Performance Modeling of Rule-Based Architectures as Discrete-Time Quasi Birth-Death Processes

Abstract

This paper deals with the examination and mathematical modeling of rule-based systems and list topologies applied in software architectures as well as in hardware solutions. In our investigation we focus on telecommunication applications utilizing list topologies. We introduce Quasi Birth-Death processes as the mathematical formalism behind our models. Besides, we extend the simple model of list topologies with respect to the input and output interfaces of the implementation. Furthermore, we present our model on the example of Access Control Lists applied in IP routers and we show results that can be derived from the model. I. INTRODUCTIONIn practice, during the examination of telecommunication or software systems that operate using sequential lists as data structures, and search through these lists by means of various search methods, we faced a significant proposition. Namely, that it might be enough to use simple averaging and to operate with mean values in case we want to optimize the behavior of these systems [17]. But, in case we also want to derive performance indices more precisely the arrival intensity of the traffic needs to be taken into consideration. When the examined system is loaded, queuing appears at the system's interfaces and that has a serious impact on the system's performance. Our aim is to develop a mathematical model that is capable of describing and calculating performance indices more precisely with the system's interfaces included in the investigation.Although, systems previously using sequential lists are replaced in some cases with other structures, e.g. hashes, balanced tree structures, etc., sequential lists are still in operation (maybe by applying a few tricks) in several application areas, e.g. databases, alternative behavior in software architectures, and firewall rules. Namely, these applications operate with lists, sequentially searching through them step-by-step. The replacement of these data structures might solve a few bottlenecks if they can be applied, but we also want to model and investigate existing systems and their performance.Recently, there have been several approaches to automate performance evaluation of software architectures. Most of them start from a software specification that can be given in various formal description languages [8], [9], [10], [11]. In most cases a mathematical formalism is targeted also, as a basis for prediction of various performance indices. Our aim is to develop models that can be easily adopted by setting their

Performance Analysis of Concurrent PCOs in TTCN-3

“…The mathematical formalism behind our evaluation method can be identified as discrete-time Quasi Birth-Death processes (QBDs) [8]. A simpler M/G/n type solution would not allow us to use finite queues and to calculate state distributions [9].…”