine Learning field).

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