R.M. Smith, K.S. Trivedi and A.V. Ramesh. Performability analysis: measures, an algorithm and a case study. IEEE Trans. on Comp., 37(4): 406-417, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....t k indicates failure (repair) of a component, # k (t) in (17) provides the mean number of failures (repairs) of that component in (0, t) 11. Performance Reliability Modelling through SPN Performance oriented reliability analysis has been the subject of an extensive literature in recent years [9, 33, 27, 45]. We will show, by means of fully elaborated examples, that 29 the SPN language, described in the previous sections, is very suitable to model this class of problems. 11.1. PARALLEL UNITS WITH SHARED RESOURCE This situation has been depicted in Figure 8, and arises very often in distributed ....

R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406--417, 1988.

....such correlations for cluster based Internet services. In the future, we may extend our methodology for designers to test their service s sensitivity to sets of potentially correlated faults. 2. 3 Performability Metric Despite much work that studies both performance and availability (e.g. [21, 30]) there is arguably no single performability metric for comparing systems. Thus, we propose a combined performability metric that allows direct comparison of systems using both performance and availability as input criteria. Our approach is to multiply the average throughput by an availability ....

....has also been a large number of system availability studies. Two approaches that are used most often include empirical measurements of actual fault rates [3, 13, 20, 16, 23] and a rich set of stochastic process models that describe system dependencies, fault likelihoods over time, and performance [10, 21, 30]. Compared to these complex stochastic models, our models are much simpler, and thus more accessible to practitioners. This stems from our more limited goal of quantifying performability to compare systems, as opposed to reasoning about system evolution as a function of time. A recent work [1] ....

R. M. Smith, K. S. Trivedi, and A. V. Ramesh. Performability Analysis: Measures, an Algorithm, and a Case Study. IEEE Transactions on Computers, 37(4), April 1998.

....because #### ###### the numerical impact of this difference in assumptions is minimal. However, a full investigation of discrepancies between these assumptions is beyond the scope of this work. 2. 3 Performability Metric Despite much work that study both performance and availability (e.g. [19, 26]) there is arguably no single performability metric for comparing systems. Thus, if we have a number of systems (or versions of the same system) that give different points of performance vs. availability in this two dimensional space, it is difficult to say which is better. We propose a combined ....

R. M. Smith, K. S. Trivedi, and A. V. Ramesh. Performability Analysis: Measures, an Algorithm, and a Case Study. IEEE Transactions on Computers, 37(4), April 1998.

....because MTTF MTTR the numerical impact of this difference in assumptions is minimal. However, a full investigation of discrepancies between these assumptions is beyond the scope of this work. 2. 3 Performability Metric Despite much work that study both performance and availability (e.g. [19, 26]) there s arguably no single performability metric for comparing systems. Thus, if we have a number of systems (or versions of the same system) that give different points of performance vs. availability in this two dimensional space, it is difficult to say which is better. We propose a combined ....

R. M. Smith, K. S. Trivedi, and A. V. Ramesh. Performability Analysis: Measures, an Algorithm, and a Case Study. IEEE Transactions on Computers, 37(4), April 1998.

....computed using uniformization for time t or by standard Gauss Seidel or SOR for the limiting case Vt 4o. For [t,t l] the expected value is easily obtained using uniformization. Techniques for cal culating the distribution of [ t,t l] are much more sophisti cated but available (see, for example, [17, 4, 11, 3, 12, 8]) To evaluate Y[ 0,TF] the methods described in [5, 2, 9, 18] can be used to compute the distribution of the reward accumulated until absorption. For Y[ t,TF] we need the state OGI han OG3b Figure 8. SAN model of fault tolerant com puter system occupancy probabilities at time t, which ....

....mode, there is one token in place Normal, and in diagnostic Table 1. Methods for evaluating the reward variables Reward Variable Solution Method Obtainable Information Uniformization Distribution Gauss Seidel, SOR Distribution Y[ t] Uniformization Expected value Special methods (e.g. [3, 4, 8, 11, 12, 17]) Distribution Y[ TF] Linear system (e.g. 2, 5, 9, 18] Moments Y[ t] Y[o,t] starting with r Distribution mode, there are zero tokens in Normal. Jobs arrive to be processed according to a Poisson process defined by timed activity arrival. The finite buffer capacity is modeled by input gate ....

R.M. Smith, K. S. Trivedi, and A. V. Ramesh. Performability analysis: Measures, an algorithm, and a case study. 1EEE Transactions on Computers, 37(2):406417, 1987.

....of view the most signi cant measure is the total amount of work done by the system in a nite interval. The accumulated reward is a random variable whose Cdf is called the performability [51] Various numerical techniques for the evaluation of the performability have appeared in the literature: [38, 24, 33, 66, 25, 60, 59, 26]. In the user oriented (or task oriented) point of view the system is regarded as a server, and the emphasis of the analysis is on the ability of the system to provide a prescribed service in due time. Consequently, the most characterizing measure becomes the probability of accomplishing an ....

R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406-417, 1988.

....does not allow to apply this approach for the analysis of MRM with large ( 100) state spaces. Other direct methods make use of a spectral or partial fraction decomposition, which is relatively easy for acyclic CTMCs, since the eigenvalues of the generator matrix are available in its diagonal [18]. The subclass of MRMs where the user has an associated Phase type distributed random work requirement was studied in [4] In this case the completion time is Phase type distributed, i.e. an extended CTMC can be defined which characterize the distribution of the completion time. There are very ....

....= 800; 000 5:79 Delta 10 Gamma6 4:13 Delta 10 Gamma4 1:92 Delta 10 Gamma3 0:018 0:022 Table 3. Example 2 In the second example, the performance parameters of a Carnegie Mellon multiprocessor system are evaluated by the proposed method. The system is similar to the one presented in [18]. The system consists of N processors, M memories, and an interconnection network (composed by switches) that allows any processor to access any memory (Figure 4) The failure rates per hour for the system are set to be 0.1, 0.05, 0.01 and 0.003 for the processors, memories, switches, and general ....

R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406--417, 1988.

....accumulated reward does not increase in S c and the completion can not occur while Z(t) 2 S c . 4 Numerical Example The results of this paper are demonstrated by the analysis of a simple multiprocessor system. The system is similar to the Carnegie Mellon multiprocessor system, presented in [15]. The system consists of N processors, M memories, and an interconnection network (i.e. a crossbar switch) that allows any processor to access any memory (Figure 1) The failure rates per hour for the system are set to be 0.2, 0.1 and 0.05 for the processors, memories and the switch, ....

R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406--417, 1988.

....of accumulated reward over a finite mission (with general reward rates) is more complex to obtain. In [12] Iyer et al. proposed an algorithm to compute recursively the moments of the accumulated reward over the mission time, with a polynomial computational complexity in the number of states. In [13], the distribution of this random variable has been derived using Laplace transform and numerical inversion procedures to get the result in the time domain. De Souza e Silva and Gail [14] proposed a method based on the uniformization RR n2254 4 H edi Nabli, Bruno Sericola technique, however ....

R. M. Smith, K. S. Trivedi, and A. V. Ramesh. Performability analysis: measures, an algorithm, and a case study. IEEE Trans. Computers, C-37:406--417, April 1988. RR n2254 36 H'edi Nabli, Bruno Sericola

....MRM M is a pair (C, #) where C is a (labelled) CTMC, and # : S # IR #0 is a reward structure that assigns to each state s # S a reward #(s) also called gain or bonus or dually, cost. Example 1. As a running example we consider a fault tolerant multiprocessor system inspired by [15]. The system consists of three processors, three memories, and a single interconnection network that allows a processor to access any memory. We model this system by a CTMC, depicted below, where state (i, j, 1) models that i processors and j memories (1 # i, j 4) are operational and are ....

....3, 1) with rate #. 3# 3# 2# 2# 3 3 3 2 2 2 # # # # # # # # # # # # # # # # # # # 3# 2# 331 321 311 211 221 231 131 121 111 F # # The reward structure can be instantiated in di#erent ways so as to specify a variety of performability measures. The following reward structures are taken from [15]. The simplest reward structure (leading to an availability model) divides the states into operational and non operational states: # 1 (F ) 0 and # 1 (i, j, k) 1. A reward structure in which varying levels of performance of the system are represented is for instance based on the capacity of ....

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R.M. Smith, K.S. Trivedi and A.V. Ramesh. Performability analysis: measures, an algorithm and a case study. IEEE Trans. on Comp., 37(4): 406--417, 1988.

....2. A (labelled) MRM M is a pair (C; where C is a (labelled) CTMC, and : S IR 0 is a reward structure that assigns to each state s 2 S a reward (s) also called gain or bonus or dually, cost. Example 1. As a running example we consider a fault tolerant multiprocessor system inspired by [15]. The system consists of three processors, three memories, and a single interconnection network that allows a processor to access any memory. We model this system by a CTMC, depicted below, where state (i; j; 1) models that i processors and j memories (1 6 i; j 4) are operational and are ....

....with rate . 3 3 2 2 3 3 3 2 2 2 3 2 331 321 311 211 221 231 131 121 111 F The reward structure can be instantiated in di erent ways so as to specify a variety of performability measures. The following reward structures are taken from [15]. The simplest reward structure (leading to an availability model) divides the states into operational and non operational states: 1 (F ) 0 and 1 (i; j; k) 1: A reward structure in which varying levels of performance of the system are represented is for instance based on the capacity of ....

[Article contains additional citation context not shown here]

R.M. Smith, K.S. Trivedi and A.V. Ramesh. Performability analysis: measures, an algorithm and a case study. IEEE Trans. on Comp., 37(4): 406-417, 1988.

....However, it is worth pointing out that the implementation of these techniques, that indeed determine the system reliability, require that some of the system performance be traded for reliability. Methodological approaches that allow one to assess these trade off issues are discussed in [1, 38, 57, 39]. The principal issues concerning the design of a RTOS are introduced below, in isolation. In particular, in the following we shall discuss (i) relevant characteristics of the RT applications that may use a RTOS, ii) two general paradigms that can be applied to the design of a RTOS, iii) time ....

Smith R. M., Trivedi K. S. , Ramesh A. V.: Performability Analysis: Measures, an Algorithm, and a Case Study. IEEE Trans. on Computers, C-37(4): April 1988, 406--417.

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R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406--417, 1988.

....to study system behavior in the presence of component faults, disregarding di erent performance levels in di erent con gurations. Several di erent types of interactions and corresponding tradeo s have prompted researchers to consider combined evaluation of performance and reliability availability [18, 27, 28, 42]. Most work on the combined evaluation is based on the extension of Markov processes to Markov reward processes [17] where a reward is attached to each state of the Markov process. Markov reward processes have the potential to re ect concurrency, contention, faulttolerance, and degradable ....

.... reward processes have the potential to re ect concurrency, contention, faulttolerance, and degradable performance; they can be used to obtain not only program system performance and system reliability availability measures, but also combined measures of performance and reliability availability [3, 9, 27, 29, 42]. Since the Markov process is generated from a concise GSPN model, it is necessary to express the reward structure in terms of GSPN entities. In other words, the GSPN becomes a GSPN reward process which can be automatically transformed into a Markov reward process. Steady state analysis of ....

R. M. Smith, K. S. Trivedi, and A. V. Ramesh. Performability analysis: measures, an algorithm, and a case study. IEEE Transactions on Computers, Apr. 1988.

.... of Y (1) representing the accumulated reward up to absorption, conditioned on the initial state i: C i (x) prfY (1) x j X 0 = ig = pr Z 1 r X(t) dt x j X 0 = i The problem of computing the distribution of Y (t) for a nite t in a Markov reward process is considered elsewhere [6]. The distribution of Y (t) in a semi Markov reward process is discussed in [7, 8] The following semi Markov reward process will be used as a running example throughout the paper. Errors arise in a system (initially in an up state) according to a Poisson process with rate . When an error is ....

R. M. Smith, K. S. Trivedi, and A. V. Ramesh, \Performability analysis: measures, an algorithm, and a case study," IEEE Transactions on Computers, Apr. 1988.

....suitable assignment of the reward rates. 5.1.3 Distribution of cumulative measures Let F (t; y) P rob fY (t) yg denote the cdf of the reward accumulated in (0; t) The expected value (13) may not give a sufficiently accurate indication about the probability of occurrence of a single event. In [109], several examples are reported revealing a behavior 17 that is not deducible from the mere analysis of the average values. However, computation of F (t; y) is a very complex task [109, 101, 53] and it is not usually available in standard SPN based tools. 6 Dealing with large state spaces SPNs ....

....(13) may not give a sufficiently accurate indication about the probability of occurrence of a single event. In [109] several examples are reported revealing a behavior 17 that is not deducible from the mere analysis of the average values. However, computation of F (t; y) is a very complex task [109, 101, 53] and it is not usually available in standard SPN based tools. 6 Dealing with large state spaces SPNs can provide a very compact representation of very large systems. This is reflected in an exponential growth of the reachable markings as a function of the primitive elements in the SPN (places ....

R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406--417, 1988.

....a suitable assignment of the reward rates. 5.1.3 Distribution of cumulative measures Let F (t; y) P rob fY (t) yg denote the cdf of the reward accumulated in (0; t) The expected value (13) may not give a suciently accurate indication about the probability of occurrence of a single event. In [115], several examples are reported revealing a behavior that is not deducible from the mere analysis of the average values. However, computation of F (t; y) is a very complex task [115, 107, 58] and it is not usually available in standard SPN based tools. 6 Dealing with large state spaces SPNs can ....

....value (13) may not give a suciently accurate indication about the probability of occurrence of a single event. In [115] several examples are reported revealing a behavior that is not deducible from the mere analysis of the average values. However, computation of F (t; y) is a very complex task [115, 107, 58] and it is not usually available in standard SPN based tools. 6 Dealing with large state spaces SPNs can provide a very compact representation of very large systems. This is re ected in an exponential growth of the reachable markings as a function of the primitive elements in the SPN (places and ....

R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406-417, 1988.

....more compact PNs than would be otherwise possible in many situations. When exhaustive state space exploration techniques are employed, their use can dramatically reduce the state space. As an example, consider the PN model for a ISDN channel depicted in Figure 2, which was originally presented in [36]. The system behaves as follows: ffl Voice and data packets arrivals are modelled through transitions Tarrival Gamma voice and Tarrival Gamma data, respectively; ffl Voice and data processing time are modeled though transitions T ser Gamma voice and T ser Gamma data; ffl The transmitter ....

....Both prs and prd memory policies are allowed. UltraSAN [35] is based on a class of SPN models known as stochastic activity networks and has been primarily used for performability analysis. Steady state as well as transient simulation are also available. Hierarchical approach is adopted in SHARPE [36]. It provides a variety of probabilistic, discrete state models used to assess the reliability and performance of computer and communication systems. GSPN is one of seven model types. Originally provided with a textual input, now a graphical interface is also available [34] SPNP [14] is a ....

R. Smith, K. Trivedi, and A.V. Ramesh. Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers, C-37:406--417, 1988.

....of SPN models. The full power and generality of C is available, but a working knowledge of C is sufficient to use SPNP effectively. The SPN models specified to SPNP are actually SPN Reward Models or Stochastic Reward Nets (SRNs) 9, 10] which are based on the Markov Reward Model paradigm [18, 37]. This provides a powerful modeling environment for the analysis of: ffl Dependability (Reliability, Availability, Safety) ffl Performance. ffl Performability. Several important Petri net constructs like marking dependency, variable cardinality arc and enabling functions [9] facilitate the ....

....net (PN) concepts. The SPN model we adopt is best described in [9, 10, 14] but it may be useful to consult [2] For a reference on the C language, see [16] For further information on Markov chains, performance modeling, and reliability modeling see [42] while for performability modeling see [37, 43]. Markov and Markov reward model solution techniques are surveyed in [36] Sensitivity analysis of Markov and Markov reward models is discussed in [3] and the sensitivity analysis of SRN models is discussed in [26] Several papers have appeared in the literature where SPNP was used [4, 5, 6, 7, 8, ....

R. M. Smith, K. S. Trivedi, and A. V. Ramesh. Performability analysis: measures, an algorithm, and a case study. IEEE Trans. Comput., C-37(4):406--417, Apr. 1988.

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R.M. Smith, K.S. Trivedi and A.V. Ramesh. Performability analysis: measures, an algorithm and a case study. IEEE Trans. on Comp., 37(4): 406-417, 1988.

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R.M. Smith, K.S. Trivedi, A.V. Ramesh, Performability Analysis: Measures, an Algorithm and a Case Study, IEEE Transactions on Computers, Vol.37, No.4, April 1988, pp.406-417.

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R.M. Smith, K.S. Trivedi, A.V. Ramesh, Performability Analysis: Measures, an Algorithm and a Case Study, IEEE Transactions on Computers, Vol.37, No.4, April 1988, pp.406-417.

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R. M. Smith, Kishor S. Trivedi, and A. V. Ramesh. Performability Analysis: Measures, an Algorithm, and a Case Study. IEEE Transactions on Computers, 37(4), April 1998.

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R.M. Smith et al. Performability analysis: measures, an algorithm and a case study. IEEE Transactions on Computers, C-37(4):406--417, April 1988.

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R.M. Smith et al. Performability analysis: measures, an algorithm and a case study. IEEE Transactions on Computers, C-37(4):406--417, April 1988.

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