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Network calculus and queueing theory: two sides of one coin
 in Proc. 4th International Conference on Performance Evaluation Methodologies and Tools (VALUETOOLS
, 2009
"... Network calculus is a theory dealing with queueing type problems encountered in computer networks, with particular focus on quality of service guarantee analysis. Queueing theory is the mathematical study of queues, proven to be applicable to a wide area of problems, generally concerning about the ( ..."
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Network calculus is a theory dealing with queueing type problems encountered in computer networks, with particular focus on quality of service guarantee analysis. Queueing theory is the mathematical study of queues, proven to be applicable to a wide area of problems, generally concerning about the (average) quantities in an equilibrium state. Since both network calculus and queueing theory are analytical tools for studying queues, a question arises naturally as is if and where network calculus and queueing theory meet. In this paper, we explore queueing principles that underlie network calculus and exemplify their use. Particularly, based on the network calculus queueing principles, we show that for GI/GI/1, similar inequalities in the theory of queues can be derived. In addition, we prove that the endtoend performance of a tandem network is independent of the order of servers in the network even under some general settings. Through these, we present a network calculus perspective on queues and relate network calculus to queueing theory. 1.
An endtoend stochastic network calculus with effective bandwidth and effective capacity
 Comput. Netw
, 2013
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A Temporal Network Calculus Approach to Service Guarantee Analysis of Stochastic Networks
"... Many computer networks such as wireless networks are stochastic in nature. In order to perform performance guarantee analysis of such networks, a theory, called stochastic network calculus, has evolved. In the stochastic network calculus literature, most results are based on spacedomain traffic and ..."
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Many computer networks such as wireless networks are stochastic in nature. In order to perform performance guarantee analysis of such networks, a theory, called stochastic network calculus, has evolved. In the stochastic network calculus literature, most results are based on spacedomain traffic and service models where the arrival process and the service process are respectively characterized by the cumulative amount of arrival and the cumulative amount of service. Recently, a novel approach called timedomain approach to stochastic network calculus (SNC) has been proposed, where the traffic and service models are defined based on the cumulative interarrival times and the cumulative service times respectively. In this paper, we concretize the timedomain SNC traffic and service models by linking some wellknown stochastic processes to them. In addition, we exemplify the temporal analysis approach by investigating the delay performance of a GilbertElliott channel. The results show that the delay bound can be improved under the independence condition. Furthermore, a comparison between the temporal and the spatial analysis results reveals that the two analytical approaches essentially yield close results. 1.
A Node Operating Point Approach for Stochastic Analysis with Network Calculus
"... Abstract — The operating point of a node is an interesting concept from large deviations theory which defines the asymptotic buffer occupancy distribution at the node. The effective bandwidth function evolved out of large deviations theory, establishes the crucial connection between the node operati ..."
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Abstract — The operating point of a node is an interesting concept from large deviations theory which defines the asymptotic buffer occupancy distribution at the node. The effective bandwidth function evolved out of large deviations theory, establishes the crucial connection between the node operating point and the theory of statistical network calculus. This paper uses the concepts of effective bandwidth and effective capacity to describe independent stochastic arrival and service processes, respectively, and to identify node operating point to perform stochastic analysis with network calculus. The two main advantages of the approach used in this paper are: (i) the use of operating point to perform stochastic analysis provides insight into the queue dynamics, and (ii) the use of effective bandwidth and effective capacity functions within the framework of statistical network calculus allows efficient evaluation of performance bounds. Index Terms — network calculus, effective bandwidth, effective capacity, QoS, node operating point, large deviations theory I.
A Network Calculus Approach to Delay Evaluation of IEEE 802.11 DCF
"... Abstract—Stochastic network calculus is an evolving theory for network performance guarantee analysis. Although many theoretical results of this theory have been developed, there still lack applicable examples to demonstrate how it may be used. This paper exemplifies applying stochastic network calc ..."
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Abstract—Stochastic network calculus is an evolving theory for network performance guarantee analysis. Although many theoretical results of this theory have been developed, there still lack applicable examples to demonstrate how it may be used. This paper exemplifies applying stochastic network calculus to delay analysis of the IEEE 802.11 distributed coordination function (DCF). Analyzing and obtaining the stochastic characteristics of the single packet service time is the primary task. Then the stochastic behavior of the DCF is characterized by a timedomain server model, which describes the cumulative service time provided to an arrival flow using a probabilistic bound. Based on this server model, we obtain delay bounds for different arrival processes. In addition, the delay bounds also take buffer size into account. The analytical bounds are further discussed using numerical results. Through these, we present a stochastic network calculus approach to delay evaluation of the DCF. Index Terms—Stochastic network calculus, IEEE 802.11 DCF, Stochastic service curve, Delay bound