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

2006
*
arXiv
*
pre-print

This paper establishes a concise,

arXiv:cs/0507004v2
fatcat:6kiixpoonnckbpq2cte3rgr4l4
*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. ...##
###
An End-to-End Probabilistic Network Calculus with Moment Generating Functions

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 ...

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

2013
*
Computer Networks
*

The main contribution of this paper is

doi:10.1016/j.comnet.2012.09.003
fatcat:id4igmrp2zdkdnvpkmnc7g72ni
*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*. ...##
###
A Simple Proof of Linear Scaling of End-to-End Probabilistic Bounds using Network Calculus
[article]

2012
*
arXiv
*
pre-print

In this paper, we present a simple

arXiv:1110.1801v5
fatcat:fkzlkybsw5dxlhg66hrkvitdhy
*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 ...##
###
A Min-Plus Calculus for End-to-End Statistical Service Guarantees

2006
*
IEEE Transactions on Information Theory
*

This paper extends the

doi:10.1109/tit.2006.880019
fatcat:thwgterru5aefd3ehw37wmjdye
*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. ...##
###
Scaling properties of statistical end-to-end bounds in the network calculus

2006
*
IEEE Transactions on Information Theory
*

It is shown that

doi:10.1109/tit.2006.874380
fatcat:y7d3gv55g5aspl3anjcq3yopo4
*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 ...##
###
A network service curve approach for the stochastic analysis of networks

2005
*
Proceedings of the 2005 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '05
*

This paper advances the stochastic

doi:10.1145/1064212.1064251
dblp:conf/sigmetrics/CiucuBL05
fatcat:z66hplkukvdiplox7o4auipsea
*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] . ...##
###
A network service curve approach for the stochastic analysis of networks

2005
*
Performance Evaluation Review
*

This paper advances the stochastic

doi:10.1145/1071690.1064251
fatcat:ousyvuqz2fakpgpnivbxhbygq4
*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] . ...##
###
A survey of envelope processes and their applications in quality of service provisioning

2006
*
IEEE Communications Surveys and Tutorials
*

Provisioning of quality of service (QoS) guarantees has become

doi:10.1109/comst.2006.253272
fatcat:66fiu2yosrhjdf3hpkbjygmeyy
*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. ...##
###
A Calculus for End-to-end Statistical Service Guarantees
[article]

2002
*
arXiv
*
pre-print

This paper addresses the problem of extending the

arXiv:cs/0205001v2
fatcat:zm5a5fb6fje43ex2wg5l7gicxa
*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. ...##
###
On the recursive nature of end-to-end delay bound for heterogeneous wireless networks

2015
*
2015 IEEE International Conference on Communications (ICC)
*

Fidler [11] investigates

doi:10.1109/icc.2015.7249278
dblp:conf/icc/PetreskaAKG15
fatcat:bqforr35mvhqpiyj5csxkfqone
*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 ...##
###
IEEE/ACM Transactions on Networking

2010
*
IEEE/ACM Transactions on Networking
*

Extending the deterministic

doi:10.1109/tnet.2010.2068170
fatcat:sdr2nfdoczcvbjff6crns6yxim
*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. ...##
###
IEEE/ACM Transactions on Networking

2010
*
IEEE/ACM Transactions on Networking
*

Extending the deterministic

doi:10.1109/tnet.2010.2086813
fatcat:qulncg7dvvefhi4rwkswji3gfi
*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. ...##
###
Delay and Backlog Analysis for 60 GHz Wireless Networks

2016
*
2016 IEEE Global Communications Conference (GLOBECOM)
*

In this work, we provide

doi:10.1109/glocom.2016.7841725
dblp:conf/globecom/YangXGAH16
fatcat:kw37qgugrvcbffmxawxwaf4gle
*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. ...##
###
Delay and Backlog Analysis for 60 GHz Wireless Networks
[article]

2016
*
arXiv
*
pre-print

In this work, we provide

arXiv:1608.00120v3
fatcat:r2wiy3tkq5esrpmijhwgqkjksu
*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. ...
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