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Online Scheduling FIFO Policies with Admission and Push-Out

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Abstract

We consider the problem of managing a bounded size First-In-First-Out (FIFO) queue buffer, where each incoming unit-sized packet requires several rounds of processing before it can be transmitted out. Our objective is to maximize the total number of successfully transmitted packets. We consider both push-out (when a policy is permitted to drop already admitted packets) and non-push-out cases. We provide worst-case guarantees for the throughput performance of our algorithms, proving both lower and upper bounds on their competitive ratio against the optimal algorithm, and conduct a comprehensive simulation study that experimentally validates predicted theoretical behavior.

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Notes

  1. Note that two cores are not allowed to process the same packet simultaneously.

  2. Here, again, there is room for different possible interpretations of LPO; we might assume that packets with zero processing left can be transmitted all at once. This would make LPO better and improve the upper bound in Theorem 5 by 1. Since our main results deal with upper bounds, we make the least favourable choice and assume that only one packet per time slot can be transmitted (C packets in the multicore case).

  3. This qualification deals with a boundary case: during the last B time slots of an iteration, when LPO is transmitting, we set M t =1 for t∈[t end−B,t end] independent of the newly arriving packets that will be processed on the next iteration; at any other time, M t is simply the maximum residual work among all packets.

References

  1. Aiello, W., Mansour, Y., Rajagopolan, S., Rosén, A.: Competitive queue policies for differentiated services. J. Algorithms 55(2), 113–141 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Azar, Y., Litichevskey, A.: Maximizing throughput in multi-queue switches. Algorithmica 45(1), 69–90 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Azar, Y., Richter, Y.: An improved algorithm for CIOQ switches. ACM Trans. Algorithms 2(2), 282–295 (2006)

    Article  MathSciNet  Google Scholar 

  4. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press (1998)

  5. Brucker, P., Heitmann, S., Hurink, J., Nieberg, T.: Job-shop scheduling with limited capacity buffers. OR Spectrum 28(2), 151–176 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. CAIDA – the cooperative association for internet data analysis. [Online] http://www.caida.org/

  7. Cavium: OCTEON II CN68XX multi-core MIPS64 processors, product brief (2010). [Online] http://www.caviumnetworks.com/OCTEON-II_CN68XX.html

  8. Chuprikov, P., Nikolenko, S.I., Kogan, K.: Priority Queueing with Multiple Packet Characteristics. In: IEEE INFOCOM. to appear, pp 1–9 (2015)

  9. Cisco: The Cisco QuantumFlow processor, product brief (2010). [Online] http://www.cisco.com/en/US/prod/collateral/routers/ps9343/solution_overview_c22-448936.html

  10. Englert, M., Westermann, M.: Lower and upper bounds on FIFO buffer management in QoS switches. Algorithmica 53(4), 523–548 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Eugster, P., Kogan, K., Nikolenko, S.I., Sirotkin, A.V.: Shared Memory Buffer Management for Heterogeneous Packet Processing. In: IEEE 34th International Conference on Distributed Computing Systems (ICDCS 2014), pp 471–480 (2014)

  12. EZChip: NP-4 network processor, product brief (2010). [Online] http://www.ezchip.com/p_np4.htm

  13. Goldwasser, M.: A survey of buffer management policies for packet switches. SIGACT News 41(1), 100–128 (2010)

    Article  Google Scholar 

  14. Kesselman, A., Kogan, K.: Nonpreemptive Scheduling of Optical Switches. IEEE Trans. Commun. 55(6), 1212–1219 (2007)

    Article  Google Scholar 

  15. Keslassy, I., Kogan, K., Scalosub, G., Segal, M.: Providing performance guarantees in multipass network processors. IEEE/ACM Trans. Networking 20(6), 1895–1909 (2012)

    Article  Google Scholar 

  16. Kesselman, A., Kogan, K., Segal, M.: Improved competitive performance bounds for CIOQ switches. Algorithmica 63(1–2), 411–424 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kesselman, A., Kogan, K., Segal, M.: Packet mode and QoS algorithms for buffered crossbar switches with FIFO queuing. Distrib. Comput. 23(3), 163–175 (2010)

    Article  MATH  Google Scholar 

  18. Kesselman, A., Kogan, K., Segal, M.: Best Effort and Priority Queuing Policies for Buffered Crossbar Switches (2012)

  19. Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviridenko, M.: Buffer overflow management in QoS switches. SIAM J. Comput. 33(3), 563–583 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kogan, K., López-Ortiz, A., Nikolenko, S.I., Sirotkin, A.V.: A taxonomy of semi-FIFO policies. In: Proceedings of the 31st IEEE International Performance Computing and Communications Conference (IPCCC 2012), pp 295–304 (2012)

  21. Kogan, K., López-Ortiz, A., Nikolenko, S.I., Sirotkin, A.V., Tugaryov, D.: FIFO queueing policies for packets with heterogeneous processing. In: Proceedings of the 1st Mediterranean Conference on Algorithms (MedAlg 2012), Lecture Notes in Computer Science. arXiv:1204.5443 [cs.NI], vol. 7659, pp 248–260 (2012)

  22. Kogan, K., López-Ortiz, A., Nikolenko, S.I., Sirotkin, A.V.: Multi-queued network processors for packets with heterogeneous processing requirements. In: Proceedings of the Fifth International Conference on Communication Systems and Networks, (COMSNETS), pp 1–10 (2013)

  23. Kogan, K., López-Ortiz, A., Nikolenko, S.I., Scalosub, G., Segal, M.: Balancing work and size with bounded buffers. In: Proceedings of the Sixth International Conference on Communication Systems and Networks, (COMSNETS). [Online] arXiv:1202.5755, pp 1–8 (2014)

  24. Kogan, K., Nikolenko, S.I., Keshav, S., López-Ortiz, A.: Efficient demand assignment in multi-connected microgrids with a shared central grid. In: SustainIT, pp 1–5 (2013)

  25. Leonardi, S., Raz, D.: Approximating total flow time on parallel machines. In: STOC, pp 110–119 (1997)

  26. Mansour, Y., Patt-Shamir, B., Lapid, O.: Optimal smoothing schedules for real-time streams. Distrib. Comput. 17(1), 77–89 (2004)

    Article  Google Scholar 

  27. Motwani, R., Phillips, S., Torng, E.: Non-clairvoyant scheduling. Theor. Comput. Sci. 130(1), 17–47 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  28. Muthukrishnan, S.M., Rajaraman, R., Shaheen, A., Gehrke, J.E.: Online scheduling to minimize average stretch. SIAM J. Comput. 34(2), 433–452 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  29. Nikolenko, S.I., Kogan, K.: Single and multiple buffer processing. Encyclopedia of Algorithms, 1–9 (2015)

  30. Pruhs, K.: Competitive online scheduling for server systems. SIGMETRICS Perform. Eval. Rev. 34(4), 52–58 (2007)

    Article  Google Scholar 

  31. Ruiz, R., Vázquez-Rodrígue, J.A.: The hybrid flow shop scheduling problem. Eur. J. Oper. Res. 205(1), 1–18 (2010)

    Article  MATH  Google Scholar 

  32. Schrage, L.: A proof of the optimality of the shortest remaining processing time discipline. Oper. Res. 16, 687–690 (1968)

    Article  MATH  Google Scholar 

  33. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  34. Wolf, T., Pappu, P., Franklin, M.A.: Predictive scheduling of network processors. Comput. Netw. 41(5), 601–621 (2003)

    Article  MATH  Google Scholar 

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Acknowledgments

The work of S.I. Nikolenko was supported by the Basic Research Program of the National Research University Higher School of Economics, 2015, grant no. 78. We also thank the anonymous referees for many useful comments that have allowed us to improve the paper.

Author information

Authors and Affiliations

  1. IMDEA Networks Institute, Madrid, Spain

    Kirill Kogan

  2. School of Computer Science, University of Waterloo, Waterloo, Canada

    Alejandro López-Ortiz

  3. Laboratory for Internet Studies, National Research University Higher School of Economics, St. Petersburg, Russian Federation

    Sergey I. Nikolenko

  4. Laboratory of Mathematical Logic, Steklov Mathematical Institute at St. Petersburg, St. Petersburg, Russian Federation

    Sergey I. Nikolenko

  5. International Laboratory for Applied Network Research, National Research University Higher School of Economics, Moscow, Russia

    Alexander V. Sirotkin

  6. Theoretical and Interdisciplinary Computer Science Laboratory, St. Petersburg Institute for Informatics and Automation of the RAS, St. Petersburg, Russia

    Alexander V. Sirotkin

Authors
  1. Kirill Kogan
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  2. Alejandro López-Ortiz
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  3. Sergey I. Nikolenko
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  4. Alexander V. Sirotkin
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Corresponding author

Correspondence to Sergey I. Nikolenko.

Additional information

A preliminary version of this paper has appeared in [21]; compared to the conference version, this paper contains new results about the two-valued case, changes our constructions so that they more strictly adhere to the FIFO processing order, and presents a modified proof of the main theorem that improves over previous results.

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Kogan, K., López-Ortiz, A., Nikolenko, S.I. et al. Online Scheduling FIFO Policies with Admission and Push-Out. Theory Comput Syst 58, 322–344 (2016). https://doi.org/10.1007/s00224-015-9626-4

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  • DOI: https://doi.org/10.1007/s00224-015-9626-4

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