Robust queueing theory: an initial study using imprecise probabilities

Stavros Lopatatzidis (), Jasper Bock (), Gert Cooman (), Stijn Vuyst () and Joris Walraevens ()
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Stavros Lopatatzidis: Ghent University
Jasper Bock: Ghent University
Gert Cooman: Ghent University
Stijn Vuyst: Ghent University
Joris Walraevens: Ghent University

Queueing Systems: Theory and Applications, 2016, vol. 82, issue 1, No 6, 75-101

Abstract: 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.

Keywords: Geo/Geo/1/L; Imprecise probabilities; Time-homogeneous; Robustness; Performance measures; Discrete-time queueing; 60K25; 90B22; 37A50; 60-08; 60G20; 68M20 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-015-9458-6

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