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Keywords
(15)
Heavy Traffic
Linear Constraint
Performance Analysis
Performance Bounds
Performance Measure
Queueing Model
Queueing Network
Queueing Theory
Robust Optimization
Satisfiability
Single Server Queue
Sojourn Time
Steady State
Upper and Lower Bounds
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Performance Analysis of Queueing Networks via Robust Optimization
Performance Analysis of Queueing Networks via Robust Optimization,10.1287/opre.1100.0879,Operations Research,Dimitris Bertsimas,David Gamarnik,Alexand
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Performance Analysis of Queueing Networks via Robust Optimization
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Dimitris Bertsimas
,
David Gamarnik
,
Alexander Anatoliy Rikun
Performance analysis
of queueing networks is one of the most challenging areas of queueing theory. Barring very specialized models such as productform type queueing networks, there exist very few results which provide provable nonasymptotic
upper and lower bounds
on key performance measures. In this paper we propose a new
performance analysis
method, which is based on the robust optimization. The basic premise of our approach is as follows: rather than assuming that the stochastic primitives of a
queueing model
satisfy certain probability laws, such as, for example, i.i.d. interarrival and service times distributions, we assume that the underlying primitives are deterministic and satisfy the implications of such probability laws. These implications take the form of simple linear constraints, namely, those motivated by the Law of the Iterated Logarithm (LIL). Using this approach we are able to obtain
performance bounds
on some key performance measures. Furthermore, these
performance bounds
imply similar bounds in the underlying stochastic queueing models. We demonstrate our approach on two types of queueing networks: a) Tandem Single Class queue ing network and b) Multiclass Single Server queueing network. In both cases, using the proposed
robust optimization
approach, we are able to obtain explicit upper bounds on some steadystate performance measures. For example, for the case of TSC system we obtain a bound of the form $\frac{C}{1\rho} \ln \ln(1/(1\rho))$ on the expected steadystate sojourn time, where C is an explicit constant and $\rho$ is the bottleneck traffic intensity. This qualitatively agrees with the correct
heavy traffic
scaling of this
performance measure
up to the $ln ln(1/(1\rho))$ correction factor.
Journal:
Operations Research
, vol. 59, no. 2, pp. 455466, 2011
DOI:
10.1287/opre.1100.0879
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