Impact of arrival burstiness on queue length: An infinitesimal perturbation analysis

Traffic burstiness has a significant impact on network performance. Burstiness can cause buffer overflows and packet drops and is particularly problematic in the context of small-buffer networks, which have been considered as a building block of the optical core infrastructure in the future Internet. To permit efficient operation of such networks, network traffic has to be “paced” by transmitting end-hosts or access links to avoid buffer overflows in the core. In this paper, we analyze the impact of traffic pacing on network performance using perturbation analysis. In particular, we study the impact of traffic burstiness on buffer occupancy of a tandem queueing network with infinite buffers. The input traffic is modeled as a marked point process which has the inter-arrival time and workload distributions containing scale parameters. Our results show that arrival traffic burstiness has a linear impact on the buffer occupancies. This linear relationship provides quantitative insight on the benefits of traffic pacing and thus provides understanding of how to improve the efficiency of small-buffer routers in the next-generation Internet.

[1]  Amit Aggarwal,et al.  Understanding the performance of TCP pacing , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[2]  Cheng-Shang Chang,et al.  Load balanced Birkhoff-von Neumann switches, part II: multi-stage buffering , 2002, Comput. Commun..

[3]  Ciro D'Apice,et al.  Queueing Theory , 2003, Operations Research.

[4]  R. Srikant,et al.  Impact of File Arrivals and Departures on Buffer Sizing in Core Routers , 2011, IEEE/ACM Transactions on Networking.

[5]  D. V. Lindley,et al.  The theory of queues with a single server , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  Cheng-Shang Chang,et al.  Load balanced Birkhoff-von Neumann switches, part I: one-stage buffering , 2002, Computer Communications.

[7]  G. Raina,et al.  Buffer sizes for large multiplexers: TCP queueing theory and instability analysis , 2005, Next Generation Internet Networks, 2005.

[8]  I. Adan,et al.  QUEUEING THEORY , 1978 .

[9]  Xi-Ren Cao,et al.  Infinitesimal and finite perturbation analysis for queueing networks , 1982, CDC 1982.

[10]  Paul Glasserman,et al.  Gradient Estimation Via Perturbation Analysis , 1990 .

[11]  Weibo Gong,et al.  Stochastic analysis for fluid queueing systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  Thomas Bonald,et al.  Statistical bandwidth sharing: a study of congestion at flow level , 2001, SIGCOMM.

[13]  R. M. Loynes,et al.  The stability of a queue with non-independent inter-arrival and service times , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[14]  Donald F. Towsley,et al.  Two-level stochastic fluid tandem queuing model for burst impact analysis , 2007, 2007 46th IEEE Conference on Decision and Control.

[15]  Weibo Gong,et al.  Perturbation Analysis for Stochastic Fluid Queueing Systems , 2002, Discret. Event Dyn. Syst..

[16]  Donald F. Towsley,et al.  Part II: control theory for buffer sizing , 2005, CCRV.

[17]  Tim Roughgarden,et al.  Routers with Very Small Buffers , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[18]  Scott Shenker,et al.  Observations on the dynamics of a congestion control algorithm: the effects of two-way traffic , 1991, SIGCOMM 1991.

[19]  Ronald W. Wolff,et al.  Stochastic Modeling and the Theory of Queues , 1989 .