The general form linearizer algorithms: A new family of approximate mean value analysis algorithms

Wang, Hai; Sevcik, Kenneth C.; Serazzi, Giuseppe; Wang, Shouhong

doi:10.1016/j.peva.2007.05.005

Cited by 6 publications

(6 citation statements)

References 37 publications

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“…• Using the mean value analysis (MVA) by Reiser and Lavenberg [35] to develop iterative or fixed-point algorithms; e.g., Schweitzer [37], Chandy and Neuse [11], Pattipati et al [31], Wang et al [44]. While these techniques improve the running time of MVA, there is no guarantee that they converge to the exact solution except for particular cases.…”

Section: Introductionmentioning

confidence: 99%

Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence

2013

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We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are determined by the solution of a strictly concave optimization problem. Then, we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only, and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.Keywords: closed queueing networks; product-form; asymptotic independence; fluid limit; large population. Acknowledgements June 2012AbstractWe analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are determined by the solution of a strictly concave optimization problem. Then, we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only, and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.

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Section: Introductionmentioning

confidence: 99%

Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence

2013

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“…Simulation accuracy for varying 𝑁 and 𝐾 when 𝐶 = 3 (Equation(12)) Verification of Theoretical Substitution by Parallel Simulation Since the simulation accuracy was confirmed in the previous section, simulations are performed at 𝐶 ≥ 4, which is more difficult to calculate. Moreover, the mean number of people in the network, one of the performance evaluation indices, is calculated.…”

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confidence: 72%

Limitations of Calculating Theoretical Solutions for Closed BCMP Queueing Networks and Verification of Alternative Theoretical Values by Parallel Simulation

Mizuno

2022

Preprint

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The global spread of the new coronavirus has caused people to rethink their ideas about waiting. In terms of building design, facilities must consider infection control measures and whether evaluations can be performed using queueing theory. Flexible definitions of queueing networks, such as Baskett, Chandy, Muntz and Palacios (BCMP) queueing networks, must be applied to large-scale models that exist in the real world, to evaluate congestion levels. This study applied a closed BCMP queueing network to a real-world model and examined the limitations of the theoretical solution calculation and the possibility of substituting theoretical values by parallel simulation. Parallel computing was applied to the mean value analysis method. Calculations were performed in a large-scale computing environment, enabling calculations on a much larger scale than with conventional models. The results also showed the computation time and required computing resources for the calculation. Since a larger customer class places a greater burden on computational resources, we conducted simulations on models for which a theoretical solution is required and assessed the accuracy of these simulations to confirm that they are sufficiently accurate as an alternative method to the theoretical solution. We proposed a process to calculate performance evaluation indices such as the average number of people in the system in parallel simulations and confirmed that the performance evaluation indices are sufficiently accurate for models with large customer classes. The study findings contribute to both social practicality and academic significance by making it possible to conduct mathematically supported congestion assessments in real-world models and to propose application scenarios for queueing theory.

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“…When the KPIs follow linear functions or simple nonlinear functions, traditional time-series forecasting techniques and/or machine learning techniques are able to yield accurate predictions. When there are queues (i.e., waiting lines) for specific resources within the shared service provider, the KPIs are typically complex nonlinear functions, and it is generally believed that queuing network models are capable of resulting in more accurate prediction of KPIs than other prediction techniques (Wang & Sevcik, 2000;Wang et al, 2008). A queuing network model is a network of queues, where certain KPIs can be Planning Journal of International Business and Management (JIBM) https://rpajournals.com/jibm computed using algorithms (Wang & Sevcik, 2000;Wang et al, 2008).…”

Section: Performance Predictive Analytics For Shared Servicesmentioning

confidence: 99%

“…When there are queues (i.e., waiting lines) for specific resources within the shared service provider, the KPIs are typically complex nonlinear functions, and it is generally believed that queuing network models are capable of resulting in more accurate prediction of KPIs than other prediction techniques (Wang & Sevcik, 2000;Wang et al, 2008). A queuing network model is a network of queues, where certain KPIs can be Planning Journal of International Business and Management (JIBM) https://rpajournals.com/jibm computed using algorithms (Wang & Sevcik, 2000;Wang et al, 2008). For example, the input of a queuing network model is the average time for an employee to complete a certain class of service requests, and the output of the queuing network is the average turnover time of this class of service requests by taking into account the waiting time in the queues.…”

Section: Performance Predictive Analytics For Shared Servicesmentioning

confidence: 99%

Performance Predictive Analytics for Operations Management of Shared Services

2020

JIBM

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Shared services have been widely used in many organizations as an alternative to outsourcing. For shared services, common services are standardized and consolidated across multiple organizations to reduce the operational cost and to increase information and knowledge sharing. Two major advantages of shared services over outsourcing are long-term stable cost-saving and knowledge sharing. One important aspect of successful operations management of shared services is to ensure the quality of services delivered by a shared service provider to each individual partner organization. This paper proposes a performance predictive analytics framework for operations management of shared services. The paper presents a case study to demonstrate the usefulness and effectiveness of this framework.

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The general form linearizer algorithms: A new family of approximate mean value analysis algorithms

Cited by 6 publications

References 37 publications

Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence

Closed Queueing Networks Under Congestion: Nonbottleneck Independence and Bottleneck Convergence

Limitations of Calculating Theoretical Solutions for Closed BCMP Queueing Networks and Verification of Alternative Theoretical Values by Parallel Simulation

Performance Predictive Analytics for Operations Management of Shared Services

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