Traffic splitting in a network: split traffic models and applications Huei-Wen Ferng * , Cheng-Ching Peng Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106, Taiwan, ROC Abstract The contemporary high-speed networks, e.g. the Internet and asynchronous transfer mode (ATM) networks provide a convenient and cost-effective communication platform to carry the emerging multimedia applications. However, problems, such as network congestion caused by overloaded traffic get worse day by day. Thus, how to properly control the system while maintaining the quality of service (QoS) for users becomes an important and challenging issue. To reach the goal of QoS guarantee, load sharing or traffic balancing is one of important techniques to improve the whole network performance. In this paper, we focus on the probabilistic routing policy and analyze split traffic models under such a probabilistic routing policy with input traffic models of the batch Markovian arrival process (BMAP) and discrete-time BMAP (D-BMAP) which can be employed to characterize the multimedia traffic in current and future networks. We successfully show that the split traffic on each routing path from an original BMAP (D-BMAP) input is still a BMAP (D-BMAP). The detailed traffic structure is also acquired. Applying traffic splitting along with the output process characterization, we propose a network-wise performance evaluation method suitable for mesh networks with a probabilistic routing algorithm to get the end-to-end delay, delay variance, and cell loss probability. With numerical experiments, we show that (i) the probabilistic routing policy with a random routing matrix performs well for systems; (ii) the proposed method of network-wise performance analysis has good accuracy. q 2004 Elsevier B.V. All rights reserved. Keywords: Traffic splitting; Probabilistic routing; Batch Markovian arrival process; Discrete-time batch Markovian arrival process; Mesh network; Network-wise performance 1. Introduction The rapid growth and development of networks have raised problems, such as congestion etc. in current high- speed networks, e.g. the Internet and ATM network [8,18, 22,23]. Therefore, corresponding issues, e.g. congestion control and admission control to solve the above problem have drawn much attention in the literature. Before considering these issues, system designers first need a powerful tool to help themselves understand the perform- ance of a whole network. However, it is hard to develop such a tool due to (i) traffic modeling to properly capture the bursty nature exhibited by multimedia sources, such as voice, data, and video etc.; (ii) large scale of networks; and (iii) complicated network operations, e.g. routing algorithms. To address the issues mentioned above, more sophisticated models, such as BMAP [19,26] and D-BMAP [4,30] are proposed and suggested in the literature. And systematic methods for performance evalu- ation, e.g. those in Refs. [8,10,12,15,16] are employed to analyze network-wise performance. As for network oper- ations, they are mostly treated specifically. Likewise, we focus on the routing mechanism only in this paper. Even only routing mechanisms are considered, this makes one hard to represent or model the traffic sources inbound to intermediate nodes in a network. To solve the problem, we develop split traffic models and discuss an application in this paper. In fact, the traffic splitting related issues also received attention in the research field because of considerations of load balance, network efficiency, and reliability. For examples, Bertsekas [2] studied routing algorithms for computer networks and showed that a routing policy that uses only a single path is not necessarily optimal from the viewpoint of an entire network even though the path is the shortest one. Bertsekas thus pointed out that the traffic splitting mechanism plays an important role on traffic load balancing. In Ref. [25], Livny and Melman illustrated that Computer Communications 27 (2004) 1152–1165 www.elsevier.com/locate/comcom 0140-3664/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2004.02.018 * Corresponding author. Tel.: þ886-2-2730-1064; fax: þ 886-2-2730- 1081. E-mail address: hwferng@mail.ntust.edu.tw (H.-W. Ferng).