E. D. Lazowska, J. Zahorjan and M. Vernon "A Comparison of Performance Petri Nets and Queueing Network Models" Modelling Techniques and Performance Evaluation, edit by S. Fdida and G. Pujolle, Elsevier Science Publishers B. V. (North-Holland), 191-202, (1987).  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... nite capacity queues are more appropriate models for systems with nite bu er and blocking, but their analysis is in general more complex than in nite capacity QNMs and it is often carried on with approximated techniques [15] This class of QNMs is referred to as Queueing networks with Blocking [2, 7, 8, 9, 10, 12, 15]. When a user tries to enter a saturated node, i.e. a node node whose queue has attained its maximum capacity, then there is a block. In the literature several proposals exist with respect to di erent types of blocking mechanisms. We just recall the Blocking After Service (BAS) mechanism that we ....

E. D. Lazowska, J. Zahorjan and M. Vernon "A Comparison of Performance Petri Nets and Queueing Network Models" Modelling Techniques and Performance Evaluation, edit by S. Fdida and G. Pujolle, Elsevier Science Publishers B. V. (North-Holland), 191-202, (1987).

....of polynomial complexity on the size of the model, have been developed for important classes of these models, contributing to their increasing success. Many proposals exist to extend the modelling power of queueing networks by adding various synchronization constraints to the basic model [SMK82, VZL87, CCS91b] Unfortunately, the introduction of synchronization primitives usually destroys the product form solution, so that general parallel and distributed systems are not easily studied with this class of models. More recently, many SPN models have been introduced as formalisms reflecting both ....

....solutions. In general, however, these extensions destroy the local balance property, so the extended queueing models with synchronizations are used mainly as system descriptions for simulation experiments. Even the computation of bounds for these classes of models is not yet well developed. In [VZL87] a comparison has been proposed between synchronized queueing networks and stochastic Petri nets, showing that the two formalisms are roughly equivalent from a modelling point of view. Here we show how the different queueing network models with synchronizations can be uniformly represented ....

M. Vernon, J. Zahorjan, and E. D. Lazowska. A comparison of performance Petri nets and queueing network models. In Proceedings of the 3 rd International Workshop on Modelling Techniques and Performance Evaluation, pages 181--192, Paris, France, March 1987. AFCET.

....needs to be complemented by the other. To overcome these insufficiencies, both model worlds have (by themselves) been enhanced in various ways by additional modelling features, giving rise to new model worlds such as Timed and Stochastic Petri Nets (e.g. 21] and Extended Queueing Networks (e.g. [29]) Those new model worlds are compared in [29] as regarding their expressive powers and their evaluation efficiencies. One important result of that study is, that certain specific deficiencies remain in both areas: Timed and Stochastic Petri Nets have, e.g. still difficulties in describing ....

.... these insufficiencies, both model worlds have (by themselves) been enhanced in various ways by additional modelling features, giving rise to new model worlds such as Timed and Stochastic Petri Nets (e.g. 21] and Extended Queueing Networks (e.g. 29] Those new model worlds are compared in [29] as regarding their expressive powers and their evaluation efficiencies. One important result of that study is, that certain specific deficiencies remain in both areas: Timed and Stochastic Petri Nets have, e.g. still difficulties in describing scheduling strategies in an appropriately compact ....

M. Vernon, J. Zahorjan, E.D. Lazowska. A comparison of performance Petri Nets and Queueing Network models. Proceedings on the International Workshop on Modelling Techniques and Performance Evaluation, Paris (France), 1987, pp. 191-202.

....time. On the other side queueing networks are not suitable for qualitative analysis, for they miss e.g. the possibility of describing forking and joining of processes. Some model worlds, like e.g. timed and stochastic Petri nets and extended queueing networks, try to eliminate these deficits. In [24] timed and stochastic Petri nets and extended queueing networks are compared due to their expressive power and evaluation efficiency. One important result of the discussion there is that timed and stochastic Petri nets have a greater modelling power if the description of scheduling strategies is ....

....customer with higher priority (class 1) preempts the service of the customer being served at that moment. The preempted customer will proceed his task at the interrupted point after completion of service of all customers with higher priority. 6 In extended queueing networks like e.g. RESQ ([20, 24]) some elements for the description of synchronization aspects are added to the queueing network world. Additional elements are passive resources, fork, join and split nodes (see figure 4) Each passive resource consists of a number of tokens representing the resource units available for customers ....

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M. Vernon, J. Zahorjan, E.D. Lazowska. A comparison of performance Petri nets and queueing network models. Proceedings on the International Workshop on Modelling Techniques and Performance Evaluation, Paris (France), 1987, pp. 191-202. 14

....either one of the above formalisms is, in its pure form, incomplete. To overcome these insufficiencies, both formalisms have been enhanced in various ways by additional modeling features leading to new formalisms such as Timed and Stochastic Petri Nets [1] and Extended Queueing Networks [15] In [16] Timed and Stochastic Petri Nets and Extended Queueing Networks are compared due to their expressive power and evaluation efficiency. One important result of the discussion there is, that certain specific deficiencies remain in both areas: Timed and Stochastic Petri Nets have, e.g. still ....

M. Vernon, J. Zahorjan, E.D. Lazowska. A comparison of performance Petri Nets and Queueing Network models. Proceedings on the International Workshop on Modelling Techniques and Performance Evaluation, Paris, 1987, pp. 191-202.

....approach based on structural analysis of stochastic Petri nets and basic queueing laws. Many monoclass queueing networks can be mapped on stochastic FC Petri nets. On the other hand, FC nets can be interpreted as monoclass queueing networks augmented with some form of synchronization primitives [15] (preserving the free choice decision scheme) In this paper we consider strongly connected (i.e. closed ) FC synchronized QNs (closed FCSQN) The reader may notice that unclever use of synchronizations in the free choice synchronized queueing networks can lead to pathological cases as ....

....solution. In general, however, these extensions destroy the local balance property so that extended queueing models with synchronization are used mainly as system descriptions for simulation experiments [13] Even the computation of bounds for these classes of models is not yet well developed. In [15] a comparison has been proposed between synchronized QNs and stochastic Petri nets, showing that the two formalisms are roughly equivalent from a modelling point of view. However, no special computation based on the Petri net structure has yet been proposed, to motivate the use of a Petri net ....

M. Vernon, J. Zahorjan, and E. D. Lazowska. A comparison of performance Petri nets and queueing network models. In Proceedings of the 3 rd International Workshop on Modelling Techniques and Performance Evaluation, pages 181--192, Paris, France, March 1987. AFCET.

....formalism. It is a stochastic extension of classical process algebras such as CCS or CSP. PEPA appears to offer several attractive features which have not previously been available to the performance modeller. As in the paper of Vernon et al. comparing queueing networks and performance Petri nets [20], we aim to compare the paradigms in terms of the facilities that they offer the modeller. We consider model construction as well as analysis techniques to produce quantitative and qualitative results. Note that our motivation is distinct from that of previous studies in which untimed Petri nets ....

....which the formalisms express the behaviour of systems. At a notational level the difference seems significant since PEPA is a textual language and GSPN has a graphical notation. However, at the other extreme, if we consider the class of Markov processes which can be expressed, it is clear, as in [20], that any Markov process can be expressed as a degenerate form of either paradigm. In GSPN a place is associated with each state and appropriate transitions are inserted between the places to represent the transitions in the Markov process. The place corresponding to the initial state is marked ....

M. Vernon, J. Zahorjan, and E. Lazowska. A comparison of performance Petri nets and queueing network models. In Proc. of Int. Workshop on Modelling Techniques and Performance Evaluation, Paris, 1987.

.... are one of the more popular and classical tools for the performance evaluation of computer systems [1] With the advent of complex distributed systems, many proposals have been made to extend the modeling power of queueing networks by adding various synchronization constraints to the basic model [2, 3, 4]. One of the most important characteristics of queueing networks determining their popularity was the development of efficient, polynomial complexity numerical solution algorithms, based on their product form solution [1] Unfortunately, the introduction of synchronization constraints usually ....

.... been introduced as a modeling tool capable of naturally representing synchronization and concurrency [5, 6, 7] The intimate relation between some classes of synchronized queueing networks and some structural subclasses of timed Petri nets has already been recognized and studied by several authors [3, 8, 9, 10]. One of the main problems in the actual use of timed and stochastic Petri net models for the performance evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance measures are obtained from the numerical solution of a ....

M. Vernon, J. Zahorjan, and E. D. Lazowska. A comparison of performance Petri nets and queueing network models. In Proceedings of the 3 rd International Workshop on Modeling Techniques and Performance Evaluation, pages 181--192, Paris, France, March 1987. AFCET.

....An example of a Petri Net is shown in figure 1.13. The places, transitions, and tokens are denoted as circles, rectangles, and discs (i.e. smaller circles) respectively. Any queueing network or extended queueing network model can be represented using a Petri Net model. The converse is not true [Vernon 86] Unfortunately, finding the performance measures of the models can require a great deal of computation. Though some classes of Petri Nets exist with low solution costs, they are no more general than the separable class of queueing network models. Several techniques have been developed to ....

....space, though with the lower number of transitions it is smaller than if the reduction technique were not used. The performance measures for the state space are still found using global balance techniques so it is again possible to examine only small models using this approach. Vernon et al. Vernon 86] consider mapping separable QNs onto GSPNs. Each queue in the QN is represented using a place, each server as a timed transition, and routing choices (probabilities) are represented using immediate transitions. Customers in the QN are represented as tokens in the GSPN. Define an initial class ....

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M. Vernon, J. Zahorjan and E.D. Lazowska. A Comparison of Performance Petri Nets and Queueing Network Models, Technical Report, University of Washington, Seattle, USA, September 1986.

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