Composite Performance and Availability Analysis of Communications Networks: A Comparison of Exact and Approximate Approaches Yue Ma Global Software Group Motorola Inc. 50 Northwest Point Road, 2nd Floor Elk Grove Village, IL 60007 Yue.Ma@motorola.com James J. Han Global Software Group Motorola Inc. 50 Northwest Point Road, 2nd Floor Elk Grove Village, IL 60007 James Han@email.mot.com Kishor S. Trivedi Department of Electrical & Computer Engineering Duke University, Box 90291 Durham, NC 27708-0291 kst@ee.duke.edu Abstract: Traditional pure performance model that ignores fail- ure and recovery but considers resource contention generally overestimates the system’s ability to perform a certain job. On the other hand, pure availability analysis tends to be too con- servative since performance considerations are not taken into account. To obtain realistic composite performance and avail- ability measures, one should consider performance changes that are associated with failure recovery behavior. In this paper, a brief review is first given over the advances in composite perfor- mance and availability analysis. Thereafter, three techniques for composite performance and availability analysis are discussed in detail through a queueing system in a wireless communica- tions network. I. I NTRODUCTION When a communication network encounters failures, either due to software, hardware, environment, human error or a com- bination of these factors, the network can generally provide its service continuously without interruption. However, the system capacity, that is, the number of active customers that the system can support, may decrease. The system performance, such as throughput and response time, may degrade. Traditional pure performance model that ignores failure and recovery but con- siders resource contention generally overestimates the system’s ability to perform a certain job. On the other hand, pure avail- ability analysis tends to be too conservative since performance considerations are not taken into account. To obtain realistic composite performance and availability measures, one should consider performance changes which are associated with failure recovery behavior. Over the last two decades, significant advances have been made in the development of techniques for evaluating the per- formance, availability and reliability of computer and com- munications systems in an integrated way. In the late 1970s, Beaudry [2] developed measures which provide quantitative in- formation about the tradeoffs between reliability and perfor- mance of degradable computing systems. Meyer [17] defined the concept of performability, where performance and reliabil- ity are considered in a unified manner. He also proposed a general framework for model-based performability evaluation. Since then, extensive research activities in performability mod- eling have been carried out ranging from model construction and solution through tool development and applications. There are several approaches [20] that have been shown to be useful for composite performance and availability analysis. One approach is to combine the performance and availability models into a single monolithic model. The advantage of this approach is that it yields accurate results. However, this direct approach generally faces two problems, namely, largeness and stiffness. The largeness problem can be alleviated by using au- tomated generation methods for Markov chains. These auto- mated generation methods address only the model specification and generation issues. To tackle the largeness problem, two ba- sic techniques can be applied: largeness tolerance and largeness avoidance [10]. Stiffness arises when the transition probabil- ities/rates of the Markov models are of widely varying orders of magnitude. This is clearly true in the performability mod- els where the performance related rates are large and the failure related rates are small. Aggregation techniques [3] and stiffness- tolerance [15] can be applied in dealing with the stiffness prob- lems. Another widely applied approach in combined performance and availability analysis is the hierarchical modeling tech- nique [16]. There are several advantages in using this approach. First, the largeness problem can be avoided through the ‘divide and conquer’ strategy, where a large system is decomposed into several submodels [8]. Second, the stiffness problem can be re- solved by separating the fast and slow rates from each other [4]. In this paper, we will illustrate three techniques for com- posite performance and availability analysis through evaluating an queueing system in a wireless communication network. These techniques include: exact composite perfor- mance and availability approach [20], pure performability ap- proach [18] and the BT approach (proposed by Bobbio and Trivedi [4]). In Section II, we give a brief description of a simplified chan- nel allocation scheme in a wireless network. In Section III, three techniques for composite performance and availability analysis are discussed in detail. Numerical results are presented in Sec- tion IV. We make our conclusions in Section V. In the Ap- pendix, a brief introduction of Stochastic Reward Net (SRN) is given.