Probabilistic application modeling for system-level performance analysis

The objective of this article is to introduce the use of Stochastic Automata Networks (SANs) as an effective formalism for application-architecture modeling in system-level average-case analysis for platform-based design. By platform, we mean a family of heterogeneous architectures that satisfy a set of architectural constraints imposed to allow re-use of hardware and software components. More precisely, we show how SANs can be used early in the design cycle to identify the best performance/power trade-offs among several application-architecture combinations. Having this information available not only helps avoid lengthy simulations for predicting power and performance figures, but also enables efficient mapping of different applications onto a chosen platform. We illustrate the benefits of our methodology by using the “Picture-in-Picture” video decoder as a driver application.

This paper presents a new methodology for system-level power and performance analysis of wireless multimedia systems. More precisely, we introduce an analytical approach based on concurrent processes modeled as Stochastic Automata Networks (SANs) that can be effectively used to integrate power and performance metrics in system-level design. We show that 1) under various input traces and wireless channel conditions, the average-case behavior of a multimedia system consisting of a video encoder/decoder pair is characterized by very different probability distributions and power consumption values and 2) in order to identify the best trade-off between power and performance figures, one must take into consideration the entire environment (i.e., encoder, decoder, and channel) for which the system is being designed. Compared to using simulation, our analytical technique reduces the time needed to find the steady-state behavior by orders of magnitude, with some limited loss in accuracy compared to the exact solution. We illustrate the potential of our methodology using the MPEG-2 video as the driver application.

To give worst case guarantees for the timing behavior of complex distributed embedded real-time systems, e.g. end-to-end latencies, different compositional approaches for system-level performance analysis have been developed which exhibit great flexibility and scalability. While these approaches are in theory able to handle arbitrary complex systems, the system-level results can easily become very pessimistic with increasing numbers of components. In this article, the basic principles of compositional system-level analysis are explained and its inherent strengths and weaknesses are elaborated. Furthermore, we present improved analysis techniques from existing research which can greatly reduce the pessimism of the system-level analysis results. Two techniques will be discussed in detail: the exploitation of a system’s communication infrastructure by usage of composition and decomposition operators and the exploitation of information w.r.t. the correlation of event processing. These techniques help to make system-level analysis not only applicable, but also a highly useful technique in the integration phase of embedded system design.

The performance evaluation of wireless networks is more complicated than fixed networks because we take into account a lot of parameters such as the cell number, buffer size for data, connection voice number in a cell, and user mobility. In this study we propose a new tool named Xsan based on Stochastic Automata Networks (SANs) which make a simplification of model representation. SANs have been introduced to allow one to model complex parallel systems. Our tool Xsan computes the steady state distribution associated to the model of wireless network which allows one to compute the performance measures like dropping handover probabilities. We give an example of wireless network which we model by SAN and we give the results of dropping handover computed by Xsan.

Stochastic Automata Networks (SANs) are widely used in modeling communication systems, manufacturing systems and computer systems. The SAN approach gives a more compact and efficient representation of the network when compared to the stochastic Petri nets approach. To find the steady state distribution of SANs, it requires solutions of linear systems involving the generator matrices of the SANs. Very often, direct methods such as the LU decomposition are inefficient because of the huge size of the generator matrices. An efficient algorithm should make use of the structure of the matrices. Iterative methods such as the conjugate gradient methods are possible choices. However, their convergence rates are slow in general and preconditioning is required. We note that the MILU and MINV based preconditioners are not appropriate because of their expensive construction cost. In this paper, we consider preconditioners obtained by circulant approximations of SANs. They have low construction cost and can be inverted efficiently. We prove that if only one of the automata is large in size compared to the others, then the preconditioned system of the normal equations will converge very fast. Numerical results for three different SANs solved by CGS are given to illustrate the fast convergence of our method.

Manufacturing systems are quite complex and many research works have been devoted to their analysis, modeling, design and operation. This work is concerned with the exact analysis of discrete part production lines. More specifically, two formalisms are provided: (a) the Markovian Queueing Network and (b) the Stochastic Automata Network (SAN). These two methods are described explicitly via the use of an example of a production line consisting of three stations. SAN methodology utilizes both classical and generalized tensor algebra. The tensor or Kronecker representation of the SAN three-station example is given and comparisons are made between these two exact methods. Their limitations are also examined regarding the numerical results concerned with throughput of discrete part production lines. It is seen that with the SAN formalism one may solve exactly much larger production line configurations than those traditional Markovian formalism can handle.

So far, large stochastic models require considerable amounts of time to be created. In fact, to simulate systems or events, there is a constant need to perform an analysis of the system and its variables. In this paper we propose a method to automatically generate Stochastic Automata Networks (SAN) models for geological events. Based on user-defined input data, the method creates a model in SAN formalism for the prediction of geological stratal stacking patterns through time. Although models automatically generated tend to be less accurate, we believe that the time saved compensates for the precision lost.

This paper is the experimental follow-up to Langville and Stewart (2002), where the theoretical background for the nearest Kronecker product (NKP) preconditioner was developed. Here we test the NKP preconditioner on both Markov chains (MCs) and stochastic automata networks (SANs). We conclude that the NKP preconditioner is not appropriate for general MCs, but is very effective for a MC stored as a SAN.

Lumpable continuous-time stochastic automata networks

Wireless ad hoc networks raised a series of challenging research tracks. In order to analyze and validate the research results achieved, thorough performance evaluation efforts are needed. In this context, the contribution of this paper is two fold: at one side we investigate the effect of forwarding in wireless ad hoc networks, drawing the throughput behavior under variation of connectivity, interference end number of sources; on the other side we propose stochastic automata networks (SAN) as a formalism well suited to the area because of its modularity, allowing model reuse and the structured stepwise representation of important aspects of the reality, and due to its ability to deal with models of considerable sizes, allowing the analytical evaluation of more complex situations.

The fourth generation has been based on the development of the Internet in the air interface. The current Internet lacks the quality of service support. A previous contribution proposed the development of a new protocol (MIR: mobile IP reservation protocol), which provides quality of service guarantees to a mobile terminal [J. Benothman et al., 2000]. To show the benefit of this protocol we propose in this study to make performance evaluation of this protocol. Performance evaluation of this kind of network is difficult because we take into account a lot of parameters such as the cell number, buffer size for data, connection voice number in a cell, handover, etc. Thus the mathematical model associated to this network cannot be solved by a numerical method because of the size of the Markov chain, which is too large. In this study, we propose to use stochastic automata networks to make our performance evaluation.

Phase-type distributions in stochastic automata networks

Simulation is an interesting alternative to solve Markovian models. However, when compared to analytical and numerical solutions it suffers from a lack of precision in the results due to the very nature of simulation, which is the choice of samples through pseudorandom generation. This paper proposes a different way to simulate Markovian models by using a Bootstrap-based statistical method to minimize the effect of sample choices. The effectiveness of the proposed method, called Bootstrap simulation, is compared to the numerical solution results for a set of examples described using Stochastic Automata Networks modeling formalism.

Performance analysis of multi–agent system can be done by experiments with real system, simulation or analytic methods. Now, multi–agent technologies, e.g., (Deloach et al., 2001; JADE), are often based on Unified Modeling Lanuage (UML) (Booch et al., 1999; UML, 2007) or its modifications. The following analytical approaches: queuing network models (Kahkipuro, 1999), stochastic automata networks (Steward et al., 1995), stochastic Petri nets (King & Pooley, 1999), stochastic process algebra (Pooley, 1999), Markov chains can be used in performance evaluation of multi–agent systems. In this chapter, an analytical approach, which is based on Petri nets, is developed. This approach is applied to performance evaluation of layered multi–agent system. These layers are associated with the following types of agents: manager, bidder, and searcher ones. Time–out mechanisms are used in communication between agents. Our method is based on approximation using Erlang distribution. Erlang distributions create the family of distributions with different number of stages. In the paper (Babczynski & Magott, 2006a), an approximation method which is based on Erlang distribution has been applied for the above layered multi–agent system. In that paper, there was no bounds for time of waiting for messages from the agents. In present chapter, time–out mechanisms are used in communication between the agents. The chapter is an extension of the paper (Babczynski & Magott, 2006b) where PERT based approach was presented. Accuracy of our approximation method is verified using simulator. This simulator has been previously used in simulation experiments with the following multi–agent systems: personalized information system (Babczynski et al., 2004a), industrial system (Babczynski et al., 2004b), system with static agents and system with mobile agent (Babczynski et al., 2005). These systems have been expressed in standard FIPA (FIPA) which the JADE technology (JADE) is complied with. The chapter is organized as follows. In section 2, the multi–agent system is described. Then our approximation method is presented. In section 4, accuracy of our approximation method is verified by comparison with simulation results. Finally, there are conclusions.

Congestion in Wireless Multimedia Sensor Networks (WMSN) may cause packet loss, buffer overflow and increases queueing delay, which has a significant negative impact on the network performance and reliability. This problem imposes more resource constraints that involve energy consumption and buffer size to meet additional requirements such as desired buffer size and limited amount of packet loss. One of the fundamental issues of congestion problem in such networks is the queue management. In fact, handling congestion without considering flexible buffer management and queueing methods, stay insignificant against dropping rate and packet loss. Consequently, a novel congestion control approach is needed to overcome these problems. In this paper, a new queue management mechanism called: Priority Queue Management based Explicit Congestion Control (PQMECC) is proposed and modeled using Stochastic Automata Networks, which are appropriate for modeling and analyzing complex systems with interacting components and complex synchronization. The congestion control technique used in PQMECC is based on priority, load repartition mechanism and explicit congestion notification which is generated only if the congestion reaches the threshold value.