近年來多媒體網路急速地成長，各式各樣的網路服務不斷推陳出新，使得現今網路環境變得多元且複雜。在過去文獻中，常用的一些網路分析模型與技術，例如：蒲松程序 (Poisson process)、網路分流、封包解離、封包匯聚與路徑繞送等機制，都必須作適當的修正與調整，才能真正貼切於現今的網路環境。因此，一些較為精緻的網路分析模型，例如：arkov-modulated Poisson process (MMPP)、batch Markovian arrival process (BMAP)、Markov-modulated Bernoulli process (MMBP)、離散型 BMAP (D-BMAP)等，相繼被提出，而且大量應用於現今多媒體網路通訊系統。然而，針對輸入源交通模型的改變，其相對應的網路分析技術該如何因應與調整，已成為當前相當重要且迫切的研究課題了。
本論文提出一些簡單且系統化的路徑層次網路效能分析方法，針對上述較為精緻的模型，納入各種網路干擾、變化因子、時間複雜度等因素，分析經由網路分流後所呈現的特徵樣貌; 使用封包解離與匯聚、機率式繞送等相關技術，給予完整深入的探討，以提供網路設計者更為貼近實體網路的分析工具。本論文所進行的效能分析評估包括：路徑層次─端點至端點封包的延遲量、端點至端點封包延遲的變異量及端點至端點封包的漏失的機率。藉由模擬方式來驗證理論分析的準確度，並且在不同的網路環境，例如：伺服器類型、網路交通叢發度、網路分流繞送機率、網路交通變異度，觀察這些因素對整體網路效能的影響。最後, 我們和相關文獻作一比較，整理出所有方法相對應的優劣勢分析。

Recently, due to multimedia network grow rapidly, all kinds of network services thrivingly develop. It makes current network environment to become complex and multidimensional. Some traditional traffic models and techniques, such as Poisson process, traffic splitting, packet decomposition and aggregation, and probabilistic routing need to make modification and adjustment so that to meet
current real network environment. To properly model diverse traffic in contemporary and future networks, more sophisticated models than Poisson have been proposed by researchers, including Markov-modulated Poisson process (MMPP), batch Markovian arrival process (BMAP), MMBP, and discrete-time BMAP (D-BMAP) etc.. They are general applied to current networks and communication systems. However, facing the changes of these input traffic models, the
adjustments of the corresponding network analysis techniques have become an important and urgent topics.
In this dissertation, we propose some simple and systematic path-wise network performance evaluation analysis methods. They aim at the aforementioned sophisticated models with diverse interfering factors to analyze traffic feature after splitting. They provide some proper analysis tools for real network environment by using packet decomposition and aggregation and probabilistic routing techniques. All the performance metrics discussions include path-wise end-to-end packet delay, end-to-end packet delay variance,
and end-to-end packet loss probability. By using simulation method to validate the accuracy of theory analysis under different network factors such as server type, traffic burstiness, routing probability, and squared coefficient of variation of inter-arrival time between successive arrivals. Of course, all the influences caused by these factors are observed and discussed. Finally, some
comparisons with the closely related methods in the literature are made and the analyses of superiority and inferiority of the proposed methods are arranged.

[1] H. Adiseshu, G. Varghese, and G. Parulkar, “An architecture for packet-striping protocols,” ACM Trans. Computer Systems, vol. 17, no. 4, pp. 249–287, 1999.
[2] D. Bertsekas, “Dynamic behavior of shortest path routing algorithms for communication networks,” IEEE Trans. Automatic Control, vol. 27, no. 1, pp. 60–74, 1982.
[3] C. Blondia and O. Casals, “Performance analysis of statistical multiplexing of VBR sources,” in Proc. IEEE INFOCOM’92, 1992, pp. 828–838.
[4] C. Blondia, “A discrete time batch Markovian arrival process as B-ISDN traffic model,” Belgian J. Oper. Res. Statist. Comput. Science, vol. 32, no. 3–4, pp. 3–23, 1993.
[5] C. Breudan, S. Traw, and J. Smith, “Striping within the network subsystem,”IEEE Network, vol. 9, no. 14, pp. 22–32, 1995.
[6] Z. Cao, Z. Wang, and E. Zegura, “Performance of hashing-based schemes for Internet load balancing,” in Proc. IEEE INFOCOM’00, 2000, pp. 332–341.
[7] H. W. Ferng and J. F. Chang, “Connection-wise end-to-end delay analysis in ATM networks,” IEICE Trans. Commun., vol. E83–B, no. 3, pp. 659–671, 2000.
[8] H. W. Ferng and J. F. Chang, “The departure process of discrete-time queueing systems with Markovian type inputs,”Queueing Systems, vol. 36, no. 1–3, pp. 201–220, 2000.
[9] H. W. Ferng and J. F. Chang, “Connection-wise end-to-end performance analysis of queueing networks with MMPP inputs,”Performance Evaluation, vol. 43, no. 2–3, pp. 39–62, 2001.
[10] H. W. Ferng and J. F. Chang, “Departure processes of BMAP/G/1 queues,”Queueing Systems, vol. 39, no. 2–3, pp. 109–135, 2001.
[11] H. W. Ferng and C. C. Peng, “Traffic splitting and its application to networkwise performance analysis,” in Proc. SCS SPECTS’03, 2003, pp. 494–501.
[12] H. W. Ferng, “Modeling of split traffic under probabilisic routing,” IEEE Communications Letters, vol. 8, no. 7, pp. 470–472, 2004.
[13] H. W. Ferng, C. C. Chao, and C. C. Peng, “Path-wise performance in a treetype network: per-stream loss probability, delay, and delay variance analyses,”Performance Evaluation, vol. 64, no. 1, pp. 55–75, 2007.
[14] W. Fischer and K. S. Meier-Hellstern, “The Markov-modulated Poisson process (MMPP) cookbook,” Performance Evaluation, vol. 18, no. 2, pp. 149–171, 1993.
[15] A. Gomez-Corral, “A tandem queue with blocking and Markovian arrival process,”Queueing Systems, vol. 41, no. 4, pp. 343–370, 2002.
[16] J. J. Hasenbein, “Stability of fluid networks with proportional routing,” Queueing System, vol. 38, no. 3, pp. 327–354, 2001.
[17] A. Heindl, “Decomposition of general tandem networks with MMPP input,”Performance Evaluation, vol. 44, no. 1–4, pp. 5–23, 2001.
[18] A. Heindl, “Decomposition of general queue networks with MMPP inputs and customer losses,” Performance Evaluation, vol. 51, no. 2–4, pp. 117–136, 2003.
[19] C. Herrmann, “The complete analysis of the discrete time finite DBMAP/G/1/N queue,” Performance Evaluation, vol. 43, no. 2–3, pp. 95–121, 2001.
[20] L. Jianxin, L. Lemin and S. Hairong, “The influence of burstiness and correlation of traffic on an ATM multiplexer,”in Proc. IEEE ICCT’96, 1996, pp. 21–23.
[21] K. Kang and C. Kim, “Performance analysis of statistical multiplexing of heterogeneous discrete-time Markov arrival processes in ATM network,” Computer Communications, vol. 20, no. 11, pp. 970–978, 1997.
[22] A. Kel, C. Lin, and M. Loh, “Modeling IP traffic using the batch Markovian arrival process,” Performance Evaluation, vol. 54, no. 2, pp. 149–173, 2003.
[23] L. Kleinrock, Queueing Systems: Theory, Vol. I, Wiley, New York, USA, 1975.
[24] V. Klimenok, L. Breuer, G. Tsarenkov, and A. Dudin, “The BMAP/G/1/N→·/PH/1/M tandem queue with losses,” Performance Evaluation, vol. 61, no. 1, pp. 17–40, 2005.
[25] J. van der Lande, “Inverse multiplexing over ATM: broadband access for less,”Computer Technology Review, vol. 18, no. 12, pp. 24–26, 1998.
[26] J. H. Lee, S. C. Liew, and Q. L. Ding, “String mode – a new concept for performance improvement of ATM networks,”IEEE Journal on Selected Areas in Communications, vol. 9, no. 9, pp. 1452–1460, 1991.
[27] T. T. Lee, S. C. Liew, and Q. L. Ding, “Parallel communications for ATM network control and management,” Performance Evaluation, vol. 30, no. 4, pp. 243–264, 1997.
[28] K. C. Leu and V. O. K. Li, “Generalized load sharing for packet-switching networks,” in Proc. IEEE Network Protocols, 2000, pp. 305–314.
[29] M. Livny and M. Melman, “Load balancing in homogeneous broadcast distributed systems,” ACM Performance Evaluation Review, vol. 11, no. 1, pp. 47–55, 1982.
[30] D. M. Lucantoni, “New results on the single server queue with a batch Markovian arrival process,” Commun. Statist. Stochastic Models, vol. 7, no. 1, pp. 1–46, 1991.
[31] M. J. Neely, “Exact queueing analysis of discrete time tandems with arbitrary arrival processes,” in Proc. IEEE ICC’04, 2004, pp. 2221–2225.
[32] R. O. Onvural, Asynchronous Transfer Mode Networks: Performance Issues, Artech House, Boston, USA, 1994.
[33] D. Park, H. G. Perros, and H. Yamashita, “Approximate analysis of discretetime tandem queueing networks with bursty and correlated input traffic and customer loss,” Oper. Res. Lett., vol. 15, no. 2, pp. 95–104, 1994.
[34] C. C. Peng and H. W. Ferng, “Derivation of moments for MMBP,” Technical Report of Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, 2004.
[35] S. C. Rhea and J. Kubiatowicz, “Probabilistic location and routing,” in Proc. IEEE INFOCOM’02, 2002, pp. 1248–1257.
[36] M. P. Saltouros, A. K. Taskaris, and I. S. Venieris, “A new route selection approach using scaling techniques: an application to hierarchical QoS-based routing,” in Proc. IEEE LCN’00, 2000, pp.8–10.
[37] M. C. Tan, S. C.Wong, J. M. Xu, Z. R. Guan, and P. F. Zhang, “An aggregation approach to short-term traffic flow prediction,” IEEE Trans. Intel. Transport. System, vol. 10, no. 1, pp. 60–69, 2009.
[38] S. Traw and J. Smith, “Striping within the network subsystem,” IEEE Trans. ACM Networking, vol. 9, no. 4, pp. 22–32, 1995.
[39] S. Wang and J. A. Silvester, “A discrete-time performance model for integrated service ATM multiplexers,” in Proc. IEEE GLOBECOM’93, 1993, pp. 757–761.
[40] W. Winston, “Optimality of the shortest-line discipline,” SIAM J. Appl. Prob., vol. 14, no. 1, pp. 181–189, 1977.
[41] M. Yu and D. G. Daut, “A new traffic aggregation technique based on Markov modulated Poisson processes,” in Proc. IEEE GLOBECOM’05, 2005, pp. 1726–1731.
[42] M. Yu, “An aggregation technique for network traffic described by MMBP models,” in Proc. IEEE GLOBECOM’08, 2008, pp. 1–6.
[43] M. Yu, and M. Zhou, “A performance modeling scheme for multistage switch networks with phase-type and bursty traffic,”IEEE Trans. ACM Networking, vol. 18, no. 4, pp. 1091–1104, 2010.