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Robust queueing theory : an initial study using imprecise probabilities

Stavros Lopatatzidis, Jasper De Bock UGent, Gert De Cooman UGent, Stijn De Vuyst UGent and Joris Walraevens UGent (2016) QUEUEING SYSTEMS . 82(1-2). p.75-101
abstract
We study the robustness of performance predictions of discrete-time finite-capacity queues by applying the framework of imprecise probabilities. More concretely, we consider the Geo/Geo/1/L model with probabilities of arrival and departure that are no longer fixed, but are allowed to vary within given intervals. We distinguish between two concepts of independence in this framework, namely repetition independence and epistemic irrelevance. In the first approach, we assume the existence of time-homogeneous probabilities for arrival and departure, which leads us to consider a collection of stationary queues. In the second, the stationarity assumption is dropped and we allow the arrival and departure probabilities to vary from time point to time point; they may even depend on the complete history of queue lengths. We calculate bounds on the expected queue length, the probability of a particular queue length and the probability of turning on the server. For the expected queue length, both approaches coincide. For the other performance measures, we observe and discuss various differences between the bounds obtained for these two approaches. One of our observations is that ergodicity may break down due to imprecision: bounds on expected time averages of certain functions on the state space are not necessarily equal to the bounds on the expectation of that function at random instants in a steady-state queue.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Geo/Geo/1/L, Imprecise probabilities, Time-homogeneous, Robustness, Performance measures, Discrete-time queueing, MARKOV-CHAINS, PERTURBATION REALIZATION, MODELS, OPTIMIZATION, SIMULATION
journal title
QUEUEING SYSTEMS
volume
82
issue
1-2
pages
75 - 101
conference name
1st European Conference on Queueing Theory
conference location
Ghent, BELGIUM
conference start
2014-08-20
conference end
2014-08-22
Web of Science type
Article; Proceedings Paper
Web of Science id
000372272400006
ISSN
1572-9443
DOI
10.1007/s11134-015-9458-6
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
7189654
handle
http://hdl.handle.net/1854/LU-7189654
date created
2016-04-19 17:39:51
date last changed
2017-01-24 09:20:24
@article{7189654,
  abstract     = {We study the robustness of performance predictions of discrete-time finite-capacity queues by applying the framework of imprecise probabilities. More concretely, we consider the Geo/Geo/1/L model with probabilities of arrival and departure that are no longer fixed, but are allowed to vary within given intervals. We distinguish between two concepts of independence in this framework, namely repetition independence and epistemic irrelevance. In the first approach, we assume the existence of time-homogeneous probabilities for arrival and departure, which leads us to consider a collection of stationary queues. In the second, the stationarity assumption is dropped and we allow the arrival and departure probabilities to vary from time point to time point; they may even depend on the complete history of queue lengths. We calculate bounds on the expected queue length, the probability of a particular queue length and the probability of turning on the server. For the expected queue length, both approaches coincide. For the other performance measures, we observe and discuss various differences between the bounds obtained for these two approaches. One of our observations is that ergodicity may break down due to imprecision: bounds on expected time averages of certain functions on the state space are not necessarily equal to the bounds on the expectation of that function at random instants in a steady-state queue.},
  author       = {Lopatatzidis, Stavros and De Bock, Jasper and De Cooman, Gert and De Vuyst, Stijn and Walraevens, Joris},
  issn         = {1572-9443},
  journal      = {QUEUEING SYSTEMS },
  keyword      = {Geo/Geo/1/L,Imprecise probabilities,Time-homogeneous,Robustness,Performance measures,Discrete-time queueing,MARKOV-CHAINS,PERTURBATION REALIZATION,MODELS,OPTIMIZATION,SIMULATION},
  language     = {eng},
  location     = {Ghent, BELGIUM },
  number       = {1-2},
  pages        = {75--101},
  title        = {Robust queueing theory : an initial study using imprecise probabilities},
  url          = {http://dx.doi.org/10.1007/s11134-015-9458-6},
  volume       = {82},
  year         = {2016},
}

Chicago
Lopatatzidis, Stavros, Jasper De Bock, Gert De Cooman, Stijn De Vuyst, and Joris Walraevens. 2016. “Robust Queueing Theory : an Initial Study Using Imprecise Probabilities.” Queueing Systems 82 (1-2): 75–101.
APA
Lopatatzidis, S., De Bock, J., De Cooman, G., De Vuyst, S., & Walraevens, J. (2016). Robust queueing theory : an initial study using imprecise probabilities. QUEUEING SYSTEMS , 82(1-2), 75–101. Presented at the 1st European Conference on Queueing Theory .
Vancouver
1.
Lopatatzidis S, De Bock J, De Cooman G, De Vuyst S, Walraevens J. Robust queueing theory : an initial study using imprecise probabilities. QUEUEING SYSTEMS . 2016;82(1-2):75–101.
MLA
Lopatatzidis, Stavros, Jasper De Bock, Gert De Cooman, et al. “Robust Queueing Theory : an Initial Study Using Imprecise Probabilities.” QUEUEING SYSTEMS 82.1-2 (2016): 75–101. Print.