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An End-to-End Probabilistic Network Calculus with Moment Generating Functions [article]

Markus Fidler
2006 arXiv   pre-print
This paper establishes a concise, probabilistic network calculus with moment generating functions.  ...  Recent research dispenses with the worst-case assumptions of network calculus to develop a probabilistic equivalent that benefits from statistical multiplexing.  ...  Liebeherr who in particular called my attention to the scaling of end-to-end performance bounds. Also, I want to specially thank A.  ... 
arXiv:cs/0507004v2 fatcat:6kiixpoonnckbpq2cte3rgr4l4

An End-to-End Probabilistic Network Calculus with Moment Generating Functions

Markus Fidler
2006 IEEE International Workshop on Quality of Service, IWQoS  
probabilistic network calculus with moment generating functions • Basic properties Jiang, Jiang, and Kong: Analysis of generalized stochastically bounded bursty traffic for communication networks, IEEE  ...  B t x − ≤ [ ] { } P ( ) P ( , ) ( , ) B t x A t S t x τ τ τ ⎡ ⎤ > = − > ⎣ ⎦ ∪ ≈ ≥ 7 (σ c (θ), ρ c (θ)) (σ c (θ), ρ c (θ)) (σ c (θ), ρ c (θ)) End-to-end through flow with statistically independent cross  ...  • Under stability the above product of MGFs decays quickly with τ • Infinite sums converge and can be solved using geometric series  ... 
doi:10.1109/iwqos.2006.250477 dblp:conf/iwqos/Fidler06 fatcat:ink2ra326reudgu3kooszlglei

An end-to-end stochastic network calculus with effective bandwidth and effective capacity

Kishore Angrishi
2013 Computer Networks  
The main contribution of this paper is to establish an end-to-end stochastic network calculus with the notions of effective bandwidth and effective capacity which provides efficient end-to-end delay and  ...  Network calculus is an elegant theory which uses envelopes to determine the worst-case performance bounds in a network.  ...  Conclusion We presented an end-to-end stochastic network calculus with effective bandwidth and effective capacity functions.  ... 
doi:10.1016/j.comnet.2012.09.003 fatcat:id4igmrp2zdkdnvpkmnc7g72ni

A Simple Proof of Linear Scaling of End-to-End Probabilistic Bounds using Network Calculus [article]

Kishore Angrishi, Sujaritha Vettukadu, Ulrich Killat
2012 arXiv   pre-print
In this paper, we present a simple general proof of computing end-to-end probabilistic performance measures using network calculus that grow linearly in the number of nodes (H).  ...  There have been many attempts to achieve a similar linear scaling for end-to-end probabilistic performance measures but with limited success.  ...  In [6] , authors have shown using the moment generating functions that the end-to-end probabilistic performance measures can scale linearly in the number of hops H traversed by the arrival traffic, if  ... 
arXiv:1110.1801v5 fatcat:fkzlkybsw5dxlhg66hrkvitdhy

A Min-Plus Calculus for End-to-End Statistical Service Guarantees

A. Burchard, J. Liebeherr, S.D. Patek
2006 IEEE Transactions on Information Theory  
This paper extends the network calculus to a probabilistic framework with statistical service guarantees.  ...  The problem of concatenating per-node statistical service curves to form an end-to-end (network) statistical service curve is explored.  ...  ACKNOWLEDGMENTS We thank Rene Cruz for pointing out problems in an earlier version of [9] . We also gratefully acknowledge valuable comments from Chengzhi Li.  ... 
doi:10.1109/tit.2006.880019 fatcat:thwgterru5aefd3ehw37wmjdye

Scaling properties of statistical end-to-end bounds in the network calculus

F. Ciucu, A. Burchard, J. Liebeherr
2006 IEEE Transactions on Information Theory  
It is shown that end-to-end 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.  ...  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.  ...  An earlier version of this paper was presented at the ACM Sigmetrics'05 conference, June  ... 
doi:10.1109/tit.2006.874380 fatcat:y7d3gv55g5aspl3anjcq3yopo4

A network service curve approach for the stochastic analysis of networks

Florin Ciucu, Almut Burchard, Jörg Liebeherr
2005 Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '05  
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.  ...  It is shown that end-to-end 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.  ...  As a remark, in the deterministic calculus, a network service curve leads to end-to-end bounds that scale with O (H), while summing up single-node results gives bounds that scale with O H 2 [15] .  ... 
doi:10.1145/1064212.1064251 dblp:conf/sigmetrics/CiucuBL05 fatcat:z66hplkukvdiplox7o4auipsea

A network service curve approach for the stochastic analysis of networks

Florin Ciucu, Almut Burchard, Jörg Liebeherr
2005 Performance Evaluation Review  
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.  ...  It is shown that end-to-end 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.  ...  As a remark, in the deterministic calculus, a network service curve leads to end-to-end bounds that scale with O (H), while summing up single-node results gives bounds that scale with O H 2 [15] .  ... 
doi:10.1145/1071690.1064251 fatcat:ousyvuqz2fakpgpnivbxhbygq4

A survey of envelope processes and their applications in quality of service provisioning

Shiwen Mao, Shivendra S. Panwar
2006 IEEE Communications Surveys and Tutorials  
Provisioning of quality of service (QoS) guarantees has become an increasingly important and challenging topic in the design of the current and the next-generation Internet.  ...  There is considerable research effort addressing QoS issues in resource-constrained access networks (such as wireless networks) and in the new multiprotocol label switching (MPLS) and peer-to-peer (P2P  ...  ACKNOWLEDGMENTS The authors are grateful to the editor, Dr. Martin Reisslein, and the seven anonymous reviewers whose comments improved the quality of this article.  ... 
doi:10.1109/comst.2006.253272 fatcat:66fiu2yosrhjdf3hpkbjygmeyy

A Calculus for End-to-end Statistical Service Guarantees [article]

A. Burchard, J. Liebeherr, S. D. Patek
2002 arXiv   pre-print
This paper addresses the problem of extending the network calculus to a probabilistic framework with statistical service guarantees.  ...  The deterministic network calculus offers an elegant framework for determining delays and backlog in a network with deterministic service guarantees to individual traffic flows.  ...  Acknowledgments We thank Rene Cruz for pointing out problems in earlier versions of the effective network service curve. The authors gratefully acknowledge the valuable comments from Chengzhi Li.  ... 
arXiv:cs/0205001v2 fatcat:zm5a5fb6fje43ex2wg5l7gicxa

On the recursive nature of end-to-end delay bound for heterogeneous wireless networks

Neda Petreska, Hussein Al-Zubaidy, Rudi Knorr, James Gross
2015 2015 IEEE International Conference on Communications (ICC)  
Fidler [11] investigates probabilistic performance guarantees of wireless fading channels using moment generating functionbased stochastic network calculus.  ...  Recent results [1] provided a methodology based on stochastic network calculus to obtain closed-form expressions describing the probabilistic end-to-end performance bounds for a multi-hop network of  ... 
doi:10.1109/icc.2015.7249278 dblp:conf/icc/PetreskaAKG15 fatcat:bqforr35mvhqpiyj5csxkfqone

IEEE/ACM Transactions on Networking

2010 IEEE/ACM Transactions on Networking  
Extending the deterministic network calculus to a probabilistic setting has shown to be challenging, in particular with respect to a multi-node analysis.  ...  Probabilistic extensions of the network calculus are commonly referred to as statistical network calculus.  ...  End-to-end delay bounds obtained with the network calculus are generally lower than the sum of the delay bounds at each node.  ... 
doi:10.1109/tnet.2010.2068170 fatcat:sdr2nfdoczcvbjff6crns6yxim

IEEE/ACM Transactions on Networking

2010 IEEE/ACM Transactions on Networking  
Extending the deterministic network calculus to a probabilistic setting has shown to be challenging, in particular with respect to a multi-node analysis.  ...  Probabilistic extensions of the network calculus are commonly referred to as statistical network calculus.  ...  End-to-end delay bounds obtained with the network calculus are generally lower than the sum of the delay bounds at each node.  ... 
doi:10.1109/tnet.2010.2086813 fatcat:qulncg7dvvefhi4rwkswji3gfi

Delay and Backlog Analysis for 60 GHz Wireless Networks

Guang Yang, Ming Xiao, James Gross, Hussein Al-Zubaidy, Yongming Huang
2016 2016 IEEE Global Communications Conference (GLOBECOM)  
In this work, we provide an alternative approach to derive a closed-form expression that characterizes the cumulative service process of the 60 GHz channel in terms of the moment generating function (MGF  ...  We then use this expression to derive probabilistic upper bounds on the backlog and delay that are experienced by a flow traversing this network, using results from the MGF-based network calculus.  ...  , where E [Y ] and M Y (θ) denote the expectation and the moment generating function (or the Laplace transform) of Y , respectively, and θ is an arbitrary nonnegative free parameter.  ... 
doi:10.1109/glocom.2016.7841725 dblp:conf/globecom/YangXGAH16 fatcat:kw37qgugrvcbffmxawxwaf4gle

Delay and Backlog Analysis for 60 GHz Wireless Networks [article]

Guang Yang, Ming Xiao, James Gross, Hussein Al-Zubaidy, Yongming Huang
2016 arXiv   pre-print
In this work, we provide an alternative approach to derive a closed-form expression that characterizes the cumulative service process of the 60 GHz channel in terms of the moment generating function (MGF  ...  We then use this expression to derive probabilistic upper bounds on the backlog and delay that are experienced by a flow traversing this network, using results from the MGF-based network calculus.  ...  , where E [Y ] and M Y (θ) denote the expectation and the moment generating function (or the Laplace transform) of Y , respectively, and θ is an arbitrary nonnegative free parameter.  ... 
arXiv:1608.00120v3 fatcat:r2wiy3tkq5esrpmijhwgqkjksu
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