Scheduling Protocols for Switches with Large Envelopes

Traditionally, switches make scheduling decisions on the granularity of a packet. However, this is becoming increasingly difficult since network bandwidth is growing rapidly whereas packet sizes remain largely unchanged. Therefore the service time of an individual packet is decreasing rapidly. In this paper we study switches that make scheduling decisions on the granularity of an envelope which can be much larger than a packet in size.For an output-queued switch with envelope size E, each output chooses one input every E time steps and transmits packets from this chosen input during the next E steps. For an input-queued switch with envelope size E, one matching from the inputs to the outputs is computed every E steps and only the input–output pairs that are defined by this matching are allowed to transmit packets during the next E steps. Traditional switches correspond to envelope size E = 1 and almost all previous scheduling work deals with this case exclusively.We first show how some stable protocols for scheduling networks of output-queued switches with E = 1 fail for arbitrary E when these protocols are generalized in the most straightforward manner. We then present an extremely simple protocol that does guarantee network stability for output-queued switches for any E ≥ 1.For input-queued switches we first present a max-weight matching protocol that is stable for a single switch with arbitrary E. We then present a more complex protocol that achieves stability for a network of input-queued switches for any E ≥ 1.

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

[2]  Lisa Zhang,et al.  Achieving stability in networks of input-queued switches , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

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

[4]  Nick McKeown,et al.  A Starvation-free Algorithm For Achieving 100% Throughput in an Input- Queued Switch , 1999 .

[5]  Nick McKeown,et al.  Matching output queueing with a combined input output queued switch , 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).

[6]  Hui Zhang,et al.  Exact emulation of an output queueing switch by a combined input output queueing switch , 1998, 1998 Sixth International Workshop on Quality of Service (IWQoS'98) (Cat. No.98EX136).

[7]  Pravin Varaiya,et al.  Scheduling cells in an input-queued switch , 1993 .

[8]  Allan Borodin,et al.  Adversarial queuing theory , 2001, JACM.

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

[10]  Nabil Kahale,et al.  Dynamic global packet routing in wireless networks , 1997, Proceedings of INFOCOM '97.

[11]  Lisa Zhang,et al.  Stability results for networks with input and output blocking , 1998, STOC '98.

[12]  Leandros Tassiulas,et al.  Reduced Complexity Input Buffered Switches , 2000 .

[13]  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.