Maximizing Throughput in Multi-queue Switches

We study a basic problem in Multi-Queue switches. A switch connects m input ports to a single output port. Each input port is equipped with an incoming FIFO queue with bounded capacity B. A switch serves its input queues by transmitting packets arriving at these queues, one packet per time unit. Since the arrival rate can be higher than the transmission rate and each queue has limited capacity, packet loss may occur as a result of insufficient queue space. The goal is to maximize the number of transmitted packets. This general scenario models most current networks (e.g., IP networks) which only support a “best effort” service in which all packet streams are treated equally. A 2-competitive algorithm for this problem was designed in [4] for arbitrary B. Recently, a \(\frac{17}{9}\approx 1.89\)-competitive algorithm was presented for B>1 in [2]. Our main result in this paper shows that for B which is not too small our algorithm can do better than 1.89, and approach a competitive ratio of \(\frac{e}{e-1}\approx 1.58\).

[1]  Susanne Albers,et al.  On the Performance of Greedy Algorithms in Packet Buffering , 2005, SIAM J. Comput..

[2]  Yishay Mansour,et al.  Competitive queue policies for differentiated services , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

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

[4]  Richard M. Karp,et al.  An optimal algorithm for on-line bipartite matching , 1990, STOC '90.

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

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

[7]  Boaz Patt-Shamir,et al.  Nearly optimal FIFO buffer management for DiffServ , 2002, PODC '02.

[8]  Yishay Mansour,et al.  Loss-bounded analysis for differentiated services , 2001, SODA '01.

[9]  Christophe Diot,et al.  Simple performance models of differentiated services schemes for the Internet , 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).

[10]  Yishay Mansour,et al.  Competitive queueing policies for QoS switches , 2003, SODA '03.

[11]  Paul W. Goldberg,et al.  A proportionate fair scheduling rule with good worst-case performance , 2003, SPAA '03.

[12]  Yossi Azar,et al.  Management of Multi-Queue Switches in QoS Networks , 2003, STOC '03.

[13]  Joseph Naor,et al.  Competitive On-Line Switching Policies , 2002, SODA '02.

[14]  Yossi Azar,et al.  The zero-one principle for switching networks , 2004, STOC '04.

[15]  Bala Kalyanasundaram,et al.  An optimal deterministic algorithm for online b-matching , 1996, Theor. Comput. Sci..

[16]  Rudolf Fleischer,et al.  Balanced Scheduling toward Loss-Free Packet Queuing and Delay Fairness , 2004, Algorithmica.