The Experts below are selected from a list of 234 Experts worldwide ranked by ideXlab platform
Samuel Rota Bulo - One of the best experts on this subject based on the ideXlab platform.
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explicit solutions for queues with hypo or hyper Exponential Service Time distribution and application to product form approximations
Performance Evaluation, 2014Co-Authors: Andrea Marin, Samuel Rota BuloAbstract:Abstract Queueing systems with Poisson arrival processes and Hypo- or Hyper-Exponential Service Time distribution have been widely studied in the literature. Their steady-state analysis relies on the observation that the infinitesimal generator matrix has a block-regular structure and, hence, the matrix analytic method may be applied. Let π n k be the steady-state probability of observing the k th phase of Service and n customers in the queue, with 1 ≤ k ≤ K , and K the number of phases, and let π n = ( π n 1 , … , π n K ) . Then, it is well-known that there exists a rate matrix R such that π n + 1 = π n R . In this paper, we give a symbolic expression for such a matrix R for both cases of Hypo- and Hyper-Exponential queueing systems. Then, we exploit this result in order to address the problem of approximating a M / HYPO K / 1 queue by a product-form model. We show that the knowledge of the symbolic expression of R allows us to specify the approximations for more general models than those that have been previously considered in the literature and with higher accuracy.
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explicit solutions for queues with hypo Exponential Service Time and applications to product form analysis
Performance Evaluation Methodolgies and Tools, 2011Co-Authors: Andrea Marin, Samuel Rota BuloAbstract:Queueing systems with Poisson arrival processes and Hypo-Exponential Service Time distribution have been widely studied in literature. Their steady-state analysis relies on the observation that the infinitesimal generator matrix has a block-regular structure and, hence, matrix-analytic method may be applied. Let πnk be the steady-state probability of observing the k-th stage of Service busy and n customers in the queue, with 1 ≤ k ≤ K, and K the number of stages, and let πn = (πn1,..., πnK). Then, it is well-known that there exists a rate matrix R such that πn+1 = πnR. In this paper we give a symbolic expression for such a matrix R. Then, we exploit this result in order to address the problem of approximating a M/HypoK/1 queue by a model with initial perturbations which yields a product-form stationary distribution. We show that the result on the rate matrix allows us to specify the approximations for more general models than those that have been previously considered in literature and with higher accuracy.
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VALUETOOLS - Explicit solutions for queues with hypo-Exponential Service Time and applications to product-form analysis
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools, 2011Co-Authors: Andrea Marin, Samuel Rota BuloAbstract:Queueing systems with Poisson arrival processes and Hypo-Exponential Service Time distribution have been widely studied in literature. Their steady-state analysis relies on the observation that the infinitesimal generator matrix has a block-regular structure and, hence, matrix-analytic method may be applied. Let πnk be the steady-state probability of observing the k-th stage of Service busy and n customers in the queue, with 1 ≤ k ≤ K, and K the number of stages, and let πn = (πn1,..., πnK). Then, it is well-known that there exists a rate matrix R such that πn+1 = πnR. In this paper we give a symbolic expression for such a matrix R. Then, we exploit this result in order to address the problem of approximating a M/HypoK/1 queue by a model with initial perturbations which yields a product-form stationary distribution. We show that the result on the rate matrix allows us to specify the approximations for more general models than those that have been previously considered in literature and with higher accuracy.
Andrea Marin - One of the best experts on this subject based on the ideXlab platform.
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explicit solutions for queues with hypo or hyper Exponential Service Time distribution and application to product form approximations
Performance Evaluation, 2014Co-Authors: Andrea Marin, Samuel Rota BuloAbstract:Abstract Queueing systems with Poisson arrival processes and Hypo- or Hyper-Exponential Service Time distribution have been widely studied in the literature. Their steady-state analysis relies on the observation that the infinitesimal generator matrix has a block-regular structure and, hence, the matrix analytic method may be applied. Let π n k be the steady-state probability of observing the k th phase of Service and n customers in the queue, with 1 ≤ k ≤ K , and K the number of phases, and let π n = ( π n 1 , … , π n K ) . Then, it is well-known that there exists a rate matrix R such that π n + 1 = π n R . In this paper, we give a symbolic expression for such a matrix R for both cases of Hypo- and Hyper-Exponential queueing systems. Then, we exploit this result in order to address the problem of approximating a M / HYPO K / 1 queue by a product-form model. We show that the knowledge of the symbolic expression of R allows us to specify the approximations for more general models than those that have been previously considered in the literature and with higher accuracy.
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explicit solutions for queues with hypo Exponential Service Time and applications to product form analysis
Performance Evaluation Methodolgies and Tools, 2011Co-Authors: Andrea Marin, Samuel Rota BuloAbstract:Queueing systems with Poisson arrival processes and Hypo-Exponential Service Time distribution have been widely studied in literature. Their steady-state analysis relies on the observation that the infinitesimal generator matrix has a block-regular structure and, hence, matrix-analytic method may be applied. Let πnk be the steady-state probability of observing the k-th stage of Service busy and n customers in the queue, with 1 ≤ k ≤ K, and K the number of stages, and let πn = (πn1,..., πnK). Then, it is well-known that there exists a rate matrix R such that πn+1 = πnR. In this paper we give a symbolic expression for such a matrix R. Then, we exploit this result in order to address the problem of approximating a M/HypoK/1 queue by a model with initial perturbations which yields a product-form stationary distribution. We show that the result on the rate matrix allows us to specify the approximations for more general models than those that have been previously considered in literature and with higher accuracy.
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VALUETOOLS - Explicit solutions for queues with hypo-Exponential Service Time and applications to product-form analysis
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools, 2011Co-Authors: Andrea Marin, Samuel Rota BuloAbstract:Queueing systems with Poisson arrival processes and Hypo-Exponential Service Time distribution have been widely studied in literature. Their steady-state analysis relies on the observation that the infinitesimal generator matrix has a block-regular structure and, hence, matrix-analytic method may be applied. Let πnk be the steady-state probability of observing the k-th stage of Service busy and n customers in the queue, with 1 ≤ k ≤ K, and K the number of stages, and let πn = (πn1,..., πnK). Then, it is well-known that there exists a rate matrix R such that πn+1 = πnR. In this paper we give a symbolic expression for such a matrix R. Then, we exploit this result in order to address the problem of approximating a M/HypoK/1 queue by a model with initial perturbations which yields a product-form stationary distribution. We show that the result on the rate matrix allows us to specify the approximations for more general models than those that have been previously considered in literature and with higher accuracy.
Natalia Osipova - One of the best experts on this subject based on the ideXlab platform.
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batch processor sharing with hyper Exponential Service Time
Operations Research Letters, 2008Co-Authors: Natalia OsipovaAbstract:We study the Processor Sharing queueing model with a hyper-Exponential Service Time distribution and Poisson batch arrival process. In the case of the hyper-Exponential Service Time distribution we find an analytical expression for the expected conditional response Time function and obtain an alternative proof of its concavity with respect to the Service Time.
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batch processor sharing with hyper Exponential Service Time
arXiv: Networking and Internet Architecture, 2007Co-Authors: Natalia OsipovaAbstract:We study Batch Processor-Sharing (BPS) queuing model with hyper-Exponential Service Time distribution and Poisson batch arrival process. One of the main goals to study BPS is the possibility of its application in size-based scheduling, which is used in differentiation between Short and Long flows in the Internet. In the case of hyper-Exponential Service Time distribution we find an analytical expression of the expected conditional response Time for the BPS queue. We show, that the expected conditional response Time is a concave function of the Service Time. We apply the received results to the Two Level Processor-Sharing (TLPS) model with hyper-Exponential Service Time distribution and find the expression of the expected response Time for the TLPS model. TLPS scheduling discipline can be applied to size-based differentiation in TCP/IP networks and Web server request handling.
Kannan Ramchandran - One of the best experts on this subject based on the ideXlab platform.
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Allerton - Faster Data-access in Large-scale Systems: Network-scale Latency Analysis under General Service-Time Distributions
2018 56th Annual Allerton Conference on Communication Control and Computing (Allerton), 2018Co-Authors: Avishek Ghosh, Kannan RamchandranAbstract:In cloud storage systems with a large number of servers, files (e.g., videos, movies) are typically not stored in single servers. Instead, they are split, replicated (to ensure reliability in case of server malfunction) and stored in different servers. We analyze the mean latency of such a split-and- replicate cloud storage system under general sub-Exponential Service Time distribution, which encapsulates most of the practical heavy-tailed distributions. We present a novel scheduling scheme that utilizes the load-balancing policy of the power of $d (\geq 2)$ choices. Exploiting the double Exponential queue length property of this policy ([1]), we obtain tight upper bounds on mean latency. An alternative to split-and-replicate is to use erasure-codes, and recently, it has been observed that they can reduce latency in data access (see [2] for details). We argue that under high redundancy (integer redundancy factor strictly greater than or equal to 2) regime, the mean latency of a coded system is upper bounded by that of a split-and-replicate system (with same replication factor) and the gap between these two is small. For example, when specialized to an Exponential Service Time distribution, our formulation recovers the result of [3], (which uses erasure codes) upto a constant factor. We also validate this claim numerically under different Service distributions such as Exponential, shift plus Exponential and the heavy-tailed Weibull distribution and compare the mean latency to that of an unsplit-replicated system. We observe that the coded system outperforms the unsplit-replication system by at least 20% for all three distributions and all possible arrival request rates. Also, we analyze the tail latency for data centers memoryless servers. Furthermore, we consider the mean latency for an erasure coded system with low redundancy (fractional redundancy factor between 1 and 2), a scenario which is more pragmatic, given the storage constraints ([4]). However under this regime, we restrict ourselves to the special case of Exponential Service Time distribution and use the randomized load balancing policy namely batch-sampling. We obtain an upper bound on mean delay that depends on the order statistics of the queue lengths, which, we further smooth out via a discrete to continuous approximation.
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Faster Data-access in Large-scale Systems: Network-scale Latency Analysis under General Service-Time Distributions
arXiv: Distributed Parallel and Cluster Computing, 2018Co-Authors: Avishek Ghosh, Kannan RamchandranAbstract:In cloud storage systems with a large number of servers, files are typically not stored in single servers. Instead, they are split, replicated (to ensure reliability in case of server malfunction) and stored in different servers. We analyze the mean latency of such a split-and-replicate cloud storage system under general sub-Exponential Service Time. We present a novel scheduling scheme that utilizes the load-balancing policy of the \textit{power of $d$ $(\geq 2)$} choices. An alternative to split-and-replicate is to use erasure-codes, and recently, it has been observed that they can reduce latency in data access (see \cite{longbo_delay} for details). We argue that under high redundancy (integer redundancy factor strictly greater than or equal to 2) regime, the mean latency of a coded system is upper bounded by that of a split-and-replicate system (with same replication factor) and the gap between these two is small. We validate this claim numerically under different Service distributions such as Exponential, shift plus Exponential and the heavy-tailed Weibull distribution and compare the mean latency to that of an unsplit-replicated system. We observe that the coded system outperforms the unsplit-replication system by at least $20\%$. Furthermore, we consider the mean latency for an erasure coded system with low redundancy (fractional redundancy factor between 1 and 2), a scenario which is more pragmatic, given the storage constraints (\cite{rashmi_thesis}). However under this regime, we restrict ourselves to the special case of Exponential Service Time distribution and use the randomized load balancing policy namely \textit{batch-sampling}. We obtain an upper bound on mean delay that depends on the order statistics of the queue lengths, which, we further smooth out via a discrete to continuous approximation.
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Faster Data-access in Large-scale Systems: Network-scale Latency Analysis under General Service-Time Distributions
2018 56th Annual Allerton Conference on Communication Control and Computing (Allerton), 2018Co-Authors: Avishek Ghosh, Kannan RamchandranAbstract:In cloud storage systems with a large number of servers, files (e.g., videos, movies) are typically not stored in single servers. Instead, they are split, replicated (to ensure reliability in case of server malfunction) and stored in different servers. We analyze the mean latency of such a split-and- replicate cloud storage system under general sub-Exponential Service Time distribution, which encapsulates most of the practical heavy-tailed distributions. We present a novel scheduling scheme that utilizes the load-balancing policy of the power of d (≥2) choices. Exploiting the double Exponential queue length property of this policy ([1]), we obtain tight upper bounds on mean latency. An alternative to split-and-replicate is to use erasure-codes, and recently, it has been observed that they can reduce latency in data access (see [2] for details). We argue that under high redundancy (integer redundancy factor strictly greater than or equal to 2) regime, the mean latency of a coded system is upper bounded by that of a split-and-replicate system (with same replication factor) and the gap between these two is small. For example, when specialized to an Exponential Service Time distribution, our formulation recovers the result of [3], (which uses erasure codes) upto a constant factor. We also validate this claim numerically under different Service distributions such as Exponential, shift plus Exponential and the heavy-tailed Weibull distribution and compare the mean latency to that of an unsplit-replicated system. We observe that the coded system outperforms the unsplit-replication system by at least 20% for all three distributions and all possible arrival request rates. Also, we analyze the tail latency for data centers memoryless servers. Furthermore, we consider the mean latency for an erasure coded system with low redundancy (fractional redundancy factor between 1 and 2), a scenario which is more pragmatic, given the storage constraints ([4]). However under this regime, we restrict ourselves to the special case of Exponential Service Time distribution and use the randomized load balancing policy namely batch-sampling. We obtain an upper bound on mean delay that depends on the order statistics of the queue lengths, which, we further smooth out via a discrete to continuous approximation.
Yang Wang - One of the best experts on this subject based on the ideXlab platform.
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A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times
arXiv: Networking and Internet Architecture, 2011Co-Authors: Quan-lin Li, Yang WangAbstract:In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as \emph{supermarket models}) with phase-type (PH) Service Times. Generalizing the Service Times to the phase-type distribution makes the analysis of the supermarket models more difficult and challenging than that of the Exponential Service Time case which has been extensively discussed in the literature. We first describe the supermarket model as a system of differential vector equations, and provide a doubly Exponential solution to the fixed point of the system of differential vector equations. Then we analyze the Exponential convergence of the current location of the supermarket model to its fixed point. Finally, we present numerical examples to illustrate our approach and show its effectiveness in analyzing the randomized load balancing schemes with non-Exponential Service requirements.
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PERFORM - A matrix-analytic solution for randomized load balancing models with PH Service Times
Performance Evaluation of Computer and Communication Systems. Milestones and Future Challenges, 2010Co-Authors: Quan-lin Li, Yang WangAbstract:In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as supermarket models ) with phase-type (PH) Service Times. Generalizing the Service Times to the phase-type distribution makes analysis of the supermarket models more difficult and challenging than that of the Exponential Service Time case which has been extensively discussed in the literature. We describe the supermarket model as a system of differential vector equations, provide a doubly Exponential solution to the fixed point of the system of differential vector equations, and analyze the Exponential convergence of the current location of the supermarket model to its fixed point.
