Competitive Scheduling of Packets with Hard Deadlines in a Finite Capacity Queue

Motivated by the quality-of-service (QoS) buffer management problem, we consider online scheduling of packets with hard deadlines in a finite capacity queue. At any time, a queue can store at most b isin Z + packets. Packets arrive over time. Each packet is associated with a non-negative value and an integer deadline. In each time step, only one packet is allowed to be sent. Our objective is to maximize the total value gained by the packets sent by their deadlines in an online manner. Due to the Internet traffic's chaotic characteristics, no stochastic assumptions are made on the packet input sequences. This model is called a finite-queue model. We use competitive analysis to measure an online algorithm's performance versus an unrealizable optimal offline algorithm who constructs the worst possible input based on the knowledge of the online algorithm. For the finite-queue model, we first present a deterministic 3-competitive memoryless online algorithm. Then, we give a randomized (Phi 2 = (1+radic(5)/2) 2 ap 2.618)-competitive memoryless online algorithm. The algorithmic framework and its theoretical analysis include several interesting features. First, our algorithms use (possibly) modified characteristics of packets; these characteristics may not be same as those specified in the input sequence. Second, our analysis method is different from the classical potential function approach. We use a simple charging scheme, which depends on a clever modification (during the course of the algorithm) on the packets in the queue of the optimal offline algorithm. We then prove that a set of invariants holds at the end of each time step. Finally, we analyze the two proposed algorithm in a relaxed model, in which packets have no hard deadlines but an order. We conclude that both algorithms have the same competitive ratios in the relaxed model.

[1]  Matthias Englert,et al.  Considering suppressed packets improves buffer management in QoS switches , 2007, SODA '07.

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

[3]  Fei Li,et al.  An optimal online algorithm for packet scheduling with agreeable deadlines , 2005, SODA '05.

[4]  Yishay Mansour,et al.  Improved Competitive Guarantees for QoS Buffering , 2003, Algorithmica.

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

[6]  Toshiya Itoh,et al.  Competitive Analysis of Multi-Queue Preemptive QoS Algorithms for General Priorities , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

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

[8]  Sally Floyd,et al.  Difficulties in simulating the internet , 2001, TNET.

[9]  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).

[10]  Marek Chrobak,et al.  Online competitive algorithms for maximizing weighted throughput of unit jobs , 2006, J. Discrete Algorithms.

[11]  Bruce Hajek.  On the Competitiveness of On-Line Scheduling of Unit-Length Packets with Hard Deadlines in Slotted Time , 2001 .

[12]  V. Paxson,et al.  WHERE MATHEMATICS MEETS THE INTERNET , 1998 .

[13]  Francis Y. L. Chin,et al.  Online Scheduling with Partial Job Values: Does Timesharing or Randomization Help? , 2003, Algorithmica.

[14]  Yossi Azar,et al.  Multiplexing Packets with Arbitrary Deadlines in Bounded Buffers , 2006, SWAT.

[15]  V. Paxson,et al.  Notices of the American Mathematical Society , 1998 .

[16]  Marek Chrobak,et al.  Improved Online Algorithms for Buffer Management in QoS Switches , 2004, ESA.

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

[18]  Fei Li,et al.  Better online buffer management , 2007, SODA '07.

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

[20]  Baruch Schieber,et al.  Further Improvements in Competitive Guarantees for QoS Buffering , 2004, ICALP.

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

[22]  Fei Li.  Online Algorithms for Scheduling Weighted Packets with Deadlines in Bounded Buffers , 2008, ArXiv.

[23]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .