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An EndtoEnd Probabilistic Network Calculus with Moment Generating Functions
, 2006
"... Network calculus is a minplus system theory for performance evaluation of queuing networks. Its elegance stems from intuitive convolution formulas for concatenation of deterministic servers. Recent research dispenses with the worstcase assumptions of network calculus to develop a probabilistic equi ..."
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Cited by 66 (5 self)
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Network calculus is a minplus system theory for performance evaluation of queuing networks. Its elegance stems from intuitive convolution formulas for concatenation of deterministic servers. Recent research dispenses with the worstcase assumptions of network calculus to develop a probabilistic equivalent that benefits from statistical multiplexing. Significant achievements have been made, owing for example to the theory of effective bandwidths, however, the outstanding scalability set up by concatenation of deterministic servers has not been shown. This paper establishes a concise, probabilistic network calculus with moment generating functions. The presented work features closedform, endtoend, probabilistic performance bounds that achieve the objective of scaling linearly in the number of servers in series. The consistent application of moment generating functions put forth in this paper utilizes independence beyond the scope of current statistical multiplexing of flows. A relevant additional gain is demonstrated for tandem servers with independent crosstraffic.
Theories and Models for Internet Quality of Service
, 2002
"... We survey recent advances in theories and models for Internet Quality of Service (QoS). We start with the theory of network calculus, which lays the foundation for support of deterministic performance guarantees in networks, and illustrate its applications to integrated services, differentiated serv ..."
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Cited by 64 (1 self)
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We survey recent advances in theories and models for Internet Quality of Service (QoS). We start with the theory of network calculus, which lays the foundation for support of deterministic performance guarantees in networks, and illustrate its applications to integrated services, differentiated services, and streaming media playback delays. We also present mechanisms and architecture for scalable support of guaranteed services in the Internet, based on the concept of a stateless core. Methods for scalable control operations are also briefly discussed. We then turn our attention to statistical performance guarantees, and describe several new probabilistic results that can be used for a statistical dimensioning of differentiated services. Lastly, we review recent proposals and results in supporting performance guarantees in a best effort context. These include models for elastic throughput guarantees based on TCP performance modeling, techniques for some quality of service differentiation without access control, and methods that allow an application to control the performance it receives, in the absence of network support.
A Network Calculus with Effective Bandwidth
, 2003
"... We present a statistical network calculus in a setting where both arrivals and service are specified interms of probabilistic bounds. We provide explicit bounds on delay, backlog, and output burstiness in a network. By formulating wellknown effective bandwidth expressions in terms of envelope func ..."
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Cited by 61 (10 self)
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We present a statistical network calculus in a setting where both arrivals and service are specified interms of probabilistic bounds. We provide explicit bounds on delay, backlog, and output burstiness in a network. By formulating wellknown effective bandwidth expressions in terms of envelope functions,we are able to apply our calculus to a wide range of traffic source models, including Fractional Brownian Motion. We present probabilistic lower bounds on the service for three scheduling algorithms: Static Priority (SP), Earliest Deadline First (EDF), and Generalized Processor Sharing (GPS).
A network service curve approach for the stochastic analysis of networks
 IN PROCEEDINGS OF ACM SIGMETRICS
, 2005
"... The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the ne ..."
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Cited by 51 (3 self)
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The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical endtoend delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that endtoend performance measures computed with a network service curve are bounded by O (H log H), where H is the number of nodes traversed by a flow. Using currently available techniques that compute endtoend bounds by adding single node results, the corresponding performance measures are bounded by O(H³).
Statistical Profilingbased Techniques for Effective Power Provisioning in Data Centers
"... Abstract: Current capacity planning practices based on heavy overprovisioning of power infrastructure hurt (i) the operational costs of data centers as well as (ii) the computational work they can support. We explore a combination of statistical multiplexing techniques to improve the utilization of ..."
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Cited by 50 (6 self)
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Abstract: Current capacity planning practices based on heavy overprovisioning of power infrastructure hurt (i) the operational costs of data centers as well as (ii) the computational work they can support. We explore a combination of statistical multiplexing techniques to improve the utilization of the power hierarchy within a data center. At the highest level of the power hierarchy, we employ controlled underprovisioning and overbooking of power needs of hosted workloads. At the lower levels, we introduce the novel notion of soft fuses to flexibly distribute provisioned power among hosted workloads based on their needs. Our techniques are built upon a measurementdriven profiling and prediction framework to characterize key statistical properties of the power needs of hosted workloads and their aggregates. We characterize the gains in terms of the amount of computational work (CPU cycles) per provisioned unit of power – Computation per Provisioned Watt (CPW). Our technique is able to double the CPW offered by a Power Distribution Unit (PDU) running the ecommerce benchmark TPCW compared to conventional provisioning practices. Overbooking the PDU by 10 % based on tails of power profiles yields a further improvement of 20%. Reactive techniques implemented on our Xen VMMbased servers dynamically modulate CPU DVFS states to ensure power draw below the limits imposed by soft fuses. Finally, information captured in our profiles also provide ways of controlling application performance degradation despite overbooking. The 95 th percentile of TPCW session response time only grew from 1.59 sec to 1.78 sec—a degradation of 12%.
A Framework for Guaranteeing Statistical QoS
, 2001
"... Continuousmedia traffic (i.e., audio and video) can tolerate some loss but has rigid delay constraints. A natural QoS requirement for a continuousmedia connection is a prescribed limit on the fraction of traffic that exceeds an endtoend delay constraint. We propose and analyze a framework that p ..."
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Cited by 44 (1 self)
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Continuousmedia traffic (i.e., audio and video) can tolerate some loss but has rigid delay constraints. A natural QoS requirement for a continuousmedia connection is a prescribed limit on the fraction of traffic that exceeds an endtoend delay constraint. We propose and analyze a framework that provides such a statistical QoS guarantee to traffic in a packetswitched network. Providing statistical guarantees in a network is a notoriously difficult problem because traffic flows lose their original statistical characterizations at the outputs of queues. Our scheme uses bufferless statistical multiplexing combined with cascaded leakybuckets for smoothing and traffic contracting. This scheme along with a novel method for bounding the loss probability gives a tractable framework for providing endtoend statistical QoS. Using MPE(] video traces, we present numerical resuits that compare the connectioncarrying capacity of our scheme with that of guaranteed service schemes (i.e., no loss) using (]PS and RCS. Our numerical work indicates that our scheme can support significantly more connections without introducing significant traffic loss.
Scaling Properties of Statistical Endtoend Bounds in the Network Calculus
"... The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the n ..."
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Cited by 43 (21 self)
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The stochastic network calculus is an evolving new methodology for backlog and delay analysis of networks that can account for statistical multiplexing gain. This paper advances the stochastic network calculus by deriving a network service curve, which expresses the service given to a flow by the network as a whole in terms of a probabilistic bound. The presented network service curve permits the calculation of statistical endtoend delay and backlog bounds for broad classes of arrival and service distributions. The benefits of the derived service curve are illustrated for the exponentially bounded burstiness (EBB) traffic model. It is shown that endtoend performance measures computed with a network service curve are bounded by O (H log H), where H is the number of nodes traversed by a flow. Using currently available techniques, which compute endtoend bounds by adding single node results, the corresponding performance measures are bounded by O (H³).
A Calculus for Endtoend Statistical Service Guarantees
, 2001
"... The deterministic network calculus offers an elegant framework for determining delays and backlog in a network with deterministic service guarantees to individual traffic flows. A drawback of the deterministic network calculus is that it only provides worstcase bounds. Here we present a network cal ..."
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Cited by 38 (6 self)
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The deterministic network calculus offers an elegant framework for determining delays and backlog in a network with deterministic service guarantees to individual traffic flows. A drawback of the deterministic network calculus is that it only provides worstcase bounds. Here we present a network calculus for statistical service guarantees, which can exploit the statistical multiplexing gain of sources. We introduce the notion of an effective service curve as a probabilistic bound on the service received by an individual flw, and construct an effective service curve for a network where capacities are provisioned exclusively to aggregates of flows. Numerical examples demonstrate that the calculus is able to extract a significant amount of multiplexing gain in networks with a large number of flows.
Application of Network Calculus to General Topologies Using TurnProhibition
 IEEE/ACM Transactions on Networking
, 2002
"... Network calculus is known to apply in general only to feedforward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. In this paper, we address the problem of using network calculus in networks of arbitrary topology. For this purpose, we introduce a no ..."
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Cited by 37 (3 self)
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Network calculus is known to apply in general only to feedforward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. In this paper, we address the problem of using network calculus in networks of arbitrary topology. For this purpose, we introduce a novel graphtheoretic algorithm, called turnprohibition (TP), that breaks all the cycles in a network and, thus, prevents any interdependence between flows. We prove that the TPalgorithm prohibits the use of at most 1/3 of the total number turns in a network, for any network topology. Using analysis and simulation, we show that the TPalgorithm significantly outperforms other approaches for breaking cycles, such as the spanning tree and up/down routing algorithms, in terms of network utilization and delay bounds. Our simulation results also show that the network utilization achieved with the TPalgorithm is within a factor of two of the maximum theoretical network utilization, for networks of up to 50 nodes of degree four. Thus, in many practical cases, the restriction of network calculus to feedforward routing networks may not represent a too significant limitation.