Optimal Scheduling Algorithms for Input-Queued Switches

The input-queued switch architecture is widely used in Internet routers, due to its ability to run at very high line speeds. A central problem in designing an input-queued switch is choosing the scheduling algorithm, i.e. deciding which packets to transfer from ingress ports to egress ports in a given timeslot. Important metrics for evaluating a scheduling algorithm are its throughput and average delay. The well-studied ‘Maximum-Weight’ algorithm has been proved to have maximal throughput [1]; later work [2]–[4] found a wider class of algorithms which also have maximal throughput. The delay performance of these algorithms is less well understood. In this paper, we present a new technique for analysing scheduling algorithms which can explain their delay performance. In particular, we are able to explain the empirical observations in [2] about the average delay in a parameterized class of algorithms akin to Maximum-Weight. We also propose an optimal scheduling algorithm. Our technique is based on critically-balanced fluid model equations.

[1]  Samuel P. Morgan,et al.  Input Versus Output Queueing on a Space-Division Packet Switch , 1987, IEEE Trans. Commun..

[2]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1992 .

[3]  Kai Y. Eng,et al.  Improving the performance of input-queued ATM packet switches , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[4]  Symmetric Crossbar Arbiters for VLSI Communication Switches , 1993, IEEE Trans. Parallel Distributed Syst..

[5]  Thomas E. Anderson,et al.  High-speed switch scheduling for local-area networks , 1993, TOCS.

[6]  Jean C. Walrand,et al.  Achieving 100% throughput in an input-queued switch , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[7]  Ruth J. Williams,et al.  An invariance principle for semimartingale reflecting Brownian motions in an orthant , 1998, Queueing Syst. Theory Appl..

[8]  Nick McKeown,et al.  A practical scheduling algorithm to achieve 100% throughput in input-queued switches , 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.

[9]  Ruth J. Williams,et al.  Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse , 1998, Queueing Syst. Theory Appl..

[10]  Maury Bramson,et al.  State space collapse with application to heavy traffic limits for multiclass queueing networks , 1998, Queueing Syst. Theory Appl..

[11]  Nick McKeown,et al.  The iSLIP scheduling algorithm for input-queued switches , 1999, TNET.

[12]  Balaji Prabhakar,et al.  The throughput of data switches with and without speedup , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[13]  Nick McKeown,et al.  Analysis of scheduling algorithms that provide 100% throughput in input-queued switches , 2001 .

[14]  Devavrat Shah,et al.  Delay bounds for approximate maximum weight matching algorithms for input queued switches , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[15]  Paolo Giaccone,et al.  Randomized scheduling algorithms for high-aggregate bandwidth switches , 2003, IEEE J. Sel. Areas Commun..

[16]  Marco Ajmone Marsan,et al.  On the stability of local scheduling policies in networks of packet switches with input queues , 2003, IEEE J. Sel. Areas Commun..

[17]  A. Stolyar.  MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic , 2004 .

[18]  Devavrat Shah,et al.  Randomization and heavy traffic theory: new approaches to the design and analysis of switch algorithms , 2005 .