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19
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.
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).
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 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 35 (5 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.
A Calculus for Stochastic QoS Analysis
, 2006
"... The issue of Quality of Service (QoS) performance analysis in packetswitched networks has drawn a lot of attention in the networking community. There is a lot of work including an elegant theory under the name of network calculus, which focuses on analysis of deterministic worst case QoS performanc ..."
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Cited by 9 (7 self)
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The issue of Quality of Service (QoS) performance analysis in packetswitched networks has drawn a lot of attention in the networking community. There is a lot of work including an elegant theory under the name of network calculus, which focuses on analysis of deterministic worst case QoS performance bounds. In the meantime, researchers have studied stochastic QoS performance for specific schedulers. However, most previous works on deterministic QoS analysis or stochastic QoS analysis have only considered a server that provides deterministic service, i.e. deterministically bounded rate service. Few have considered the behavior of a stochastic server that provides input flows with variable rate service, for example wireless links. In this paper, we propose a stochastic network calculus to analyze the endtoend stochastic QoS performance of a system with stochastically bounded input traffic over a series of deterministic and stochastic servers. We also prove that a server serving an aggregate of flows can be regarded as a stochastic server for individual flows within the aggregate. Based on this, the proposed framework is further applied to analyze perflow stochastic QoS performance under aggregate scheduling.
Scaling Properties in the Stochastic Network Calculus
, 2007
"... Modern networks have become increasingly complex over the past years in terms of control algorithms, applications and service expectations. Since classical theories for the analysis of telephone networks were found inadequate to cope with these complexities, new analytical tools have been conceived ..."
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Cited by 6 (2 self)
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Modern networks have become increasingly complex over the past years in terms of control algorithms, applications and service expectations. Since classical theories for the analysis of telephone networks were found inadequate to cope with these complexities, new analytical tools have been conceived as of late. Among these, the stochastic network calculus has given rise to the optimism that it can emerge as an elegant mathematical tool for assessing network performance. This thesis argues that the stochastic network calculus can provide new analytical insight into the scaling properties of network performance metrics. In this sense it is shown that endtoend delays grow as Θ(H log H) in the number of network nodes H, as opposed to the Θ(H) order of growth predicted by other theories under simplifying assumptions. It is also shown a comparison between delay bounds obtained with the stochastic network calculus and exact results available in some productform queueing networks. The main technical contribution of this thesis is a construction of a statistical network service curve that expresses the service given to a flow by a network as if the flow traversed a single node only. This network service curve enables the proof of the O(H log H) scaling
Connection Admission Control for Flow Level QoS in Bufferless Models
, 2005
"... Admission control algorithms used in acces networks for multiplexed voice sources are typically based on aggregated system characteristics, such as aggregate loss probability ..."
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Cited by 5 (0 self)
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Admission control algorithms used in acces networks for multiplexed voice sources are typically based on aggregated system characteristics, such as aggregate loss probability
An Estimator of Regulator Parameters in a Stochastic Setting
, 2005
"... This paper develops a new network provisioning and resource allocation scheme. We introduce the concept of the effective burstiness curve (EBC), which is defined as a percentile of the maximum burstiness curve. For a fixed service rate, EBC represents the size of a buffer for which the probability ..."
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Cited by 1 (0 self)
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This paper develops a new network provisioning and resource allocation scheme. We introduce the concept of the effective burstiness curve (EBC), which is defined as a percentile of the maximum burstiness curve. For a fixed service rate, EBC represents the size of a buffer for which the probability of buffer overflow is arbitrarily small. We show that EBC is a convex nonincreasing function of the service rate. We also introduce the empirical effective burstiness curve (EEBC), an estimator of EBC, which can be obtained with a waterfilling algorithm. For discrete queue size, EEBC can be evaluated with a recursive algorithm. The technique is applied to MPEG4 encoded video traces.