Analysis of Stochastic Service Guarantees in Communication Networks: A Basic Calculus

A basic calculus is presented for stochastic service guarantee analysis in communication networks. Central to the calculus are two definitions, maximum-(virtual)-backlog-centric (m.b.c) stochastic arrival curve and stochastic service curve, which respectively generalize arrival curve and service curve in the deterministic network calculus framework. With m.b.c stochastic arrival curve and stochastic service curve, various basic results are derived under the (min, +) algebra for the general case analysis, which are crucial to the development of stochastic network calculus. These results include (i) superposition of flows, (ii) concatenation of servers, (iii) output characterization, (iv) per-flow service under aggregation, and (v) stochastic backlog and delay guarantees. In addition, to perform independent case analysis, stochastic strict server is defined, which uses an ideal service process and an impairment process to characterize a server. The concept of stochastic strict server not only allows us to improve the basic results (i) -- (v) under the independent case, but also provides a convenient way to find the stochastic service curve of a serve. Moreover, an approach is introduced to find the m.b.c stochastic arrival curve of a flow and the stochastic service curve of a server.

[1]  Kam Lee,et al.  Performance bounds in communication networks with variable-rate links , 1995, SIGCOMM '95.

[2]  Mukesh Taneja.  A service curve approach for quality of service management in integrated services networks , 1998 .

[3]  Florin Ciucu,et al.  A network service curve approach for the stochastic analysis of networks , 2005, SIGMETRICS '05.

[4]  Cheng-Shang Chang,et al.  Stability, queue length, and delay of deterministic and stochastic queueing networks , 1994, IEEE Trans. Autom. Control..

[5]  Chengzhi Li,et al.  A Network Calculus With Effective Bandwidth , 2007, IEEE/ACM Transactions on Networking.

[6]  Moshe Sidi,et al.  Performance and stability of communication networks via robust exponential bounds , 1993, TNET.

[7]  Richard F. Serfozo,et al.  Extreme Values of Queue Lengths in M/G/1 and GI/M/1 Systems , 1988, Math. Oper. Res..

[8]  Moshe Sidi,et al.  Stochastically bounded burstiness for communication networks , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[9]  Cheng-Shang Chang,et al.  Performance guarantees in communication networks , 2000, Eur. Trans. Telecommun..

[10]  Rene L. Cruz,et al.  A calculus for network delay, Part I: Network elements in isolation , 1991, IEEE Trans. Inf. Theory.

[11]  Edward W. Knightly,et al.  Second moment resource allocation in multi-service networks , 1997, SIGMETRICS '97.

[12]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[13]  Jean-Yves Le Boudec,et al.  Network Calculus: A Theory of Deterministic Queuing Systems for the Internet , 2001 .

[14]  Jean-Yves Le Boudec,et al.  Application of Network Calculus to Guaranteed Service Networks , 1998, IEEE Trans. Inf. Theory.

[15]  Geert Jan Olsder,et al.  Synchronization and Linearity: An Algebra for Discrete Event Systems , 1994 .

[16]  Almut Burchard,et al.  A Calculus for End-to-end Statistical Service Guarantees , 2002, ArXiv.

[17]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[18]  Cheng-Shang Chang,et al.  On the exponentiality of stochastic linear systems under the max-plus algebra , 1996, IEEE Trans. Autom. Control..

[19]  Rajeev Agrawal,et al.  Performance bonds for flow control protocols , 1999, TNET.

[20]  C. Anderson.  Extreme value theory for a class of discrete distributions with applications to some stochastic processes , 1970 .

[21]  Yong Liu,et al.  Conformance Study for Networks with Service Level Agreements , 2004 .

[22]  Yuming Jiang,et al.  Relationship between guaranteed rate server and latency rate server , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[23]  Yuming Jiang,et al.  Analysis of Stochastic Service Guarantees in Communication Networks: A Traffic Model , 2005 .

[24]  N. L. Lawrie,et al.  Comparison Methods for Queues and Other Stochastic Models , 1984 .

[25]  Chen-Khong Tham,et al.  Conformance analysis in networks with service level agreements , 2005, Comput. Networks.

[26]  Anujan Varma,et al.  Latency-rate servers: a general model for analysis of traffic scheduling algorithms , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[27]  Wu-chun Feng,et al.  A systematic approach for providing end-to-end probabilistic QoS guarantees , 2004, Proceedings. 13th International Conference on Computer Communications and Networks (IEEE Cat. No.04EX969).

[28]  Cheng-Shang Chang,et al.  A min, + system theory for constrained traffic regulation and dynamic service guarantees , 2002, TNET.

[29]  Harrick M. Vin,et al.  Generalized guaranteed rate scheduling algorithms: a framework , 1997, TNET.

[30]  Ward Whitt,et al.  Comparison methods for queues and other stochastic models , 1986 .

[31]  Rene L. Cruz,et al.  A calculus for network delay, Part II: Network analysis , 1991, IEEE Trans. Inf. Theory.

[32]  James F. Kurose,et al.  On computing per-session performance bounds in high-speed multi-hop computer networks , 1992, SIGMETRICS '92/PERFORMANCE '92.

[33]  Yong Liu,et al.  Stochastic Network Calculus , 2008 .

[34]  Dapeng Wu,et al.  Effective capacity: a wireless link model for support of quality of service , 2003, IEEE Trans. Wirel. Commun..

[35]  Yuming Jiang,et al.  Analysis of Stochastic Service Guarantees in Communication Networks: A Server Model , 2005, IWQoS.

[36]  Edward W. Knightly,et al.  Inter-class resource sharing using statistical service envelopes , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[37]  Rene L. Cruz,et al.  Quality of Service Guarantees in Virtual Circuit Switched Networks , 1995, IEEE J. Sel. Areas Commun..

[38]  Yuming Jiang,et al.  Analysis on generalized stochastically bounded bursty traffic for communication networks , 2002, 27th Annual IEEE Conference on Local Computer Networks, 2002. Proceedings. LCN 2002..

[39]  Wojciech Szpankowski,et al.  Maximum Queue Length and Waiting Time Revisited: Multserver G/G/c Queue , 1992, Probability in the Engineering and Informational Sciences.