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Wojciech M. Kempa - One of the best experts on this subject based on the ideXlab platform.
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Queue-Size Distribution in Energy-Saving Model Based on Multiple Vacation Policy
Trends in Mathematics, 2020Co-Authors: Wojciech M. KempaAbstract:An energy-saving model based on the M/G/1/N-type finite-buffer Queue with independent and generally distributed repeated vacations is considered. Using the formula of total probability and the idea of embedded Markov chain, a system of integral equations for conditional transient Queue-Size distributions is found. A closed-form representation for the solution of the corresponding system built for Laplace transforms is obtained. Numerical example is attached as well.
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on transient Queue Size distribution in a finite buffer model with threshold waking and early setup policy
Performance Evaluation, 2020Co-Authors: Wojciech M. Kempa, Kamil KsiązekAbstract:Abstract A finite-buffer Queueing system with threshold waking and early setup policy is investigated. The arrival stream is governed by a Poisson process while service times are assumed to be generally distributed. The natural FIFO processing discipline is used. Every time when the system empties, a type-specific energy saving policy is initialized that is a mixture of the classical N-type policy and an early setup mechanism. Namely, if the level of accumulated messages reaches M ≤ N , a generally distributed setup time is started, during which the service station achieves full readiness for processing. If, at the completion epoch of the setup time, the state of the system (the number of accumulated messages) equals at least N , then the service begins immediately. Otherwise, the service station waits (being ready for processing) for the N th arrival. The representation for the Laplace transform of the transient Queue-Size distribution is obtained using the analytical approach based on the idea of embedded Markov chain, the formula of total probability, linear algebra and renewal theory. A numerical example and simulational study are attached.
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transient solution for the Queue Size distribution in a finite buffer model with general independent input stream and single working vacation policy
Applied Mathematical Modelling, 2018Co-Authors: Wojciech M. Kempa, Martyna KobielnikAbstract:Abstract A single-channel finite-buffer Queueing model with a general independent input stream of customers, exponential processing times and a working vacation policy is considered. Every time , when the server becomes idle, an exponentially distributed single working vacation period is being initialized, during which the processing is provided with another (slower) rate. After the completion of the vacation period, the service is being continued normally, with the original speed. Using the idea of an embedded Markov chain, the systems of Volterra-type integral equations for the time-dependent Queue-Size distributions, conditioned by the initial buffer state and related to each other, are built for models beginning the operation in normal and working vacation modes, separately. The solutions of the corresponding systems written for the Laplace transforms are obtained in compact forms using the linear algebraic approach. The numerical illustrative examples are attached as well.
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transient Queue Size distribution in a finite capacity Queueing system with server breakdowns and bernoulli feedback
AIP Conference Proceedings, 2017Co-Authors: Wojciech M. KempaAbstract:A finite-capacity Queueing system with server breakdowns is investigated, in which successive exponentially distributed failure-free times are followed by repair periods. After the processing a customer may either rejoin the Queue (feedback) with probability q, or definitely leave the system with probability 1 − q. The system of integral equations for transient Queue-Size distribution, conditioned by the initial level of buffer saturation, is build. The solution of the corresponding system written for Laplace transforms is found using the linear algebraic approach. The considered Queueing system can be successfully used in modelling production lines with machine failures, in which the parameter q may be considered as a typical fraction of items demanding corrections. Morever, this Queueing model can be applied in the analysis of real TCP/IP performance, where q stands for the fraction of packets requiring retransmission.
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a comprehensive study on the Queue Size distribution in a finite buffer system with a general independent input flow
Performance Evaluation, 2017Co-Authors: Wojciech M. KempaAbstract:Abstract A finite-buffer G I / M / 1 / N − type Queueing model is considered. The explicit formula for the Laplace transform of the transient Queue-Size distribution, conditioned by the number of packets present in the system at the starting time, is derived. The shape of the formula allows for finding the stationary distribution by applying the key renewal theorem. Moreover, the convergence rate of the transient Queue-Size distribution to the stationary one is determined with the constant value given explicitly. Numerical example is attached as well.
Yuan Zhong - One of the best experts on this subject based on the ideXlab platform.
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SIGMETRICS (Abstracts) - Improved Queue-Size Scaling for Input-Queued Switches via Graph Factorization
Abstracts of the 2019 SIGMETRICS Performance Joint International Conference on Measurement and Modeling of Computer Systems, 2019Co-Authors: Jiaming Xu, Yuan ZhongAbstract:This paper studies the scaling of the expected total Queue Size in an $n\times n$ input-Queued switch, as a function of both the load ρ and the system scale n. We provide a new class of scheduling policies under which the expected total Queue Size scales as Oleft( n(1-ρ)^-4/3 log left(\max\\frac1 1-ρ, n\ \right)\right)$, over all n and ρ
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improved Queue Size scaling for input Queued switches via graph factorization
Measurement and Modeling of Computer Systems, 2019Co-Authors: Jiaming Xu, Yuan ZhongAbstract:This paper studies the scaling of the expected total Queue Size in an $n\times n$ input-Queued switch, as a function of both the load ρ and the system scale n. We provide a new class of scheduling policies under which the expected total Queue Size scales as Oleft( n(1-ρ)^-4/3 log left(\max\\frac1 1-ρ, n\ \right)\right)$, over all n and ρ
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improved Queue Size scaling for input Queued switches via graph factorization
arXiv: Networking and Internet Architecture, 2019Co-Authors: Jiaming Xu, Yuan ZhongAbstract:This paper studies the scaling of the expected total Queue Size in an $n\times n$ input-Queued switch, as a function of both the load $\rho$ and the system scale $n$. We provide a new class of scheduling policies under which the expected total Queue Size scales as $O\left( n(1-\rho)^{-4/3} \log \left(\max\{\frac{1}{1-\rho}, n\}\right)\right)$, over all $n$ and $\rho<1$, when the arrival rates are uniform. This improves over the previously best-known scalings in two regimes: $O\left(n^{1.5}(1-\rho)^{-1} \log \frac{1}{1-\rho}\right)$ when $\Omega(n^{-1.5}) \le 1-\rho \le O(n^{-1})$ and $O\left(\frac{n\log n}{(1-\rho)^2}\right)$ when $1-\rho \geq \Omega(n^{-1})$. A key ingredient in our method is a tight characterization of the largest $k$-factor of a random bipartite multigraph, which may be of independent interest.
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on Queue Size scaling for input Queued switches
Stochastic Systems, 2016Co-Authors: Devavrat Shah, John N Tsitsiklis, Yuan ZhongAbstract:We study the optimal scaling of the expected total Queue Size in an n × n input-Queued switch, as a function of the number of ports n and the load factor ρ, which has been conjectured to be Θ(n/(1 − ρ)) (cf. [15]). In a recent work [16], the validity of this conjecture has been established for the regime where 1 − ρ = O(1/n2). In this paper, we make further progress in the direction of this conjecture. We provide a new class of scheduling policies under which the expected total Queue Size scales as O(n1.5(1 − ρ)−1 log (1/(1 − ρ))) when 1 − ρ = O(1/n). This is an improvement over the state of the art; for example, for ρ = 1 − 1/n the best known bound was O(n3), while ours is O(n2.5 log n).
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optimal Queue Size scaling in switched networks
Annals of Applied Probability, 2014Co-Authors: Devavrat Shah, Neil Walton, Yuan ZhongAbstract:We consider a switched (queuing) network in which there are constraints on which Queues may be served simultaneously; such networks have been used to effectively model input-Queued switches and wireless networks. The scheduling policy for such a network specifies which Queues to serve at any point in time, based on the current state or past history of the system. In the main result of this paper, we provide a new class of online scheduling policies that achieve optimal Queue-Size scaling for a class of switched networks including input-Queued switches. In particular, it establishes the validity of a conjecture (documented in Shah, Tsitsiklis and Zhong [Queueing Syst. 68 (2011) 375-384]) about optimal Queue-Size scaling for input-Queued switches.
Iti Saha Misra - One of the best experts on this subject based on the ideXlab platform.
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ICON - Queue Size analysis of QoS-aware Weighted Hybrid Packet Scheduling Scheme for BWA networks
2013 19th IEEE International Conference on Networks (ICON), 2013Co-Authors: Prasun Chowdhury, Iti Saha MisraAbstract:The increasing demand for multimedia communication over wireless platform necessitates the QoS-aware packet scheduling schemes in Broadband Wireless Access (BWA) networks. This paper deals with the analysis of Queue Size of QoS-aware Weighted Hybrid Packet Scheduling Schemes (WHPSS) for heterogeneous traffic classes in BWA networks. By categorizing the heterogeneous traffics of BWA networks into several classes (i.e. Class-1, Class-2, Class-3) depending upon their QoS requirement, we analyze the effect of Queue Size in WHPSS using three dimensional Continuous Time Markov Chain (CTMC) model. The analysis has been carried out with respect to the several performance parameters such as queuing delay, packet loss rate and throughput. This paper aims to observe the effect of Queue Size for each traffic flow to maximize the throughput of the network under the specified constraint of queuing delay and packet loss rate. Thus, the analysis helps to determine suitable Queue Size in the BWA network under varied traffic condition satisfying the required QoS constraints.
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Queue Size analysis of QoS-aware Weighted Hybrid Packet Scheduling Scheme for BWA networks
2013 19th IEEE International Conference on Networks (ICON), 2013Co-Authors: Prasun Chowdhury, Iti Saha MisraAbstract:The increasing demand for multimedia communication over wireless platform necessitates the QoS-aware packet scheduling schemes in Broadband Wireless Access (BWA) networks. This paper deals with the analysis of Queue Size of QoS-aware Weighted Hybrid Packet Scheduling Schemes (WHPSS) for heterogeneous traffic classes in BWA networks. By categorizing the heterogeneous traffics of BWA networks into several classes (i.e. Class-1, Class-2, Class-3) depending upon their QoS requirement, we analyze the effect of Queue Size in WHPSS using three dimensional Continuous Time Markov Chain (CTMC) model. The analysis has been carried out with respect to the several performance parameters such as queuing delay, packet loss rate and throughput. This paper aims to observe the effect of Queue Size for each traffic flow to maximize the throughput of the network under the specified constraint of queuing delay and packet loss rate. Thus, the analysis helps to determine suitable Queue Size in the BWA network under varied traffic condition satisfying the required QoS constraints.
K.e. Barner - One of the best experts on this subject based on the ideXlab platform.
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Median RED algorithm for congestion control
2004 IEEE International Conference on Acoustics Speech and Signal Processing, 2004Co-Authors: G.r. Arce, K.e. BarnerAbstract:The paper focuses on the Queue Size estimation problem in random early detection (RED) gateways. Queue Size estimation plays a critical role in gateways' packet dropping/marking decisions. Conventional RED gateways use exponentially weighted moving averages (EWMA) to estimate the Queue Size. These IIR filters require very small weights in order to avoid nonlinear instabilities and accommodate transient congestion. Small weights, however, lead to failure of gateways to track rapid Queue Size depletion closely and thus causes link under utilization. We use adaptive weighted median filters for Queue Size estimation and study the corresponding Queue dynamics. Simulation results show that the proposed algorithm provides better stability in Queue dynamics, greater network power, less global synchronization, and a fairer treatment to bursty traffic than the RED algorithm.
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RED gateway congestion control using median Queue Size estimates
IEEE Transactions on Signal Processing, 2003Co-Authors: G.r. Arce, K.e. BarnerAbstract:This paper focuses on the Queue Size estimation problem in random early detection (RED) gateways. Queue Size estimation plays a fundamental role in the congestion control dynamics of RED, as it determines gateways' awareness of network congestion, which in turn determines the packet dropping/marking decision. Conventional RED gateways use exponentially weighted moving averages (EWMA) to estimate the Queue Size. These infinite impulse response (IIR) filters require very small EWMA weights in order to effectively avoid nonlinear instabilities in RED and to filter out bursty increases in the Queue Size. While small EWMA weights enable gateways to accommodate transient congestion, they also lead to gateways' failure to closely track rapid Queue Size depletion and thus causes link under utilization. We investigate the use of simple nonlinear Queue Size estimators. In particular, we study the congestion control dynamics of a network where adaptive weighted median filters are used for Queue Size estimation by the gateways. Analytical results for the expected Queue Size in the steady state are derived. Under this new Queue Size estimation framework, design guidelines for the remaining RED parameters are provided. Simulation results show that the proposed algorithm provides greater network power, better prevention of global synchronization, and a fairer treatment to bursty traffic than the RED algorithm does.
Prasun Chowdhury - One of the best experts on this subject based on the ideXlab platform.
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ICON - Queue Size analysis of QoS-aware Weighted Hybrid Packet Scheduling Scheme for BWA networks
2013 19th IEEE International Conference on Networks (ICON), 2013Co-Authors: Prasun Chowdhury, Iti Saha MisraAbstract:The increasing demand for multimedia communication over wireless platform necessitates the QoS-aware packet scheduling schemes in Broadband Wireless Access (BWA) networks. This paper deals with the analysis of Queue Size of QoS-aware Weighted Hybrid Packet Scheduling Schemes (WHPSS) for heterogeneous traffic classes in BWA networks. By categorizing the heterogeneous traffics of BWA networks into several classes (i.e. Class-1, Class-2, Class-3) depending upon their QoS requirement, we analyze the effect of Queue Size in WHPSS using three dimensional Continuous Time Markov Chain (CTMC) model. The analysis has been carried out with respect to the several performance parameters such as queuing delay, packet loss rate and throughput. This paper aims to observe the effect of Queue Size for each traffic flow to maximize the throughput of the network under the specified constraint of queuing delay and packet loss rate. Thus, the analysis helps to determine suitable Queue Size in the BWA network under varied traffic condition satisfying the required QoS constraints.
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Queue Size analysis of QoS-aware Weighted Hybrid Packet Scheduling Scheme for BWA networks
2013 19th IEEE International Conference on Networks (ICON), 2013Co-Authors: Prasun Chowdhury, Iti Saha MisraAbstract:The increasing demand for multimedia communication over wireless platform necessitates the QoS-aware packet scheduling schemes in Broadband Wireless Access (BWA) networks. This paper deals with the analysis of Queue Size of QoS-aware Weighted Hybrid Packet Scheduling Schemes (WHPSS) for heterogeneous traffic classes in BWA networks. By categorizing the heterogeneous traffics of BWA networks into several classes (i.e. Class-1, Class-2, Class-3) depending upon their QoS requirement, we analyze the effect of Queue Size in WHPSS using three dimensional Continuous Time Markov Chain (CTMC) model. The analysis has been carried out with respect to the several performance parameters such as queuing delay, packet loss rate and throughput. This paper aims to observe the effect of Queue Size for each traffic flow to maximize the throughput of the network under the specified constraint of queuing delay and packet loss rate. Thus, the analysis helps to determine suitable Queue Size in the BWA network under varied traffic condition satisfying the required QoS constraints.
