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43
Stochastic Network Calculus
, 2008
"... A basic calculus is presented for stochastic service guarantee analysis in communication networks. Central to the calculus are two definitions, maximum(virtual)backlogcentric (m.b.c) stochastic arrival curve and stochastic service curve, which respectively generalize arrival curve and service c ..."
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Cited by 118 (22 self)
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A basic calculus is presented for stochastic service guarantee analysis in communication networks. Central to the calculus are two definitions, maximum(virtual)backlogcentric (m.b.c) stochastic arrival curve and stochastic service curve, which respectively generalize arrival curve and service curve in the deterministic network calculus framework. With m.b.c stochastic arrival curve and stochastic service curve, various basic results are derived under the (min, +) algebra for the general case analysis, which are crucial to the development of stochastic network calculus. These results include (i) superposition of flows, (ii) concatenation of servers, (iii) output characterization, (iv) perflow service under aggregation, and (v) stochastic backlog and delay guarantees. In addition, to perform independent case analysis, stochastic strict server is defined, which uses an ideal service process and an impairment process to characterize a server. The concept of stochastic strict server not only allows us to improve the basic results (i) – (v) under the independent case, but also provides a convenient way to find the stochastic service curve of a serve. Moreover, an approach is introduced to find the m.b.c stochastic arrival curve of a flow and the stochastic service curve of a server.
An endtoend probabilistic network calculus with moment generating functions
 in Proc. IEEE 14th International Workshop on Quality of Servic (IWQoS
"... Abstract — 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 probabi ..."
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Cited by 70 (5 self)
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Abstract — 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. I.
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 67 (13 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).
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 65 (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 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 54 (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).
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 46 (23 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 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.
A minplus calculus for endtoend statistical service guarantees
 IEEE TRANSACTION ON INFORMATION THEORY
, 2006
"... The network calculus offers an elegant framework for determining worstcase bounds on delay and backlog in a network. This paper extends the network calculus to a probabilistic framework with statistical service guarantees. The notion of a statistical service curve is presented as a probabilistic b ..."
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Cited by 38 (9 self)
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The network calculus offers an elegant framework for determining worstcase bounds on delay and backlog in a network. This paper extends the network calculus to a probabilistic framework with statistical service guarantees. The notion of a statistical service curve is presented as a probabilistic bound on the service received by an individual flow or an aggregate of flows. The problem of concatenating pernode statistical service curves to form an endtoend (network) statistical service curve is explored. Two solution approaches are presented that can each yield statistical network service curves. The first approach requires the availability of time scale bounds at which arrivals and departures at each node are correlated. The second approach considers a service curve that describes service over time intervals. Although the latter description of service is less general, it is argued that many practically relevant service curves may be compliant to this description.
Analysis of stochastic service guarantees in communication networks: A server model
 In Proc. of the International Workshop on Quality of Service (IWQoS 2005
, 2005
"... Abstract. The arrival curve has been used as a powerful concept for deterministic service guarantee analysis in communication networks. Since many applications and networks do not require or provide deterministic service guarantees, stochastic service guarantee analysis is becoming increasingly impo ..."
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Cited by 29 (10 self)
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Abstract. The arrival curve has been used as a powerful concept for deterministic service guarantee analysis in communication networks. Since many applications and networks do not require or provide deterministic service guarantees, stochastic service guarantee analysis is becoming increasingly important and has attracted a lot of research attention in recent years. For this, several probabilistic versions of the arrival curve have been proposed in the literature. They extend the concept of arrival curve to the stochastic case based on its traffic amount property. In this paper, we explore another property, called the virtual backlog property, of an arrival curve. Based on the virtual backlog property, we introduce the concept of virtualbacklogcentric (v.b.c) stochastic arrival curve to facilitate the analysis of stochastic service guarantees. We prove that a v.b.c stochastic arrival curve has a similar duality as a (deterministic) arrival curve. With the concept of v.b.c stochastic arrival curve, we derive results for stochastic service guarantee analysis of systems with the timevarying setting. In addition, we prove that many wellknown types of traffic can be readily represented using v.b.c stochastic arrival curves.
Statistical PerFlow Service Bounds in a Network with Aggregate Provisioning
 In Proceedings of IEEE Infocom 2003
, 2003
"... Scalability concerns of QoS implementations have stipulated service architectures where QoS is not provisioned separately to each flow, but instead to aggregates of flows. This paper determines stochastic bounds for the service experienced by a single flow when resources are managed for aggregates o ..."
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Cited by 23 (4 self)
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Scalability concerns of QoS implementations have stipulated service architectures where QoS is not provisioned separately to each flow, but instead to aggregates of flows. This paper determines stochastic bounds for the service experienced by a single flow when resources are managed for aggregates of flows and when the scheduling algorithms used in the network are not known. Using a recently developed statistical network calculus, perflow bounds can be calculated for backlog, delay, and the burstiness of output traffic.