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50
SCED+: Efficient Management of Quality of Service Guarantees
 In Proceedings of INFOCOM'98
, 1998
"... Current proposals for the provision of deterministic quality of service guarantees in integrated services networks require persession management of traffic flowing in network switches, raising scalability questions for practical implementation of high speed packet switching in large scale networks. ..."
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Cited by 57 (3 self)
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Current proposals for the provision of deterministic quality of service guarantees in integrated services networks require persession management of traffic flowing in network switches, raising scalability questions for practical implementation of high speed packet switching in large scale networks. At the same time, the endtoend delay bounds associated with current proposals can be overly conservative, limiting the utility of the bounds to guide efficient resource allocation. In this paper, we introduce SCED+, a network scheduling algorithm that yields scalable provision of tight deterministic endtoend delay bounds. These features are achieved through the use of aggregation and efficient statistical multiplexing between besteffort and guaranteed traffic. The SCED+ algorithm also supports statistical multiplexing between "guaranteed" traffic streams, providing tight endto end delay bounds for traffic streams which can tolerate nonzero packet loss rates. In order to facilitate ...
Performance Bounds for Flow Control Protocols
 IEEE/ACM Transactions on Networking
, 1998
"... In this paper, we discuss a simple conceptual framework for analyzing the flow of data in integrated services networks. The framework allows us to easily model and analyze the behavior of open loop, rate based flow control protocols, as well as closed loop, window based flow control protocols. Ce ..."
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Cited by 52 (3 self)
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In this paper, we discuss a simple conceptual framework for analyzing the flow of data in integrated services networks. The framework allows us to easily model and analyze the behavior of open loop, rate based flow control protocols, as well as closed loop, window based flow control protocols. Central to the framework is the concept of a service curve element, whose departure process is bounded between the convolution of the arrival process with a minimum service curve and the convolution of the arrival process with a maximum service curve. Service curve elements can model links, propagation delays, schedulers, regulators, and window based throttles. The mathematical properties of convolution allow us to easily analyze complex configurations of service curve elements to obtain bounds on endtoend performance. We demonstrate this by examples, and investigate tradeoffs between buffering requirements, throughput, and delay, for different flow control strategies. Keywords: Gua...
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 49 (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 39 (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).
Application of Network Calculus to Guaranteed Service Networks
, 1998
"... We use recent network calculus results to study some properties of lossless multiplexing as it may be used in guaranteed service networks. We call network calculus a set of results that apply minplus algebra to packet networks. We provide a simple proof that shaping a traffic stream to conform to a ..."
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Cited by 37 (6 self)
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We use recent network calculus results to study some properties of lossless multiplexing as it may be used in guaranteed service networks. We call network calculus a set of results that apply minplus algebra to packet networks. We provide a simple proof that shaping a traffic stream to conform to a burstiness constraint preserves the original constraints satisfied by the traffic stream We show how all ratebased packet schedulers can be modeled with a simple rate latency service curve. Then we define a general form of deterministic effective bandwidth and equivalent capacity. We find that call acceptance regions based on deterministic criteria (loss or delay) are convex, in contrast to statistical cases where it is the complement of the region which is convex. We thus find that, in general, the limit of the call acceptance region based on statistical multiplexing when the loss probability target tends to 0 may be strictly larger than the call acceptance region based on lossless mult...
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 33 (8 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.
On Service Guarantees for Input Buffered Crossbar Switches: A Capacity Decomposition Approach by Birkhoff and von Neumann
, 1999
"... Based on a decomposition result by Birkhoff and von Neumann for a doubly substochastic matrix, in this paper we propose a scheduling algorithm that is capable of providing service guarantees for inputbuffered crossbar switches. Our service guarantees are uniformly good for all nonuniform traffic, ..."
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Cited by 30 (3 self)
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Based on a decomposition result by Birkhoff and von Neumann for a doubly substochastic matrix, in this paper we propose a scheduling algorithm that is capable of providing service guarantees for inputbuffered crossbar switches. Our service guarantees are uniformly good for all nonuniform traffic, and thus imply 100% throughput. The offline computational complexity to identify the scheduling algorithm is O(N ) for an N \Theta N switch. Once the algorithm is identified, its online computational complexity is O(log N) and its online memory complexity is O(N log N). Neither framing nor internal speedup is required for our approach.
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 28 (2 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).
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 28 (2 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.
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 25 (15 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).