Generalized processor sharing queues

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.

[1]  W. R. Scheinhardt,et al.  Markov-modulated and feedback fluid queues , 1998 .

[2]  Donald F. Towsley,et al.  Statistical Analysis of Generalized Processor Sharing Scheduling Discipline , 1994, SIGCOMM.

[3]  C. Klüppelberg.  Subexponential distributions and integrated tails. , 1988 .

[4]  Sem Borst,et al.  A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows , 2003, Advances in Applied Probability.

[5]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[6]  D. Wischik.  Sample path large deviations for queues with many inputs , 2001 .

[7]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks-the multiple node case , 1993, IEEE INFOCOM '93 The Conference on Computer Communications, Proceedings.

[8]  Onno Boxma,et al.  Two coupled queues with heterogeneous traffic , 2001 .

[9]  Matthias Grossglauser,et al.  On the relevance of long-range dependence in network traffic , 1996, SIGCOMM '96.

[10]  Fabrice Guillemin,et al.  Analysis of the fluid weighted fair queueing system , 2003, Journal of Applied Probability.

[11]  Petteri Mannersalo.  Gaussian and multifractal processes in teletraffic theory , 2003 .

[12]  François Toutain,et al.  Decoupled generalized processor sharing: a fair queueing principle for adaptive multimedia applications , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[13]  Predrag R. Jelenkovic,et al.  Reduced Load Equivalence under Subexponentiality , 2004, Queueing Syst. Theory Appl..

[14]  Scott Shenker,et al.  Analysis and simulation of a fair queueing algorithm , 1989, SIGCOMM '89.

[15]  Gennady Samorodnitsky,et al.  Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models , 1998, Math. Oper. Res..

[16]  Q. Deng,et al.  Queues with regular variation , 2001 .

[17]  Gennady Samorodnitsky,et al.  Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues , 1999, Queueing Syst. Theory Appl..

[18]  Ilkka Norros.  Busy periods of fractional Brownian storage: a large deviations approach , 1999 .

[19]  Ilkka Norros,et al.  A storage model with self-similar input , 1994, Queueing Syst. Theory Appl..

[20]  P. Jelenkovic,et al.  Asymptotic loss probability in a finite buffer fluid queue with hetergeneous heavy-tailed on--off processes , 2003 .

[21]  V. Dumas,et al.  Asymptotic bounds for the fluid queue fed by sub-exponential On/Off sources , 2000, Advances in Applied Probability.

[22]  J. Cohen.  SOME RESULTS ON REGULAR VARIATION FOR DISTRIBUTIONS IN QUEUEING AND FLUCTUATION THEORY , 1973 .

[23]  Nick G. Duffield,et al.  Queueing at large resources driven by long-tailed M/G/∞-modulated processes , 1998, Queueing Syst. Theory Appl..

[24]  Isi Mitrani,et al.  Sharing a Processor Among Many Job Classes , 1980, JACM.

[25]  Anwar Elwalid,et al.  The Importance of Long-Range Dependence of VBR Video Traffic in ATM Traffic Engineering: Myths and Realities , 1996, SIGCOMM.

[26]  Walter Willinger,et al.  Self‐Similar Network Traffic: An Overview , 2002 .

[27]  Sally Floyd,et al.  Wide-area traffic: the failure of Poisson modeling , 1994 .

[28]  Atm Switches,et al.  BUFFER OVERFLOW ASYMPTOTICS FOR A BUFFER HANDLING MANY TRAFFIC SOURCES , 1996 .

[29]  Sandy L. Zabell,et al.  Large Deviations of the Sample Mean in General Vector Spaces , 1979 .

[30]  T. V. Lakshman,et al.  Fundamental Bounds and Approximations for ATM Multiplexers with Applications to Video Teleconferencing , 1995, IEEE J. Sel. Areas Commun..

[31]  Constantinos Kotopoulos,et al.  Buffer Occupancy and Delay Asymptotics in Multi-buffered Systems with Generalized Processor Sharing Handling a Large Number of Independent Traffic Streams ∗ , 2002 .

[32]  Venkat Anantharam,et al.  How large delays build up in a GI/G/1 queue , 1989, Queueing Syst. Theory Appl..

[33]  A. P. Zwart,et al.  Tail Asymptotics for the Busy Period in the GI/G/1 Queue , 2001, Math. Oper. Res..

[34]  A. Pakes.  ON THE TAILS OF WAITING-TIME DISTRIBUTIONS , 1975 .

[35]  Ilkka Norros,et al.  Most probable paths and performance formulae for buffers with gaussian input traffic , 2002, Eur. Trans. Telecommun..

[36]  John N. Tsitsiklis,et al.  Large deviations analysis of the generalized processor sharing policy , 1999, Queueing Syst. Theory Appl..

[37]  R. Núñez Queija,et al.  Processor-Sharing Models for Integrated-Services Networks , 2000 .

[38]  Ravi R. Mazumdar,et al.  Asymptotic analysis of GPS systems fed by heterogeneous long-tailed sources , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[39]  S. F. Yashkov,et al.  Processor-sharing queues: Some progress in analysis , 1987, Queueing Syst. Theory Appl..

[40]  D. Mitra,et al.  Novel techniques for the design and control of generalized processor sharing schedulers for multiple QoS classes , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[41]  Michel Mandjes,et al.  Large Deviations for Small Buffers: An Insensitivity Result , 2001, Queueing Syst. Theory Appl..

[42]  Predrag R. Jelenkovic,et al.  Induced burstiness in generalized processor sharing queues with long-tailed traffic flows , 2000 .

[43]  Sem C. Borst,et al.  Generalized processor sharing with heterogeneous traffic classes , 2001, PERV.

[44]  Ilkka Norros.  Most probable paths in Gaussian priority queues , .

[45]  O. Boxma,et al.  The M/M\1 queue in a heavy‐tailed random environment , 2000 .

[46]  Ivo J. B. F. Adan,et al.  A two-level traffic shaper for an on-off source , 2000, Perform. Evaluation.

[47]  Alexander L. Stolyar,et al.  Load characterization, overload prediction, and anomaly detection for voice over IP traffic , 2001, SIGMETRICS 2001.

[48]  Catherine Rosenberg,et al.  Tail Asymptotics for HOL Priority Queues Handling a Large Number of Independent Stationary Sources , 2002, Queueing Syst. Theory Appl..

[49]  Gustavo de Veciana,et al.  Bandwidth allocation for multiple qualities of service using generalized processor sharing , 1996, IEEE Trans. Inf. Theory.

[50]  Ravi Mazumdar,et al.  Cell loss asymptotics in buffers fed with a large number of independent stationary sources , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[51]  Onno J. Boxma,et al.  The busy period in the fluid queue , 1998, SIGMETRICS '98/PERFORMANCE '98.

[52]  Sem C. Borst,et al.  Generalized processor sharing with light-tailed and heavy-tailed input , 2003, TNET.

[53]  N. Bingham,et al.  Asymptotic properties of supercritical branching processes I: The Galton-Watson process , 1974, Advances in Applied Probability.

[54]  Jin Cao,et al.  A Poisson limit for buffer overflow probabilities , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[55]  G. Fayolle,et al.  Two coupled processors: The reduction to a Riemann-Hilbert problem , 1979 .

[56]  Michel Mandjes,et al.  Finding the Conjugate of Markov Fluid Processes , 1995 .

[57]  Michael Shalmon,et al.  A Tandem Network of Queues with Deterministic Service and Intermediate Arrivals , 1984, Oper. Res..

[58]  E. Willekens,et al.  Asymptotic expansions for waiting time probabilities in an M/G/1 queue with long-tailed service time , 1992, Queueing Syst. Theory Appl..

[59]  Vincent Hodgson,et al.  The Single Server Queue. , 1972 .

[60]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks-the single node case , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[61]  A. Stegeman,et al.  Heavy tails versus long‐range dependence in self‐similar network traffic , 2000 .

[62]  Zhi-Li Zhang,et al.  Large deviations and the generalized processor sharing scheduling for a multiple-queue system , 1998, Queueing Syst. Theory Appl..

[63]  Kavita Ramanan,et al.  Large deviation properties of data streams that share a buffer , 1998 .

[64]  Ward Whitt,et al.  Squeezing the Most Out of ATM , 1995, IEEE Trans. Commun..

[65]  Donald F. Towsley,et al.  Call admission control schemes under generalized processor sharing scheduling , 1997, Telecommun. Syst..

[66]  Ioannis Ch. Paschalidis.  Class-specific quality of service guarantees in multimedia communication networks , 1999, Autom..

[67]  J. Geluk.  Π-regular variation , 1981 .

[68]  A. P. Zwart,et al.  Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers , 2002, Queueing Syst. Theory Appl..

[69]  Sem Borst,et al.  Subexponential asymptotics of hybrid fluid and ruin models , 2003 .

[70]  A. Konheim,et al.  Processor-sharing of two parallel lines , 1981, Journal of Applied Probability.

[71]  N. K. Boots.  Rare event simulation in models with heavy-tailed random variables , 2002 .

[72]  Sem C. Borst,et al.  Asymptotic behavior of generalized processor sharing with long-tailed traffic sources , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[73]  P. Glynn,et al.  Logarithmic asymptotics for steady-state tail probabilities in a single-server queue , 1994, Journal of Applied Probability.

[74]  Debasis Mitra,et al.  Effective bandwidth of general Markovian traffic sources and admission control of high speed networks , 1993, TNET.

[75]  Dimitrios Stiliadis,et al.  Traffic scheduling in packet-switched networks: analysis, design, and implementation , 1996 .

[76]  Mark H. A. Davis.  Piecewise‐Deterministic Markov Processes: A General Class of Non‐Diffusion Stochastic Models , 1984 .

[77]  Ward Whitt,et al.  Effective bandwidths with priorities , 1998, TNET.

[78]  Debasis Mitra,et al.  Analysis and design of rate-based congestion control of high speed networks, I: stochastic fluid models, access regulation , 1991, Queueing Syst. Theory Appl..

[79]  Kiran M. Rege,et al.  A decomposition theorem and related results for the discriminatory processor sharing queue , 1994, Queueing Syst. Theory Appl..

[80]  Alan Weiss,et al.  An Introduction to Large Deviations for Communication Networks , 1995, IEEE J. Sel. Areas Commun..

[81]  Zhi-Li Zhang.  End-to-end support for statistical quality-of-service guarantees in multimedia networks , 1997 .

[82]  Walter Willinger,et al.  Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level , 1997, TNET.

[83]  WillingerWalter,et al.  On the self-similar nature of Ethernet traffic , 1993 .

[84]  Sem C. Borst,et al.  Heavy Tails: The Effect of the Service Discipline , 2002, Computer Performance Evaluation / TOOLS.

[85]  Sem C. Borst,et al.  GPS queues with heterogeneous traffic classes , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[86]  Ilkka Norros,et al.  A most probable path approach to queueing systems with general Gaussian input , 2002, Comput. Networks.

[87]  Hui Zhang,et al.  Hierarchical packet fair queueing algorithms , 1996, SIGCOMM '96.

[88]  Ilkka Norros,et al.  GPS schedulers and Gaussian traffic , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[89]  W. Sutton.  The Asymptotic Expansion of a Function Whose Operational Equivalent is Known , 1934 .

[90]  Predrag R. Jelenkovic,et al.  Finite buffer queue with generalized processor sharing and heavy-tailed input processes , 2002, Comput. Networks.

[91]  Marc Lelarge.  Asymptotic behavior of Generalized Processor Sharing queues under subexponential hypothesis , 2001 .

[92]  Jean C. Walrand,et al.  Effective bandwidths for multiclass Markov fluids and other ATM sources , 1993, TNET.

[93]  Michel Mandjes,et al.  Sample-path large deviations for tandem and priority queues with Gaussian inputs , 2005, math/0505214.

[94]  Michel Mandjes,et al.  Sample-path large deviations for generalized processor sharing queues with Gaussian inputs , 2005, Perform. Evaluation.

[95]  Sem C. Borst,et al.  Coupled processors with regularly varying service times , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[96]  Michel Mandjes,et al.  Exact overflow asymptotics for queues with many Gaussian inputs , 2003, Journal of Applied Probability.

[97]  R. Srikant,et al.  Many-Sources Delay Asymptotics with Applications to Priority Queues , 2001, Queueing Syst. Theory Appl..

[98]  A. Lazar,et al.  Asymptotic results for multiplexing subexponential on-off processes , 1999, Advances in Applied Probability.

[99]  Ilkka Norros,et al.  Approximate formulae for Gaussian priority queues , 2001 .

[100]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

[101]  Ward Whitt,et al.  Waiting-time tail probabilities in queues with long-tail service-time distributions , 1994, Queueing Syst. Theory Appl..

[102]  Sem C. Borst,et al.  A Reduced-Load Equivalence for Generalised Processor Sharing Networks with Long-Tailed Input Flows , 2002, Queueing Syst. Theory Appl..

[103]  J. Teugels,et al.  On the asymptotic behaviour of the distributions of the busy period and service time in M/G/1 , 1980, Journal of Applied Probability.

[104]  Kavita Ramanan,et al.  A Skorokhod Problem formulation and large deviation analysis of a processor sharing model , 1998, Queueing Syst. Theory Appl..

[105]  Sem C. Borst,et al.  Pna Probability, Networks and Algorithms the Asymptotic Workload Behavior of Two Coupled Queues , 2022 .

[106]  Moshe Sidi,et al.  Generalized Processor Sharing Networks with Exponentially Bounded Burstiness Arrivals , 1994, J. High Speed Networks.

[107]  Ilkka Norros.  Most Probable Path Techniques for Gaussian Queueing Systems , 2002, NETWORKING.

[108]  Onno Boxma,et al.  Boundary value problems in queueing system analysis , 1983 .

[109]  Sem C. Borst,et al.  Generalised processor sharing networks fed by heavy-tailed traffic flows , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[110]  Charles Knessl,et al.  Small and Large Time Scale Analysis of a Network Traffic Model , 2003, Queueing Syst. Theory Appl..

[111]  Sem C. Borst,et al.  Reduced-Load Equivalence and Induced Burstiness in GPS Queues with Long-Tailed Traffic Flows , 2003, Queueing Syst. Theory Appl..

[112]  R. Adler.  An introduction to continuity, extrema, and related topics for general Gaussian processes , 1990 .

[113]  Edgar Reich,et al.  On the Integrodifferential Equation of Takacs. II , 1958 .

[114]  Michel Mandjes,et al.  Large Deviations for Complex Buffer Architectures: The Short-Range Dependent Case , 2006 .

[115]  Michel Mandjes,et al.  Sample-path large deviations for tandem queues with Gaussian inputs , 2003 .

[116]  Walter Willinger,et al.  Proof of a fundamental result in self-similar traffic modeling , 1997, CCRV.

[117]  Kiran M. Rege,et al.  Queue-Length Distribution for the Discriminatory Processor-Sharing Queue , 1996, Oper. Res..

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

[119]  A. Arvidsson,et al.  On traffic models for TCP/IP , 1999 .

[120]  Sem C. Borst,et al.  User-level performance of elastic traffic in a differentiated-services environment , 2002, Perform. Evaluation.

[121]  Armand M. Makowski,et al.  On a reduced load equivalence for fluid queues under subexponentiality , 1999, Queueing Syst. Theory Appl..

[122]  Nick G. Duffield,et al.  Large deviations, the shape of the loss curve, and economies of scale in large multiplexers , 1995, Queueing Syst. Theory Appl..

[123]  Zhi-Li Zhang.  Large deviations and the generalized processor sharing scheduling for a two-queue system , 1997, Queueing Syst. Theory Appl..

[124]  Michel Mandjes,et al.  Generalized processor sharing queues with heterogeneous traffic classes , 2003, Advances in Applied Probability.

[125]  Nelson Luis Saldanha da Fonseca,et al.  On the performance of generalized processor sharing servers under long-range dependent traffic , 2002, Comput. Networks.

[126]  Samuli Aalto,et al.  Tandem fluid queues fed by homogeneous on-off sources , 2000, Oper. Res. Lett..

[127]  Debasis Mitra,et al.  Design of generalized processor sharing schedulers which statistically multiplex heterogeneous QoS classes , 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).

[128]  S. Resnick,et al.  Is network traffic approximated by stable Levy motion or fractional Brownian motion , 2002 .