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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 end-to-end 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 Analysis on Error Servers for Stochastic Network Calculus
"... Abstract—Network calculus is a recently developed theory dealing with queuing systems found in computer networks with focus on service guarantee analysis. In the current network calculus literature, the behavior of a server is typically modeled with the cumulative amount of service it successfully d ..."
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Abstract—Network calculus is a recently developed theory dealing with queuing systems found in computer networks with focus on service guarantee analysis. In the current network calculus literature, the behavior of a server is typically modeled with the cumulative amount of service it successfully delivers, and the successfulness of service delivery implies no error in the delivered service. However, there are many networks such as wireless networks, where, not only is the service prone to error due to multi-access contention and/or random error on the communication link, but different error handling methods may also be applied. In such cases, it is difficult to directly apply the existing network calculus results due to lack of server models taking error into account. In this paper, an error server model is proposed for stochastic network calculus, based on which, an analysis on error servers is performed. Particularly, the corresponding concatenation property is derived, which shows that under some general conditions, the tandem of error servers can be treated as an equivalent error server. In addition, to demonstrate the use and implication of the proposed error server model, performance bounds are derived and compared for a simple network. The study of the simple network shows that error handling may have significant impact on the performance bounds, and the proposed error server model can facilitate the analysis. I.
Stochastic Network Calculus for Performance Analysis of Internet Networks – An Overview and Outlook
"... Abstract—Stochastic network calculus is a theory for performance guarantee analysis of Internet networks. Originated in early 1990s, stochastic network calculus has its foundation on the min-plus convolution and max-plus convolution queueing principles. Although challenging, it has shown tremendous ..."
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Abstract—Stochastic network calculus is a theory for performance guarantee analysis of Internet networks. Originated in early 1990s, stochastic network calculus has its foundation on the min-plus convolution and max-plus convolution queueing principles. Although challenging, it has shown tremendous potential in dealing with queueing type problems encountered in Internet networks. By focusing on bounds, stochastic network calculus compliments the classical queueing theory. This paper provides an overview of stochastic network calculus from the queueing principle perspective and presents an outlook by discussing crucial yet still open challenges in the area. I.
Stochastic service curve and delay bound analysis: a single node case
- Computer Science from University of Kaiserslautern
, 2013
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End-to-end delay analysis for networks with partial assumptions of statistical independence
- IN PROCEEDINGS OF THE FOURTH INTERNATIONAL ICST CONFERENCE ON PERFORMANCE EVALUATION METHODOLOGIES AND TOOLS (VALUETOOLS), 2009
, 2009
"... By accounting for statistical properties of arrivals and service, stochastic formulations of the network calculus yield significantly tighter backlog and delay bounds than those obtained in a purely deterministic framework. This paper proposes a stochastic network calculus formulation which can acco ..."
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By accounting for statistical properties of arrivals and service, stochastic formulations of the network calculus yield significantly tighter backlog and delay bounds than those obtained in a purely deterministic framework. This paper proposes a stochastic network calculus formulation which can account for partial assumptions on statistical independence of arrivals and service across multiple network nodes. Scenarios where this can be useful are packet tandem networks with cross traffic and independent arrivals, where identical packet sizes create correlations across the nodes. As an application, the paper investigates the role of partial statistical independence on end-to-end delay bounds in four main scenarios arising by combining assumptions on the statistical independence of arrivals and packet sizes at different network nodes.
Fundamental calculus on generalized . . .
, 2008
"... 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 stochastic versions of deterministic traffic mode ..."
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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 stochastic versions of deterministic traffic models have been proposed in the literature. Unlike previous stochastic models that are based on the traffic amount property of an input process, we present another stochastic model, generalized Stochastically Bounded Burstiness (gSBB), which is based on the virtual backlog property of the input process. We show the advantages of this approach. We study the superposition of gSBB traffic, and set up the input-output relation. Under various service disciplines, we characterize the output process for each source and investigate the bounding probability for delay. Finally, we introduce a stochastic ordering monotonicity property of gSBB. With this property, we show that many well-known traffic models can be readily represented using the proposed gSBB model. These results set up the basis for a network calculus for gSBB traffic.
Selected Topics in Internet Service Guarantees
- IN TM8102 TRAFFIC ANALYSIS OF COMMUNICATION NETWORKS
, 2005
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doi:10.1155/2012/154038 Review Article Asymptotic Identity in Min-Plus Algebra: A Report on CPNS
, 2011
"... which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, wheremin-plus algebra plays a role. C ..."
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which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, wheremin-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Thoughmin-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions. 1.
