Abstract
The Generalized Processor Sharing (GPS) is an important service differentiation scheme in telecommunication systems and has attracted great research interests due to the desirable properties of fairness, traffic isolation, and work conservation. The major limitation of the existing analytical performance models of GPS systems subject to self-similar traffic is that these models have been restricted to a simplified scenario with only two traffic flows. To overcome such a limitation, this study proposes a new flow-decomposition approach to modelling GPS systems subject to multiple self-similar traffic flows. We present and prove the existence of a feasible ordering of GPS systems based on the required and guaranteed service rates of traffic flows. With the aid of the feasible ordering, we decompose the GPS system into a group of single-queue systems and then derive the queue length distributions and loss probabilities of individual self-similar traffic flows in the original GPS system. Extensive simulation experiments are conducted to validate the accuracy of the developed analytical model.
Similar content being viewed by others
References
Berger, A. W., & Whitt, W. (1998). Effective bandwidths with priorities. IEEE/ACM Transactions on Networking, 6(4), 447–460.
Berger, A. W., & Whitt, W. (2000). Workload bounds in fluid models with priorities. Performance Evaluation, 41(4), 249–267.
Borst, S., Mandjes, M., & van Uitert, M. (2003). Generalized processor sharing with light-tailed and heavy-tailed input. IEEE/ACM Transactions on Networking, 11(5), 821–834.
Hanada, M., & Nakazato, H. (2007). Output rate-controlled scheduling policy: End-to-end delay bounds calculation. In Proceedings of the 9th international conference on advanced communication technology (ICACT’07) (Vol. 2, pp. 1370–1375).
Jiang, H., & Zhuang, W. (2006). Resource allocation with service differentiation for wireless video transmission. IEEE Transactions on Wireless Communications, 5(6), 1456–1468.
Jin, X., & Min, G. (2007). An analytical model for generalized processor sharing scheduling with heterogeneous network traffic. In Proceedings of the 22nd annual ACM symposium on applied computing (SAC’07).
Jin, X., & Min, G. (2007). Flow-decomposition for performance prediction of GPS mechanism under homogeneous self-similar traffic. In Proceedings of the 2007 IEEE international conference on networking, sensing and control (ICNSC’07).
Jin, X., & Min, G. (2007). Modelling priority queueing systems with multi-class self-similar network traffic. In Proceedings of the 2007 IEEE international conference on communications (ICC’07).
Kim, H. S., & Shroff, N. B. (2001). Loss probability calculations and asymptotic analysis for finite buffer multiplexers. IEEE/ACM Transactions on Networking, 9(6), 755–768.
Lee, J. F., Chen, M. C., & Sun, Y. (2007). WF2Q-M: Worst-case fair weighted fair queueing with maximum rate control. Computer Networks, 51, 1403–1420.
Lee, J. Y., Kim, S., Kim, D., & Sung, D. (2005). Bandwidth optimization for Internet traffic in generalized processor sharing servers. IEEE Transactions on Parallel and Distributed Systems, 16(4), 324–334.
Liu, Z., Almhana, J., Choulakian, V., & McGorman, R. (2006). A long-range dependent model for Internet traffic with power transformation. IEEE Communications Letters, 10(8), 632–634.
Mannersalo, P., & Norros, I. (2002). GPS schedulers and Gaussian traffic. In Proceedings of the 21st annual joint conference of the IEEE computer and communications societies (INFOCOM’02) (Vol. 3, pp. 1660–1667).
Mielniczuk, J., & Wojdyllo, P. (2007). Decorrelation of wavelet coefficients for long-range dependent processes. IEEE Transactions on Information Theory, 53(5), 1879–1883.
Min, G., & Ould-Khaoua, M. (2004). A performance model for wormhole-switched interconnection networks under self-similar traffic. IEEE Transactions on Computers, 53(5), 601–613.
Norros, I. (1994). A storage model with self-similar input. Queueing Systems, 16(3–4), 387–396.
Norros, I., Mannersalo, P., & Wang, J. L. (1999). Simulation of fractional Brownian motion with conditionalized random midpoint displacement. Advances in Performance Analysis, 2, 77–101.
Oottamakorn, C., Mao, S., & Panwar, S. S. (2006). On generalized processor sharing with regulated multimedia traffic flows. IEEE Transactions on Multimedia, 8(6), 1209–1218.
Parekh, A. K., & Gallager, R. G. (1993). A generalized processor sharing approach to flow control in integrated services networks: The single-node case. IEEE/ACM Transactions on Networking, 1(3), 344–357.
Park, K., & Willinger, W. (2000). Self-similar network traffic and performance evaluation. New York: Wiley.
Park, W., Lee, J. Y., & Sung, D. K. (2006). Bandwidth optimization algorithm based on bandwidth ratio adjustment in generalized processor sharing servers. In Proceedings of the 2006 IEEE international conference on communications (ICC’06) (Vol. 2, pp. 699–703).
Quan, Z., & Chung, J. M. (2003). Priority queueing analysis for self-similar traffic in high-speed networks. In Proceedings of the 2003 IEEE international conference on communications (ICC’03) (Vol. 3, pp. 1606–1610).
Sahoo, A., & Manjunath, D. (2007). Revisiting WFQ: Minimum packet lengths tighten delay and fairness bounds. IEEE Communications Letters, 11(4), 366–368.
Tickoo, O., & Sikdar, B. (2003). On the impact of IEEE 802.11 MAC on traffic characteristics. IEEE Journal on Selected Areas in Communications, 21(2), 189–203.
Wang, H., Huang, C., & Yan, J. (2006). A feedback control model for multiple-link adaptive bandwidth provisioning systems. In Proceedings of the 2006 IEEE international conference on communications (ICC’06) (Vol. 3, pp. 987–993).
Wang, X. (2005). An FDD wideband CDMA MAC protocol with minimum-power allocation and GPS-scheduling for wireless wide area multimedia networks. IEEE Transactions on Mobile Computing, 4(1), 16–28.
Xu, L., Shen, X., & Mark, J. W. (2004). Dynamic fair scheduling with QoS constraints in multimedia wideband CDMA cellular networks. IEEE Transactions on Wireless Communications, 3(1), 60–73.
Xu, L., Shen, X., & Mark, J. W. (2005). Fair resource allocation with guaranteed statistical QoS for multimedia traffic in wideband CDMA cellular network. IEEE Transactions on Mobile Computing, 4(2), 166–177.
Yousefizadeh, H., & Jonckheere, E. A. (2005). Dynamic neural-based buffer management for queuing systems with self-similar characteristics. IEEE Transactions on Neural Networks, 16(5), 1163–1173.
Yu, J., & Petropulu, A. P. (2006). Study of the effect of the wireless gateway on incoming self-similar traffic. IEEE Transactions on Signal Processing, 54(10), 3741–3758.
Yu, X., Thng, I. L. J., Jiang, Y., & Qiao, C. (2005). Queueing processes in GPS and PGPS with LRD traffic inputs. IEEE/ACM Transactions on Networking, 13(3), 676–689.
Zhang, J., Hamalainen, T., & Joutsensalo, J. (2004). Stochastic analysis of upper delay bound of GPS-based packetized fair queueing algorithms. In Proceedings of the 12th IEEE international conference on networks (ICON’04) (Vol. 1, pp. 35–40).
Zhang, J., & Konstantopoulos, T. (2005). Multiple-access interference processes are self-similar in multimedia CDMA cellular networks. IEEE Transactions on Information Theory, 51(3), 1024–1038.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by the UK EPSRC research grant (EP/C525027/1).
Rights and permissions
About this article
Cite this article
Jin, X., Min, G. Performance modelling of generalized processor sharing systems with multiple self-similar traffic flows. Telecommun Syst 38, 111–120 (2008). https://doi.org/10.1007/s11235-008-9098-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11235-008-9098-9