C.H. Sauer and K.M. Chandy. Computer Systems Performance Modeling. Prentice-Hall, Englewood Cliffs, N.J., 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....with the remaining networks. In other words, this queue should be flow equivalent to the replaced network assuming equal load. This is done by setting the conditional throughputs of the isolated subnetwork equal to the load dependent service rates of the flowequivalentserver. For more details see [21], pp. 165. In the case of a kanban controlled stage, the machines servers m k( machine i of stage k) are considered as the subnetwork. To obtain the conditional throughputs of the subnetwork any appropriate technique can be used. We used Marie s Method( 17, 18] as suggested by Dallery [5] 14 ....

Charles H. Sauer and K. Mani Chandy. Computer Systems PerformanceModeling. Prentice-Hall, Englewood Cliffs, NJ, 1981.

.... (LCFS PR) service discipline has been subject of many investigations due to its outstanding property as a product form queueing node (see BCMP [2P Applications of the M=G=1 LCFS PR system can be found in the performance analysis of computer systems as stated by Sauer and Chandy [16]. They report on the state transition diagram of the M=M=1 queue with LCFS PR service. Durr [8] gives an explicit formula for the waiting time distribution of the M=G=1 system with an arbitrary number of priorities having either LCFS PR or LCFS nonpreemptive priority queueing discipline. A ....

Charles H. Sauer and K. Mani Chandy. Computer Systems Performance Modeling. Prentice-Hall, Englewood Cliffs, NJ, 1981.

....of mean queue lengths and chain throughputs directly. It avoids the problem of floating point overflows (Floating point underflows may still occur [20] However, its time and space requirements also grow exponentialiv with K. Other computational algorithms available (such as LBANC and CCNC in [ 7,24] and NCA in [2] are variants of the basic convolution and M7VA algorithms and thus also suffer from the exponential growth in space and time requirements as K increases. The modeling of distributed systems and communication networks often require the use of a large number of routing chains ....

....degenerates to a single value, namely, the normalization constant G( The com putation of network performance measures, such as chain throughputs and mean queue lengths, requires the computation of various other normalization constants. For a tutorial treatment of this topic, see [3] or [24]. The throughput of chain k at center m for a network of closed chains with population vector is [4, 7, 22] Tmk(N) mk = k G(N) for k = 1,2, K, m 1,2, M and N (11) where G( is the normalization constant of the same network with population vector J k and mk is the ....

[Article contains additional citation context not shown here]

Sauer, C. H. and K M. Chandy, .Computer Systems Performance Modeling, Prentice-Hall, Englewood Cliffs, New Jersey, 1981.

....matrices, state spaces) multiplicatively, it is a crucial issue to keep these orders to a minimum, i.e. two states in our case. Several (acyclic) PH representations of order 2 prevalently for the continuous case have been published, but are either based on the first two moments only (e.g. [Sauer and Chandy, 1981, Marie, 1980, Heindl and Telek, 2001] or are restricted to the hyperexponential situation (i.e. the squared coefficient of variation of the considered continuous distribu tion is greater than 1.0 [Whitt, 1982, Altiok, 1984] Another analytic method matches three feasible moments into a ....

C. H. Sauer and K. M. Chandy, Computer Systems Performance Modeling, Prentice-Hall, 1981.

....of mean queue lengths and chain throughputs directly. It avoids the problem of floating point overflows (Floating point underflows may still occur [20] However, its time and space requirements also grow exponentially with K. Other computational algorithms available (such as LBANC and CCNC in [7,24] and NCA in [2] are variants of the basic convolution and MVA algorithms and thus also suffer from the exponential growth in space and time requirements as K increases. The modeling of distributed systems and communication networks often require the use of a large number of routing chains ....

....degenerates to a single value, namely, the normalization constant G( o The com putation of network performance measures, such as chain throughputs and mean queue lengths, requires the computation of various other normalization constants. For a tutorial treatment of this topic, see [3] or [24]. The throughput of chain k at center m for a network of closed chains with population vector is [4, 7 22] Tmk( mk G(N) for k = 1,2, K, m = 1,2, M and N 1 k (tl) where G( is the normalization constant of the same network with population vector 1 k and mk is the relative ....

[Article contains additional citation context not shown here]

Sauer C. H. and K. M. Chandy, .Computer Systems Performance Modeling, Prentice-Hall, Englewood Cliffs, New Jersey, 1981.

....of matrices, state spaces) multiplicatively, it is a crucial issue to keep these orders to a minimum, i.e. two states in our case. Several (acyclic) PH representations of order 2 prevalently for the continuous case have been published, but are either based on the rst two moments only (e.g. [18, 11, 7]) or are restricted to the hyperexponential situation (i.e. the squared coecient of variation of the considered continuous distribution is greater than 1.0 [20, 2] Another analytic method matches three feasible moments into a four state continuous PH representation [9] Note that although ....

C. H. Sauer and K. M. Chandy. Computer Systems Performance Modeling. Prentice-Hall, 1981.

....submitted his Ph.D. thesis. Since then, great progress has been made in this area. It has become a distinct discipline independent of others, such as computer architecture, system organization, operating system, and so forth. Many textbooks are devoted to this subject (see for example [Drummond73; Sauer81; Jain91] Performance evaluation can be defined as assigning quantitative values to the indices of the performance of the system under study. So, what is performance To answer this question is not easy, for performance involves many aspects. Here, we do not mean to give our definition, for ....

Sauer, C. H. and Chandy, K. M., Computer Systems Performance Modeling, Prentice-Hall, Englewood Cliffs, NJ, 1981.

.... due to Ashenhurst [4, 16] The same idea has been studied in other areas under different titles, including: compound simple games in game theory [24, 27] compound clutters in set theory [9] and modules in reliability theory [10, 24] Several measures have been proposed to analyze coteries [3, 7, 8, 12, 22, 23, 26, 28, 29]. These measures include availability, communication latency, expected number of operational nodes, quorum size, node and edge vulnerability, reliability, and success rate. None of these measures address the relative importance of each node in the system. In this paper, we present such a measure, ....

C.H. Sauer and K.M. Chandy. Computer Systems Performance Modeling. Prentice-Hall, 1981.

....to its transient or, more often, its stationary distribution (provided always that the QN description permits this mapping, that the process allows for stationarity, etc. In the framework of this methodology, a large subset of the sketched standard QNs, the so called product form class (e.g. [24]) exhibits analytic solutions for its stationary population distributions which are, moreover, amenable to comparatively extremely efficient evaluation algorithms. Beyond that product form class, and also covering the majority of Extended QNs with finite population state spaces as far as the ....

C.H. Sauer, K.M. Chandy. Computer systems performance modeling. Prentice Hall, New Jersey, 1981.

....all jobs are fully sequential. When N = 1, the EQS system is identical to an M M P processor sharing (PS) system and thus REQS (N = 1) RM=M=P PS . On the other hand ASP is identical to FCFS when N = 1 and thus for exponential demands RASP (N = 1) RM=M=P FCFS . Since RM=M=P PS = RM=M=P FCFS [31], RASP = REQS for CD = 1, r = 0, and Sn = 1. 10 Next consider how these policies compare as job parallelism increases, that is, as Sn decreases. Figure 6a plots RASP =REQS versus Sn for the workload ( FN ; exp(1=D) r = 0; fl l ; E(j) fl(j) Consider only the solid curves in the figure, ....

C. Sauer, and K. M. Chandy. Computer System Performance Modeling. Prentice-Hall, Englewood Cliffs, New Jersey, 1981.

....= 52 comparisons are required to determine if a set contains a quorum of a nondominated coterie Q. On the other hand, using a direct approach could require a total of 2 27 Gamma1 = 67; 108; 864 comparisons. 8. 2 Availability Several measures have been proposed to analyze quorum structures [4, 8, 9, 23, 52, 65, 70, 75]. One of the most commonly used measures is availability the steady state probability that a quorum of nodes is operational at any given time. Let U = fx 1 ; x 2 ; Delta Delta Delta ; xN g be a non empty set of nodes, and let Q be a quorum set under U . Let G 2 Q. The probability that only ....

C.H. Sauer and K.M. Chandy. Computer Systems Performance Modeling. Prentice-Hall, 1981.

.... whether based on queueing models or on computer simula3 tion, is more highly developed and more broadly accepted in computer systems engineering than in manufacturing, and closed network models are generally considered to be more important in the computer systems domain than open network models [28, 29, 35]. Closed network models of computer systems are typically justified by the fact that user populations are literally fixed, and if one has several fixed and distinct user populations, all competing for common processing resources, the appropriate queueing network model is a so called multichain ....

Sauer, C. H. and Chandy, K. M. Computer Systems Performance Modeling. Prentice-Hall, 1981.

....Although this is one of the goals of parallel algorithm design, in practice there is often some imbalance of load. ffl Variance of owner process service demands. We have assumed a deterministic owner process service demand when in fact typical processes experience a much larger variance [11]. Assuming a distribution with more variance could cause some parallel tasks to be delayed much longer than T (T Theta O) ffl Guaranteeing the parallel task at least one unit of execution between requests. In a real system owner processes may be reissued in less time, thus parallel tasks could ....

....and hence can not experimentally validate this result. 5 Sensitivity to Workstation Owner Process Variance As noted before, most workloads running on computers have a significant amount of variation in processor demands. For many system the coeffecient of variation has been found to be around 10 [11]. In this section we study the effect of workstation owner process variance on parallel job performance. We first compare weighted speedup predictions of our deterministic analysis with those obtained 0 200 400 600 800 1000 1200 0 2 4 6 8 10 12 Job Response Time in Seconds Number of Processors ....

C.H. Sauer and K.M. Chandy, Computer System Performance Modeling, Prentice-Hall, 1981.

....] 12. Thus, a PEPA description of this activity would be: actiontype; 16; p 12) Similarly, it is possible to describe deterministic transitions by setting the third parameter to 0, although the method of stages is not appropriate when the coefficient of variation (C x = oe E[X] is small [8]. Again, it is stressed that it is the responsibility of the modelling tool designer to determine appropriate translations from the non exponential pdfs to an equivalent Markov process. 6 Renaming Revisited The proposed extensions require changes to the renaming operatational semantics to ....

Charles H Sauer and K Mani Chandy. Computer Systems Performance Modeling. Prentice Hall International, 1981.

....(first come first served, round robin, last come first served preemptive resume) A service center provides some necessary service. Examples include a bank teller, hardware device, or database. Each service center has an associated 1 For a more detailed treatment see Lazowska [8] or Sauer [9]. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 3.5 4 time Exponential PDF (lambda = 1) exp( x) Figure 2: Exponential PDF, 1 queue containing jobs to be processed by that service center. A service center may also be replicated with degree m. A replicated service center ....

....of using nonexponential distributions, however, is an item for future research. 8 RELATED WORK Two bodies of related work exist. The first area is classical results in queueing theory. A great deal of work has been done in queueing theory, and many texts are available (e.g. Lazowska [8] Sauer [9], Jain [5] We build on this work by applying it in a different domain and interpreting the results in the software design world. As we have noted, several issues must be resolved in order to do this. The second area is architecture based analysis. Architecture based static analysis is an ....

C. H. Sauer and K. M. Chandy. Computer systems performance modeling. Prentice-Hall, Englewood Cliffs, NJ, 1981.

....producer consumer relationships between the user tasks. The traffic relationships presented below are an extension of similar relationships in classical queuing networks (e.g. Jackson [4] Gordon and Newell [5] and computer and communications performance models (e.g. Sauer and Chandy [6]) However, task messages do not represent customers in a queuing network because messages are not conserved; a message arriving at a task may stimulate zero, one, or several further messages. In this aspect, messages are more similar to procedure call frequencies in software models (e.g. 7] ....

Sauer, C.H.; Chandy, K.M.; "Computer Systems Performance Modeling", Prentice-Hall, Inc., Englewood Cliffs, N.J. 07632, 1981.

....other. Space limitations and the size of the very extensive literature prevent a complete survey of the relevant literature, but more reference material is available from the author in [2] Extending the Classical Queueing Network Model The classical queueing network model (e.g. Sauer and Chandy [3]) captures much of the behaviour of such systems, especially when it is adapted in a few simple ways as shown by M P M P M P Bus or Interconnection M P M P Local Net Wide Area Net Figure 1: Various Hardware Environments for Concurrent and Parallel Software with Message Passing (buses, local ....

....all hardware devices, managed by schedulers. There may be multiple classes of customers representing, for instance, batch and timesharing jobs. The key to the popularity of this model is the existence of a relatively simple solution in product form for a restricted but interesting class of systems [3]. Mean Value Analysis, as described e.g. in [1] is commonly used to compute solutions. In practice certain advanced model features, outside the range of simple analytic productform solutions, are required for example to represent memory contention, or combinations of execution time ....

C.H. Sauer and K.M. Chandy, Computer Systems Performance Modeling. Englewood Cliffs, New Jersey 07632: Prentice-Hall, Inc., 1981.

.... (LCFS PR) service discipline has been subject of many investigations due to its outstanding property as a product form queueing node (see BCMP [2] Applications of the M=G=1 LCFS PR system can be found in the performance analysis of computer systems as stated by Sauer and Chandy [16]. They report on the state transition diagram of the M=M=1 queue with LCFS PR service. Durr [8] gives an explicit formula for the waiting time distribution of the M=G=1 system with an arbitrary number of priorities having either LCFS PR or LCFS nonpreemptive priority queueing discipline. A ....

Charles H. Sauer and K. Mani Chandy. Computer Systems Performance Modeling. Prentice-Hall, Englewood Cliffs, NJ, 1981.

.... 28, 34, 42] Regarding the former assumption, experience from uniprocessor systems suggests that relative policy performance can be highly sensitive to the (second moment of) job service demand distribution, and that total job demand can have significantly higher variability than the exponential [33, 43]. Relative scheduling policy performance for parallel systems may also be sensitive to the degree of correlation between available job parallelism and total job service requirement. Thus, the particular assumptions in previous analytic models potentially limit the applicability of the results, as ....

....in [32] for the mean number in a GI G c queue, which leads to the following approximate formula for RM=G=c : RM=G=c x ae p 2(c 1) 1 C 2 x ) 2(1 Gamma ae) 1) Note that this approximation is exact for c = 1 and c = 1. Using this approximation and the fact that RM=G=c PS = RM=M=c [33], one can derive the following approximation: RM=G=c PS x ae p 2(c 1) 1 Gamma ae) 2) We note that this approximation has a much simpler form than the exact expression for mean response time in the M=G=c PS queue. It is also exact for c = 1 and very accurate as shown by validations in ....

[Article contains additional citation context not shown here]

C. Sauer, and K. M. Chandy. Computer System Performance Modeling. Prentice-Hall, Englewood Cliffs, New Jersey, 1981.

....the remaining networks. In other words, this queue should be flow equivalent to the replaced network assuming equal load. This is done by setting the conditional throughputs of the isolated subnetwork equal to the load dependent service rates of the flow equivalent server. For more details see [21], pp. 165. In the case of a kanban controlled stage, the machines servers m i k (i.e. machine i of stage k) are considered as the subnetwork. To obtain the conditional throughputs of the subnetwork any appropriate technique can be used. We used Marie s Method (cf. 17, 18] as suggested by ....

Charles H. Sauer and K. Mani Chandy. Computer Systems Performance Modeling. Prentice-Hall, Englewood Cliffs, NJ, 1981.

....efficient Markov chain Monte Carlo algorithm for closed product form networks. Supported in part under NSF grants DMI 9414630 and DMI 9713730 1 Introduction 1. 1 Overview Closed multiclass product form (CMP) queueing networks are useful as models for manufacturing and communication systems [5, 7, 20, 26, 31, 34, 46, 49]. These networks are of interest because their steady state distributions are known explicitly up to a normalization constant. There are three well known non randomized computational methods for throughput the most important performance measure in CMP networks: convolution algorithms and ....

Sauer, C.H., and Chandy, K.M. Computer Systems Performance Modeling. Prentice-Hall, Englewood Cliffs, N.J. 1981.

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C.H. Sauer and K.M. Chandy. Computer Systems Performance Modeling. Prentice-Hall, Englewood Cliffs, N.J., 1981.

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C.H. Sauer and K.M. Chandy. Computer Systems Performance Modeling. Prentice-Hall, Englewood Cliffs, N.J., 1981.

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Charles H. Sauer and K. Mani Chandy, Computer Systems Performance Modeling, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981.

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C. Sauer and K. Chandy, Computer Systems Performance Modeling, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1981).

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