Adversarial queuing theory

We consider packet routing when packets are injected continuously into a network. We develop an adversarial theory of queuing aimed at addressing some of the restrictions inherent in probabilistic analysis and queuing theory based on time-invariant stochastic generation. We examine the stability of queuing networks and policies when the arrival process is adversarial, and provide some preliminary results in this direction. Our approach sheds light on various queuing policies in simple networks, and paves the way for a systematic study of queuing with few or no probabilistic assumptions.

[1]  Baruch Awerbuch,et al.  Universal stability results for greedy contention-resolution protocols , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[2]  Lisa Zhang,et al.  The effects of temporary sessions on network performance , 2000, SODA '00.

[3]  R. Pemantle,et al.  Moment conditions for a sequence with negative drift to be uniformly bounded in Lr , 1999, math/0404093.

[4]  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.

[5]  Frank Thomson Leighton,et al.  Average case analysis of greedy routing algorithms on arrays , 1990, SPAA '90.

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

[7]  J. R. Perkins,et al.  Stable, distributed, real-time scheduling of flexible manufacturing/assembly/diassembly systems , 1989 .

[8]  Rafail Ostrovsky,et al.  Universal O(congestion + dilation + log1+εN) local control packet switching algorithms , 1997, STOC '97.

[9]  Jean Walrand An introduction to queuing networks , 1988 .

[10]  Alan M. Frieze,et al.  A general approach to dynamic packet routing with bounded buffers , 2001, JACM.

[11]  Yuval Rabani,et al.  Distributed packet switching in arbitrary networks , 1996, STOC '96.

[12]  John N. Tsitsiklis,et al.  The efficiency of greedy routing in hypercubes and butterflies , 1991, SPAA '91.

[13]  M. Bramson Instability of FIFO Queueing Networks , 1994 .

[14]  Michael Mitzenmacher,et al.  Bounds on the greedy routing algorithm for array networks , 1994, SPAA '94.

[15]  Sean P. Meyn,et al.  Stability and convergence of moments for multiclass queueing networks via fluid limit models , 1995, IEEE Trans. Autom. Control..

[16]  David Gamarnik Stability of adversarial queues via fluid models , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[17]  M. Bramson Instability of FIFO Queueing Networks with Quick Service Times , 1994 .

[18]  Gideon Weiss,et al.  Stability and Instability of Fluid Models for Reentrant Lines , 1996, Math. Oper. Res..

[19]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[20]  Baruch Awerbuch,et al.  Universal-stability results and performance bounds for greedy contention-resolution protocols , 2001, JACM.

[21]  Mor Harchol-Balter,et al.  Bounding delays in packet-routing networks , 1995, STOC '95.

[22]  Ashish Goel Stability of networks and protocols in the adversarial queueing model for packet routing , 1999, SODA '99.

[23]  Michel Loève,et al.  Probability Theory I , 1977 .

[24]  J. Tsitsiklis,et al.  Stability conditions for multiclass fluid queueing networks , 1996, IEEE Trans. Autom. Control..

[25]  Allan Borodin,et al.  Adversarial queueing theory , 1996, STOC '96.

[26]  Rafail Ostrovsky,et al.  Adaptive packet routing for bursty adversarial traffic , 1998, STOC '98.

[27]  Mor Harchol-Balter,et al.  Queueing analysis of oblivious packet-routing networks , 1994, SODA '94.

[28]  P. R. Kumar,et al.  Stable distributed real-time scheduling of flexible manufacturing/assembly/disassembly systems , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[29]  Alan M. Frieze,et al.  A general approach to dynamic packet routing with bounded buffers , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[30]  Boaz Patt-Shamir,et al.  Greedy Packet Scheduling on Shortest Paths , 1993, J. Algorithms.

[31]  Baruch Awerbuch,et al.  Improved approximation algorithms for the multi-commodity flow problem and local competitive routing in dynamic networks , 1994, STOC '94.

[32]  Donald F. Towsley,et al.  Product Form and Local Balance in Queueing Networks , 1977, JACM.

[33]  J. Dai On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models , 1995 .

[34]  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.

[35]  Maury Bramson,et al.  Convergence to equilibria for fluid models of FIFO queueing networks , 1996, Queueing Syst. Theory Appl..

[36]  Sean P. Meyn,et al.  Stability of Generalized Jackson Networks , 1994 .

[37]  Debasis Mitra,et al.  Randomized Parallel Communications , 1986, ICPP.

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

[39]  Frank Thomson Leighton,et al.  Greedy dynamic routing on arrays , 1995, SODA '95.

[40]  R. Durrett Probability: Theory and Examples , 1993 .

[41]  David Gamarnik,et al.  Stability of adaptive and non-adaptive packet routing policies in adversarial queueing networks , 1999, STOC '99.

[42]  Leonard Kleinrock,et al.  Theory, Volume 1, Queueing Systems , 1975 .

[43]  J. Sztrik An introduction to queuing networks , 1990 .

[44]  Matthew Andrews,et al.  Instability of FIFO in session-oriented networks , 2000, SODA '00.

[45]  Debasis Mitra,et al.  Randomized parallel communications on an extension of the omega network , 1987, JACM.

[46]  Sean P. Meyn,et al.  Stability of acyclic multiclass queueing networks , 1995, IEEE Trans. Autom. Control..

[47]  Leandros Tassiulas,et al.  Any work-conserving policy stabilizes the ring with spatial re-use , 1996, TNET.

[48]  Bruce M. Maggs,et al.  Fast Algorithms for Finding O(Congestion + Dilation) Packet Routing Schedules , 1995, Proceedings of the Twenty-Eighth Annual Hawaii International Conference on System Sciences.

[49]  B. Hajek Hitting-time and occupation-time bounds implied by drift analysis with applications , 1982, Advances in Applied Probability.

[50]  Boaz Patt-Shamir,et al.  Greedy packet scheduling on shortest paths (preliminary version) , 1991, PODC '91.

[51]  P. R. Kumar,et al.  Distributed scheduling based on due dates and buffer priorities , 1991 .

[52]  BorodinAllan,et al.  Adversarial queuing theory , 2001 .

[53]  J. Dai On Positive Harris Recurrence of Multiclass Queueing Networks: A Unified Approach Via Fluid Limit Models , 1995 .

[54]  Bruce M. Maggs,et al.  Packet routing and job-shop scheduling inO(congestion+dilation) steps , 1994, Comb..

[55]  Thomas I. Seidman,et al.  "First come, first served" can be unstable! , 1994, IEEE Trans. Autom. Control..