Asymptotic analysis of multiclass closed queueing networks: Multiple bottlenecks

Balbo, Gianfranco; Serazzi, Giuseppe

doi:10.1016/s0166-5316(97)00005-9

Cited by 56 publications

(63 citation statements)

References 12 publications

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“…Importantly, the characterization in Section 4.2 explains what optimization problem the heuristic is trying to solve, i.e., the asymptotic limit of the revenue maximization problem (6). From this, we observe clear structural similarities with known non-asymptotic formulations, used in applications, which are helpful to understand the experimental results in Section 5.…”

Section: Heavy-traffic Approximationsmentioning

confidence: 77%

“…This result, proven recently in [40] and [3] under different perspectives, is known to have relationships with the proportionally-fair allocation achieved in communication networks with congestion control, and, to the best of our knowledge, it has not been applied to revenue maximization in the sense of (6). By investigating the KKT conditions of the resulting formulation, it is possible to establish a connection between this asymptotic formulation and the most common formulation of the revenue maximization problem based on the BardSchweitzer approximate MVA algorithm [33], which probably is the approximation for closed models that is most popular among practitioners [29].…”

Section: Revenue Maximization In Heavy-trafficmentioning

confidence: 91%

“…Other constraints may be added to the optimization model (6). In particular, we may require that the utilization of each queue i, i.e., the proportion of time in which queues are busy processing customers, is less 3 When c = 1, the optimization problem (6) is equivalent to the problem of minimizing the network response time, i.e., the mean time that customers take to complete a cycle in the network.…”

Section: Revenue Maximization Problemmentioning

confidence: 99%

“…In this section, we study the revenue maximization problem (6) in the limiting regime where the number of customers grows to infinity and remains proportionate in each class, i.e., N is multiplied by the positive integer k and we let k → ∞. This limiting regime has been used in several works, see [2,3,6,30,32,40] and references therein; we refer to this regime as heavy-traffic.…”

Section: Heavy-traffic Approximationsmentioning

confidence: 99%

“…This limiting regime has been used in several works, see [2,3,6,30,32,40] and references therein; we refer to this regime as heavy-traffic. In this heavy-traffic limit, we provide two results:…”

Section: Heavy-traffic Approximationsmentioning

confidence: 99%

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Heavy-traffic revenue maximization in parallel multiclass queues

Anselmi

Casale

2013

Performance Evaluation

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Motivated by revenue maximization in server farms with admission control, we investigate optimal scheduling in parallel processor-sharing queues. Incoming customers are distinguished in multiple classes and we define revenue as a weighted sum of class throughputs. Under these assumptions, we describe a heavy-traffic limit for the revenue maximization problem and study the asymptotic properties of the optimization model as the number of clients increases. Our main result is a simple heuristic that is able to provide tight guarantees on the optimality gap of its solutions. In the general case with M queues and R classes, we prove that our heuristic is (1 + 1 M −1 )-competitive in heavy-traffic. Experimental results indicate that the proposed heuristic is remarkably accurate, despite its negligible computational costs, both in random instances and using service rates of a web application measured on multiple cloud deployments. 1

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Section: Heavy-traffic Approximationsmentioning

confidence: 77%

Section: Revenue Maximization In Heavy-trafficmentioning

confidence: 91%

Section: Revenue Maximization Problemmentioning

confidence: 99%

Section: Heavy-traffic Approximationsmentioning

confidence: 99%

Section: Heavy-traffic Approximationsmentioning

confidence: 99%

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Heavy-traffic revenue maximization in parallel multiclass queues

Anselmi

Casale

2013

Performance Evaluation

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Performance Engineering

Landrieu¹

2001

Lecture Notes in Computer Science

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The author wishes to thank Giuliano Casale for his important effort in supporting the JMT project. Thanks to his fundamental coordination and co-development work, the JMT suite has achieved the technical level it is recognized for. Thanks for your scientific support! Special thanks also go to Marco Gribaudo, for the enlightening and endless discussions that have increased my knowledge on performance modeling. Thanks for your patience! The author is grateful to Andrea Sianesi and Eugenio Gatti, respectively, President and General Director of the Fondazione Politecnico di Milano, for supporting the publication of this book as Open Access. Thanks for your enthusiasm in accepting my request!

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Object Allocation for Distributed Applications with Complex Workloads

Litoiu

Rolia

2000

Computer Performance Evaluation.Modelling Techniques and Tools

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Asymptotic analysis of multiclass closed queueing networks: Multiple bottlenecks

Cited by 56 publications

References 12 publications

Heavy-traffic revenue maximization in parallel multiclass queues

Heavy-traffic revenue maximization in parallel multiclass queues

Performance Engineering

Object Allocation for Distributed Applications with Complex Workloads

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