Abstract
We present an analysis of the queueing system in which arriving jobs are dropped with probability depending on the queue size. The arrivals are assumed to be autocorrelated and they are modeled by the Markov-modulated Poisson process. Both transient and stationary distributions of the queue size, as well as the system loss ratio and throughput are obtained. The analytical results are accompanied with numerical examples based on the autocorrelated traffic recorded in an IP computer network.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Athuraliya S et al (2001) REM: Active queue management. IEEE Netw 15 (3):48–53
Baiocchi A, Blefari-Melazzi N (1992) Steady-state analysis of the MMPP/G/1/K queue. IEEE Trans Commun 41(4):531–534
Bekker R (2009) Queues with Levy input and hysteretic control. Queueing Syst 63(1):281–299
Bonald T, May M, Bolot J-C (2000) Analytic evaluation of RED performance, Proceedings of INFOCOM, 1415–1424
Chydzinski A (2002) The M/G-G/1 oscillating queueing system. Queueing Systems 42(3):255–268
Chydzinski A (2006a) Transient analysis of the MMPP/g/1/k queue. Telecommun Syst 32(4):247–262
Chydzinski A (2006b) Queue size in a BMAP queue with finite buffer. Proceedings of next generation teletraffic and Wired/Wireless advanced networking ’06. Lect Notes Comput Sci 4003:200–210
Chydzinski A (2006c) Duration of the buffer overflow period in a batch arrival queue. Perform Eval 63(4-5):493–508
Chydzinski A, Chrost L (2011) Analysis of AQM queues with queue-size based packet dropping. Int J Appl Math Comput Sci 21(3):567–577
Deng L, Mark J (1993) Parameter estimation for Markov modulated Poisson processes via the EM algorithm with time discretization. Telecommun Syst 1:321–338
Farzaneh N et al (2013) A novel congestion control protocol with AQM support for IP-based networks. Telecommun Syst 52(1):229–244
Feng W et al (2002) The BLUE active queue management algorithms. IEEE/ACM Trans Networking 10(4):513–528
Fischer W, Meier-Hellstern K (1992) The Markov-modulated poisson process (MMPP) cookbook. Perform Eval 18(2):149–171
Floyd S, Jacobson V (1993) Random early detection gateways for congestion avoidance. IEEE/ACM Trans Networking 1:397–413
Hao W, Wei Y (2005) Extended G I X/M/1/n Queueing Model for Evaluating the Performance of AQM Algorithms with Aggregate Traffic, Proceedings of ICCNMC, pp. 395–414, LNCS 3619
Hollot CV et al (2002) Analysis and design of controllers for AQM routers supporting TCP flows. IEEE Trans Autom Control 47(6):945–959
Kahe G, Jahangir A, Ebrahimi B (2013) AQM controller design for TCP networks based on a new control strategy, Telecommunication Systems. doi:10.1007/s11235-013-9859-y
Kempa W (2013a) On non-stationary queue-size distribution in a finite-buffer queue controlled by a dropping function. Proc. International Conference on Informatics, pp. 67–72, Spisska Nova Ves
Kempa W (2013b) A direct approach to transient queue-size distribution in a finite-buffer queue with AQM. Appl Math Inf Sci 7(3):909–915
Kunniyur SS, Srikant R (2004) An adaptive virtual queue (AVQ) algorithm for active queue management. IEEE/ACM Trans Networking 12(2):286–299
Na Z et al (2012) A novel adaptive traffic prediction AQM algorithm journal. Telecommun Syst 49(1):149–160
Pacheco A, Ribeiro H (2008) Consecutive customer losses in oscillating G I X/m//n systems with state dependent services rates. Ann Oper Res 162(1):143–158
Rosolen V, Bonaventure O, Leduc G (1999) A RED discard strategy for ATM networks and its performance evaluation with TCP/IP traffic. ACM SIGCOMM Comput Commun Rev 29(3):23–43
Ryden T (1996) An EM algorithm for parameter estimation in Markov modulated poisson processes. Comput Stat Data Anal 21:431–447
Salvador P, Valadas R, Pacheco A (2003) Multiscale fitting procedure using Markov modulated poisson processes. Telecommun Syst 23(1-2):123–148
Singh LN, Dattatreya GR (2004) A novel approach to parameter estimation in Markov-modulated poisson processes, Proc. IEEE Emerging Technologies Conference (ETC) Richardson, TX
Spinelli RA (1966) Numerical inversion of laplace transforms. SIAM J Num Anal 3:636–649
Suzer MH, Kang K-D, Basaran C (2012) Active queue management via event-driven feedback control. Comput Commun 35(4):517–529
Tikhonenko O, Kempa W (2013) Queue-size distribution in M/G/1-type system with bounded capacity and packet dropping. Commun Comput Inf Sci 356:177–186
Wu W, Ren Y, Shan X (2001) A self-configuring PI controller for active queue management. In: Asia-Pacific Conference on Communications (APCC), Japan
Wydrowski B, Zukerman M (2002) GREEN: An active queue management algorithm for a self managed Internet. In: Proceeding of IEEE international conference on communications ICC2002, vol 4, pp 2368–2372
Yoshihara T, Kasahara S, Takahashi Y (2001) Practical time-scale fitting of self-similar traffic with Markov-modulated poisson process. Telecommun Syst 17 (1/2):185–211
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Mrozowski, P., Chydzinski, A. Queues with Dropping Functions and Autocorrelated Arrivals. Methodol Comput Appl Probab 20, 97–115 (2018). https://doi.org/10.1007/s11009-016-9534-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11009-016-9534-3
Keywords
- Queueing system
- Dropping function
- Markov-modulated Poisson process
- Queue size distribution
- Active queue management