Monotonicity Properties for Multi-Class Queueing Systems

Verloop, Ina Maria; Ayesta, Urtzi; Borst, Sem

doi:10.1007/s10626-009-0069-4

Cited by 21 publications

(17 citation statements)

References 43 publications

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“…However, the optimization problem (7) allows us to prove that Property 3.1' is satisfied then as well. The proof may be found in the technical report [26].…”

Section: Weighted α-Fair Policiesmentioning

confidence: 94%

Comparison of bandwidth-sharing policies in a linear network

Verloop¹,

Ayesta²,

Borst³

2008

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools

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In bandwidth-sharing networks, users of various classes require service from different subsets of shared resources simultaneously. These networks have been proposed to analyze the performance of wired and wireless networks. For general arrival and service processes, we give sufficient conditions in order to compare sample-path wise the workload and the number of users under different policies in a linear bandwidth-sharing network. This allows us to compare the performance of the system under various policies in terms of stability, the mean overall delay and the weighted mean number of users.For the important family of weighted α-fair policies, we derive stability results and establish monotonicity of the weighted mean number of users with respect to the fairness parameter α and the relative weights. In order to broaden the comparison results, we investigate a heavy-traffic regime and perform numerical experiments.

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“…However, the optimization problem (7) allows us to prove that Property 3.1' is satisfied then as well. The proof may be found in the technical report [26].…”

Section: Weighted α-Fair Policiesmentioning

confidence: 94%

Comparison of bandwidth-sharing policies in a linear network

Verloop¹,

Ayesta²,

Borst³

2008

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools

Self Cite

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“…The proportional fairness concept can be advocated from a game theoretic point of view as a proportionally fair allocation is also the Nash bargaining solution, satisfying certain axioms of fairness (Bertsimas et al, 2011;Crowcroft & Oechslin, 1998;Kelly, Maulloo, & Tan, 1998;Morell et al, 2008;Bonald et al, 2006;Kelly, Massoulié, & Walton, 2009;Walton, 2011); see also Köppen (2013), Köppen, Yoshida, Ohnishi, and Tsuru (2012) for a discussion of proportional fairness within a relational framework and a symmetric version of this concept, -rank-ordered proportional fairness). Proportional fairness is a specific case of a more general fairness scheme called α − f airness, which maximize the following parametric class of utility functions for α ≥ 0 ) (see also Verloop, Ayesta, and Borst (2010) for a discussion of α − f airness in multi-class queuing systems):…”

Section: Definition 3 a Function F Is Strictly Schur-concave (Schur-mentioning

confidence: 99%

Inequity averse optimization in operational research

Karsu

Morton

2015

European Journal of Operational Research

149

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a b s t r a c tThere are many applications across a broad range of business problem domains in which equity is a concern and many well-known operational research (OR) problems such as knapsack, scheduling or assignment problems have been considered from an equity perspective. This shows that equity is both a technically interesting concept and a substantial practical concern. In this paper we review the operational research literature on inequity averse optimization. We focus on the cases where there is a tradeoff between efficiency and equity.We discuss two equity related concerns, namely equitability and balance. Equitability concerns are distinguished from balance concerns depending on whether an underlying anonymity assumption holds. From a modeling point of view, we classify three main approaches to handle equitability concerns: the first approach is based on a Rawlsian principle. The second approach uses an explicit inequality index in the mathematical model. The third approach uses equitable aggregation functions that can represent the DM's preferences, which take into account both efficiency and equity concerns. We also discuss the two main approaches to handle balance: the first approach is based on imbalance indicators, which measure deviation from a reference balanced solution. The second approach is based on scaling the distributions such that balance concerns turn into equitability concerns in the resulting distributions and then one of the approaches to handle equitability concerns can be applied.We briefly describe these approaches and provide a discussion of their advantages and disadvantages. We discuss future research directions focussing on decision support and robustness.

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“…It is therefore natural to ask which values should the shares have in order to optimize the performance (for example to minimize response times). The selection of optimal shares attracted the attention of several researchers, but so far analysis focused on a limited number of VMs; e.g., [20,26,11,18]. Using the expressions obtained from the large-scale analysis, we are able to derive the optimal weights for the system as the number of VMs grows to infinite (N → ∞).…”

Section: Selection Of Optimal Sharesmentioning

confidence: 99%

“…Hence, by the complementary slackness condition we obtain B r = 0, ∀r. Now, noting that y r > 0, (26) and (27) …”

Section: Selection Of Optimal Sharesmentioning

confidence: 99%

“…We note that for the standard GPS system, i.e., fixed capacity, the optimal choice for the shares has been studied in [26] for the two-VM case (N = 2). It was shown that the shares that minimize the mean overall response time are trivial, i.e., under the optimal shares the GPS policy behaves as a priority queue where priority is given to the VM having largest service rate µ r .…”

Section: Selection Of Optimal Sharesmentioning

confidence: 99%

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Energy-aware capacity scaling in virtualized environments with performance guarantees

Anselmi

Verloop

2011

Performance Evaluation

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We investigate the trade-off between performance and power consumption in servers hosting virtual machines running IT services. The performance behavior of such servers is modeled through Generalized Processor Sharing (GPS) queues enhanced with a green speed-scaling mechanism that controls the processing capacity to use depending on the number of active virtual machines. When the number of virtual machines grows large, we show that the stochastic evolution of our model converges to a system of ordinary differential equations for which we derive a closed-form formula for its unique stationary point. This point is a function of the capacity and the shares that characterize the GPS mechanism. It allows us to show that speed-scaling mechanisms can provide large reduction in power consumption having only small performance degradation in terms of the delays experienced in the virtual machines. In addition, we derive the optimal choice for the shares of the GPS discipline, which turns out to be non-trivial. Finally, we show how our asymptotic analysis can be applied to the dimensioning and service partitioning in data-centers. Experimental results show that our asymptotic formulas are accurate even when the number of virtual machines is small.

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Monotonicity Properties for Multi-Class Queueing Systems

Cited by 21 publications

References 43 publications

Comparison of bandwidth-sharing policies in a linear network

Comparison of bandwidth-sharing policies in a linear network

Inequity averse optimization in operational research

Energy-aware capacity scaling in virtualized environments with performance guarantees

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