Competitive On-Line Switching Policies

Consider the following problem. A switch connecting n input channels to a single output channel must deliver all incoming messages through this channel. Messages are composed of packets , and in each time slot the switch can deliver a single packet from one of the input queues to the output channel. In order to prevent packet loss, a buffer is maintained for each input channel. The goal of a switching policy is to minimize the maximum buffer size. The setting is on-line; decisions must be made based on the current state without knowledge of future events. This general scenario models multiplexing tasks in various systems such as communication networks, cable modem systems, and traffic control. Traditionally, researchers analyzed the performance of a given policy assuming some distribution on the arrival rates of messages at the input queues, or assuming that the service rate is at least the aggregate of all the input rates. We use competitive analysis, avoiding any prior assumptions on the input. We show O(log n )-competitive switching policies for the problem and demonstrate matching lower bounds.

[1]  Marek Chrobak,et al.  The Buffer Minimization Problem for Multiprocessor Scheduling with Conflicts , 2001, ICALP.

[2]  Boaz Patt-Shamir,et al.  Buffer Overflow Management in QoS Switches , 2004, SIAM J. Comput..

[3]  Yossi Azar,et al.  The competitiveness of on-line assignments , 1992, SODA '92.

[4]  Albert G. Greenberg,et al.  How fair is fair queuing , 1992, JACM.

[5]  Yossi Azar On-line Load Balancing , 1996, Online Algorithms.

[6]  Galen H. Sasaki Input Buffer Requirements for Round Robin Polling Systems , 1993, Perform. Evaluation.

[7]  Israel Cidon,et al.  Real-time packet switching: a performance analysis , 1988, IEEE J. Sel. Areas Commun..

[8]  Roch Guérin,et al.  Buffer Size Requirements Under Longest Queue First , 1993, Perform. Evaluation.

[9]  Michael J. Franklin,et al.  Scheduling for large-scale on-demand data broadcasting , 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.

[10]  Boaz Patt-Shamir,et al.  Buffer overflow management in QoS switches , 2001, STOC '01.

[11]  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.

[12]  Moshe Sidi,et al.  An optimal service policy for buffer systems , 1995, JACM.

[13]  Abhay Parekh,et al.  A generalized processor sharing approach to flow control in integrated services networks: the single-node case , 1993, TNET.