DOI QR코드

DOI QR Code

QUEUEING ANALYSIS FOR TRAFFIC CONTROL WITH COMBINED CONTROL OF DYNAMIC MMPP ARRIVALS AND TOKEN RATES

  • Choi, Doo Il (Department of Applied Mathematics, Halla University)
  • Received : 2013.01.21
  • Accepted : 2013.02.28
  • Published : 2013.06.25

Abstract

We analyze the queueing model for leaky bucket (LB) scheme with dynamic arrivals and token rates. In other words, in our LB scheme the arrivals and token rates are changed according to the buffer occupancy. In telecommunication networks, the LB scheme has been used as a policing function to prevent congestion. By considering bursty and correlated properties of input traffic, the arrivals are assumed to follow a Markov-modulated Poisson process (MMPP). We derive the distribution of system state, and obtain the loss probability and the mean waiting time. The analysis is done by using the embedded Markov chain and supplementary variable method. We also present some numerical examples to show the effect of our proposed model.

Keywords

References

  1. J. Tunner, New Directions in Communications(or Which Way to the Information Age), IEEE Communications Magazine, 24 (1986), 17-24.
  2. M. Sidi, Z. Lin, I. Cidon, I. Gopal, Congestion Control through Input Rate Regulation, Proceedings of IEEE Globecom'89 1989.
  3. Y. H. Kim, B. C. Shin, C. K. Un, Performance Analysis of Leaky Bucket Band-width Enforcement Strategy for Bursty Traffics in an ATM Networks, Computer Networks and ISDN System 25 (1992) 295-303. https://doi.org/10.1016/0169-7552(92)90096-9
  4. H. Ahmadi, R. Guerin, K. Sohraby, Analysis of Leaky Bucket Access Control Mechanism with Batch Arrival Process, IEEE Globecom'90 (1990) 344-349.
  5. K. Sohraby, M. Sidi, On the Performance of Bursty and Modulated Sources subject to Leaky Bucket Rate based Access Control Schemes, IEEE Transactions on Communications 42 (1994) 477-487. https://doi.org/10.1109/TCOMM.1994.577075
  6. G. L. Wu, J. W. Mark, Discrete Time Analysis of Leaky Bucket Congestion Control, Computer Networks and ISDN System 26 (1993) 79-94. https://doi.org/10.1016/0169-7552(93)90038-6
  7. J. Y. Lee, C. K. Un, Performance of Dynamic Rate Leaky Bucket Algorithm, IEE Electronics Letters 29 (17) (1993) 1560-1561. https://doi.org/10.1049/el:19931040
  8. C. G. Park, B. D. Choi, D. K. Sung, Performance Analysis of Leaky Bucket Scheme with a Threshold in the Data Buffer, Computer Networks and ISDN System 29 (1997) 781-795. https://doi.org/10.1016/S0169-7552(96)00104-3
  9. B. D. Choi, D. I. Choi, Discrete-time Analysis of the Leaky Bucket Scheme with Threshold-based Token Generation Intervals, IEE Proceedings of Communications 143 (1996) 105-111.
  10. J. Zeng, L. F. Merakos, Analysis of a Priority Leaky Bucket Regulator for Virtual Path Traffic in ATM Networks, Proceedings of IEEE Globecom'94 (1994) 606-611.
  11. D. I. Choi, B. D. Choi, D. K. Sung, Performance Analysis of Priority Leaky Bucket Scheme with Queue-lengththreshold Scheduling Policy, IEE Proceedings of Communications 145(6) (1998) 395-401.
  12. D. I. Choi, S. Lee, Performance analysis of the leaky bucket scheme with queue length dependent arrival rates, Bulletin of the Korean Mathematical Society 43(3) (2006) 657-669. https://doi.org/10.4134/BKMS.2006.43.3.657
  13. D. I. Choi, T. S. Kim, S. Lee, Analysis of an MMPP/G/1/K queue with queue length dependent arrival rates, and its application to preventive congestion control in telecommunication networks, European J. of Operational Research 187 (2008) 652-659. https://doi.org/10.1016/j.ejor.2007.03.030

Cited by

  1. Analysis of the State-Dependent Queueing Model and Its Application to Battery Swapping and Charging Stations vol.12, pp.6, 2013, https://doi.org/10.3390/su12062343