E. D. Lazowska, J. Zahorjan, G. S. Graham, and K. C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queuing Network Models, Prentice Hall, Englewood Cliffs, N. J., 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....model is presented for verifying the results of the simulator. 5.1 The analytical model The system can be modelled as an Open Queueing Network Model with Multiple Job Classes. The solution adopted here follows the Mean Value Analysis (or Operational Analysis) approach described by Lazowska in [LZGS84] The approach is based on the idea of observations where inputs and outputs are average values rather than a probabilistic description of the system behaviour. The technique allows computation of performance measures such as utilisation, throughput and response time by analysing the long term ....

.... k = D c;k 1 GammaU k The solution technique used is based on the assumption that for separable queueing network models the mean queue length seen upon arrival at resource k, A k ( is equal to the time averaged queue length Q k ( The derivation of the above equations can be found in [LZGS84] In our model, S c;k is not the same for all classes. In order to be able to apply the above solution, we can think of S c;k = 1 and V c;k = S c;k V c;k while deriving the solution. However, since D c;k = S c;k V c;k = S c;k V c;k and since in the final equations, as shown, the ....

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E. Lazowska, J. Zahorjan, G. Graham, and K. Sevcik. Quantitative system performance: computer system analysis using queueing network models. Prentice-Hall, 1984.

....compared against simulation results. Section 6 reviews the related work in the area of static and symbolic performance prediction. Finally, the paper is concluded in Section 7. Contention plays a fundamental role in traditional performance modeling techniques based on e.g. queueing networks [24]. Essentially probabilistic, the use of high cost, numeric analysis methods prohibits compile time application. 2 Mathematical Preliminaries Since the formalism and calculus directly relate to the concept of reduction it is convenient to define a generic reduction operator. Definition 1 ....

....between T and the lower bound T becomes negligible. The fact, that steady state operation is often characteristic for system performance is essentially the justification for the wide spread use of probabilistic modeling formalisms, such as (timed) Petri nets [1] and queuing networks [24]. The typical analysis method involves solving the steady state probability vector from the state transition matrix. The time delays, such as l and s are assumed to be stochastic (negative exponential distribution for Markov analysis) Note, in this respect, that randomness in the overlap ....

E.D. Lazowska et al., Quantitative System Performance: Computer System Analysis Using Queueing Network Models. Englewood Cliffs, N.J.: Prentice-Hall, 1984.

....before. The aggressiveness of freeloaders is modeled by properly choosing , 1 # and 1 # . V. SOLVING THE MODEL In this section we describe an approximate solution technique that will be used to numerically solve the model described above. This technique is based on bottleneck analysis [13], with an extension to handle multiple classes of customers [14] Consider a closed queueing network consisting of a set Q of single server queues and infinite server queues, and C classes of customers. The visit ratio V ,k# Q, c =1, C is defined as the average number of visits of ....

E. D. Lazowska, J. Zahorjan, G. S. Graham, and K. C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queueing Network Models. Prentice-Hall, Inc., 1984.

.... of mobiles in a cell is much greater than the number of channels and have been widely used in literature [7, 8, 2, 3] The exponential channel holding time assumption is shown to be valid for a wide range of system under certain conditions [9] which allows us to conduct the mean value analysis [10]. We further assume that both voice and data occupy one unit of bandwidth. Scheme DTR Q can be modelled as a three dimensional Markov chain. Let k j i P , be the steady state probability that there are i voice calls, j data calls in the system, and k data calls in the data buffer. The ....

E. Lazowska et al, Quantitative system performance: computer system analysis using queuing network models, Prentice-hall, 1984

....of these stereotypes are shown. For sake of conciseness and readability, we do not discuss the details of the dispatchers State Diagrams, rather we focus on the CPU one. The CPU is modeled as a queued service center that extracts jobs from the queue following a quantum based round robin strategy [7, 8]. In the idle state the queue is supposed to be empty and no job is being served. Upon the arrival of a job, the CPU becomes busy and it returns to the idle state in any moment the queue is idle and no job is being served. Two state transitions originate from the busy state. In case of a new ....

Lazowska, E.D., Zahorjan, J., Graham, G.S., Sevcik K.C., "Quantitative system performance : computer system analysis using queueing network models", Englewood Cliffs, N.J., Prentice-Hall, 1984.

....time distribution. Most realworld systems to be modeled, including ours, do not meet product form requirements exactly. However, the techniques for solving product form networks, with appropriate extensions, have been shown to give accurate results even when product form requirements are not met [LZGS84, Bar79, HL84, dSeSM89] Our results indicate the extensions are sufficiently accurate to be useful in understanding our problem. To use a queueing network model, we must provide the model with a description of the service centers, customer classes, and class service demand requirements. The ....

....for the service time per visit, the distribution will not be exponential. This change affects the amount of service time remaining for a customer being served at arrival. We describe the required equation change below. In response to these three differences, the MVA equations become [Rei79a, LZGS84] 1. Little s Law applied to the network to calculate system throughput per class from the mean residence time per class at each server. X c (N) N c k=1 R c;k (N) 2. Little s Law applied to each service center to calculate the mean queue length per class at each server from system ....

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E. Lazowska, J. Zahorjan, G. S. Graham, and K. Sevcik. Quantitative System Performance: Computer System Analysis Using Queueing Network Models. PrenticeHall, Inc., 1984.

....are j 1 other users either active or idle, i.e. holding windows, then the expected number Mj of active users already at node Active is the same as the expected number of active users in a closed network with j 1 users and only nodes Active and Idle. By mean value analysis (Lazowska et al. [8]) permits us to denote the first user s window by the symbol Wo that we have used for the full round trip window. We use this model to size windows in the following way. We pick a parameter s, here called the idle time parameter, approximately equal to A, and solve the recurrence (3) Our ....

E.D. Lazowska, J. Zahorjan, G.S. Graham, and K.C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queueing Network Models, Prentice Hall (1984), pp 112-116.

.... the probabilities of insert, delete, update and read operations are, say, q, q, 1 2q 2 and 1 2q 2 , respectively, we can compute the throughput of the B link tree, X,as X# X d#1 j#0 P#j# i qN i #j##qN d #j# # 1 2q 2 N u #j## 1 2q 2 N r #j# j # 3# By Little s Law [7], the average response time per operation (transaction) is given as R # NX #4# Note that the computation of X above excludes the case when the degradation level is d because the system is not doing useful work (i.e. servicing operations) during a maintenance period. 4. CASE STUDY As a ....

Lazowska, E.D., Zahorjan, J., Graham, G.S. and Sevcik, K.C. (1984) Quantitative System Performance: Computer System Analysis Using Queueing Network Models. Prentice Hall, NJ.

....areas. 2. BACKGROUND, ASSUMPTION AND NOTATION 2.1. Assumptions 1. The database is in a closed system in which the multigramming level is MPL. The database contains SZ db data items. Each transaction on the average accesses SZ tr data items. The unit of physical lock is called a granule [21] which contains SZ lock data items. If a transaction locks a granule then it essentially locks all the data items contained in the granule. Of course, when SZ lock # 1 each data item is a granule itself and has its own separate lock, thus covering the special case considered in [12, 13] Not ....

....case considered in [12, 13] Not placing a separate lock on a data item may be desirable for performance reasons for certain transaction accessing patterns described below. The database system being modeled is characterized by dynamic locking policy and well placed transaction accessing pattern [21]. Dynamic locking means that locks are requested one at a time by a transaction as they are needed and there is no pre determined sequence on the locks. Well placed accessing means that the data items referenced by a transaction are packed into as few granules as possible. This assumes that a ....

Lazowska, E. D., Zahorjan, J., Graham, G. S. and Sevcik, K. C. (1984) Quantitative System Performance: Computer System Analysis Using Queueing Network Models. Prentice Hall, Englewood Cliffs, NJ.

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E. D. Lazowska, J. Zahorjan, G. S. Graham, and K. C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queuing Network Models, Prentice Hall, Englewood Cliffs, N. J., 1984.

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LAZOWSKA, E. D., ZAHORIAN, J., GRAHAM, G. S., AND SEVCIK, K. C. Quantitative System Performance : Computer System Analysis Using Queueing Network Models. PrenticeHall, Englewood Cliffs, N.J, 1984.

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E. Lazowska, J. Zahorjan, S. Graham, and K. Sevcik. Quantitative system performance: computer system analysis using queuing network models. Prentice Hall, 1984.

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E. Lazowska, J. Zahorjan, S. Graham, and K. Sevcik, Quantitative system performance: computer system analysis using queuing network models. Prentice Hall, 1984.

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E. Lazowska, J. Zahorjan, S. Graham, and K. Sevcik. Quantitative system performance: computer system analysis using queuing network models. Prentice Hall, 1984.

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E. Lazowska, J. Zahorjan, S. Graham, and K. Sevcik, Quantitative system performance: computer system analysis using queuing network models. Prentice Hall, 1984.

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LAZOWSKA, E. D., ZAHORIAN, J., GRAHAM, G. S., AND SEVCIK, K. C. Quantitative System Performance : Computer System Analysis Using Queueing Network Models. PrenticeHall, Englewood Cliffs, N.J, 1984.

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Lazowska, E. D.; Zahorjan, J.; Graham, G. S. and Sevcik, K. (1984) Quantitative System Performance: Computer System Analisys Using Queueing Network Models, Prentice Hall, 1984.

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E. D. Lazowska, J. Zahorjan, G. S. Graham, K. C. Sevcik, "Quantitative System Performance Computer System Analysis Using Queueing Network Models", Prentice-Hall, Inc., 1984.

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E. Lazowska, J. Zahorjan, G. Scott Graham, and C. Sevcik. Quantitative System Performance: Computer System Analysis Using Queueing Network models. Prentice-Hall, 1984.

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E. D. Lazowska, J. Zahorjan, G. S. Graham, and K. C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queuing Network Models, Prentice Hall, Englewood Cliffs, N. J., 1984.

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Lazowska, E.D., Zahorjan, J., Graham, G.C., Sevcik, K.C., Quantitative System Performance -- Computer System Analysis Using Queueing Network Models, Prentice-Hall, 1984.

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D. Lazowska, J. Zahorjan, G.S. Graham and K.C. Sevcik, Quantitative System Performance: Computer System Analysis using Queuing Network Models, Prentice-Hall Inc., 1984.

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D. Lazowska, J. Zahorjan, J. S. Graham and K. C. Sevcik, Quantitative System Performance-Computer System Analysis Using Queueing Network Models, Prentice-Hall, 84.

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E.D. Lazowska, J. Zahorjan, G.S. Graham, and K.C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queueing Network Models. Prentice Hall, 1984.

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E. D. Lazowska, J. Zahorjan, G.S. Graham, and K.C. Sevcik, Quantitative System Performance: Computer System Analysis Using Queueing Network Models, PrenticeHall, Englewood Cliffs, N. J., 1984.

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