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Synchronization and linearity: an algebra for discrete event systems
, 2001
"... The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific ..."
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Cited by 279 (10 self)
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The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX crossreferences are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The
Performance Bounds for Queueing Networks and Scheduling Policies
, 1994
"... Except for the class of queueing networks and scheduling policies admitting a product form solution for the steadystate distribution, little is known about the performance of such systems. For example, if the priority of a part depends on its class (e.g., the buffer that the part is located in), t ..."
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Cited by 71 (16 self)
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Except for the class of queueing networks and scheduling policies admitting a product form solution for the steadystate distribution, little is known about the performance of such systems. For example, if the priority of a part depends on its class (e.g., the buffer that the part is located in), then there are no existing results on performance, or even stability. However, in most applications such as manufacturing systems, one has to choose a control or scheduling policy, i.e., a priority discipline, that optimizes a performance objective. In this paper we introduce a new technique for obtaining upper and lower bounds on the performance of Markovian queueing networks and scheduling policies. Assuming stability, and examining the consequence of a steadystate for general quadratic forms, we obtain a set of linear equality constraints on the mean values of certain random variables that determine the performance of the system. Further, the conservation of time and material gives an au...
Properties and Performance Bounds for Closed Free Choice Synchronized Monoclass Queueing Networks
 IEEE Transactions on Automatic Control
, 1991
"... Several proposals exist for the introduction of synchronization constraints into Queueing Networks (QN). We show that many monoclass QN with synchronizations can naturally be modelled with a subclass of Petri Nets (PN) called Free Choice nets (FC), for which a wide gamut of qualitative behavioural a ..."
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Cited by 31 (21 self)
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Several proposals exist for the introduction of synchronization constraints into Queueing Networks (QN). We show that many monoclass QN with synchronizations can naturally be modelled with a subclass of Petri Nets (PN) called Free Choice nets (FC), for which a wide gamut of qualitative behavioural and structural results have been derived. We use some of these net theoretic results to characterize the ergodicity, boundedness and liveness of closed Free Choice Synchronized Queueing Networks (FCSQN). Moreover we define upper and lower throughput bounds based on the mean value of the service times, without any assumption on the probability distributions (thus including both the deterministic and the stochastic cases). We show that monotonicity properties exist between the throughput bounds and the parameters of the model in terms of population and service times. We propose (theoretically polynomial and practically linear complexity) algorithms for the computation of these bounds, based on ...
A New Ordering for Stochastic Majorization: Theory and Applications
 Advances in Applied Probability
, 1991
"... In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, Lsubadditive and convex in each variable. This ..."
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Cited by 22 (7 self)
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In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, Lsubadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing deterministic vectors but differ for random vectors. Sample path criteria and a probability enumeration method for the new stochastic ordering are established and the ordering is applied to various forkjoin queues, routing and scheduling problems. Our results generalize previous work and can be extended to multivariate stochastic majorization which includes tandem queues and queues with finite buffers. Keywords: load balancing, stochastic convexity, majorization ordering, routing, scheduling, forkjoin queues 0 1 Introduction Recently, stochastic comparison has received a great deal of attention. ...
Properties and Performance Bounds for Timed Marked Graphs
 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS  I: FUNDAMENTAL THEORY AND APPLICATIONS
, 1992
"... A class of synchronized queueing networks with deterministic routing is identified to be equivalent to a subclass of timed Petri nets called marked graphs. First some structural and behavioral properties of marked graphs are recalled and used to show interesting properties of this class of performan ..."
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Cited by 19 (7 self)
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A class of synchronized queueing networks with deterministic routing is identified to be equivalent to a subclass of timed Petri nets called marked graphs. First some structural and behavioral properties of marked graphs are recalled and used to show interesting properties of this class of performance models. In particular, ergodicity is derived from boundedness and liveness of the underlying Petri net representation, which can be efficiently computed in polynomial time on the net structure. In case of unbounded (i.e., nonstronglyconnected) marked graphs, ergodicity is computed as a function of the average transition firing delays. Then the problem of computing both upper and lower bounds for the steadystate performance of timed and stochastic marked graphs is studied. In particular, linear programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., attainable) bounds for the throughput of transitions for marked graphs with dete...
On the Performance of Synchronized Programs in Distributed Networks with Random Processing Times and Transmission Delays
, 1994
"... A synchronizer is a compiler that transforms a program designed to run in a synchronous network into a program that runs in an asynchronous network. The behavior of a simple synchronizer, which also represents a basic mechanism for distributed computing and for the analysis of marked graphs, was stu ..."
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Cited by 15 (2 self)
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A synchronizer is a compiler that transforms a program designed to run in a synchronous network into a program that runs in an asynchronous network. The behavior of a simple synchronizer, which also represents a basic mechanism for distributed computing and for the analysis of marked graphs, was studied in [ER1] and [ER2] under the assumption that message transmission delays and processing times are constant. In this paper we study the behavior of the simple synchronizer when processing times and transmission delays are random. Our main performance measure is the rate of a network, i.e., the average number of computational steps executed by a processor in the network, per unit time. We analyze the effect of the topology and the probability distributions of the random variables on the behavior of the network. For random variables with exponential distribution we provide tight (i.e. attainable) bounds and study the effect of a bottleneck processor on the rate. Keywords: Distributed Netwo...
Analysis on Packet Resequencing for Reliable Network Protocols
 Proc. IEEE INFOCOM
, 2003
"... Protocols such as TCP requires packets to be accepted (i.e., delivered to the receiving application) in the order they are transmitted at the sender. Packets are sometimes misordered in the network. In order to deliver the arrived packets to the application in sequence, the receiver’s transport laye ..."
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Cited by 12 (2 self)
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Protocols such as TCP requires packets to be accepted (i.e., delivered to the receiving application) in the order they are transmitted at the sender. Packets are sometimes misordered in the network. In order to deliver the arrived packets to the application in sequence, the receiver’s transport layer needs to temporarily buffer outoforder packets and resequence them as more packets arrive. Even when the application can consume the packets infinitely fast, the packets may still be delayed for resequencing. In this paper, we model packet misordering by adding an IID random propagation delay to each packet and analyze the required buffer size for packet resequencing and the resequencing delay for an average packet. We demonstrate that these two quantities can be significant and show how they scale with the network bandwidth. I.
Polling Systems with Synchronization Constraints
, 1992
"... We introduce a new service discipline, called the synchronized gated discipline, for polling systems. It arises when there are precedence (or synchronization) constraints between the order that jobs in different queues should be served. These constraints are described as follows: There are N station ..."
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Cited by 11 (8 self)
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We introduce a new service discipline, called the synchronized gated discipline, for polling systems. It arises when there are precedence (or synchronization) constraints between the order that jobs in different queues should be served. These constraints are described as follows: There are N stations which are "fathers" of (zero or more) synchronized stations ("children"). Jobs that arrive at synchronized stations have to be processed only after jobs that arrived prior to them at their corresponding "father" station have been processed. We analyze the performance of the synchronized gated discipline and obtain expressions for the first two moments and the LaplaceStieltjes transform (LST) of the waiting times in different stations, and expressions for the moments and LST of other quantities of interest, such as cycle duration and generalized station times. We also obtain a "pseudo" conservation law for the synchronized gated discipline, and determine the optimal network topology that minimizes the weighted sum of the mean waiting times, as defined in the "pseudo" conservation law. Numerical examples are given for illustrating the dependence of the performance of the synchronized gated discipline on different parameters of the network.
Bounds on the Speedup and Efficiency of Partial Synchronization in Parallel Processing Systems
 Journal of the ACM
, 1993
"... In this paper, we derive bounds on the speedup and efficiency of applications that schedule tasks on a set of parallel processors. We assume that the application runs an algorithm that consists of N iterations and before starting its i + 1'st iteration, a processor must wait for data (i.e., ..."
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Cited by 7 (1 self)
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In this paper, we derive bounds on the speedup and efficiency of applications that schedule tasks on a set of parallel processors. We assume that the application runs an algorithm that consists of N iterations and before starting its i + 1'st iteration, a processor must wait for data (i.e., synchronize) calculated in the i'th iteration by a subset of the other processors of the system. Processing times and interconnections between iterations are modeled by random variables with possibly deterministic distributions. Scientific applications consisting of iterations of recursive equations are examples of applications that can be modeled within this formulation. We consider the efficiency of such applications and show that, although efficiency decreases with an increase in the number of processors, it has a nonzero limit when the number of processors increases to infinity. We obtain a lower bound for the efficiency by solving a equation which depends on the distribution of task ...
Introduction to Probabilistic Performance Modelling of Parallel Applications
 in Proc. Parallel Computing '93
, 1993
"... This report describes the results of preliminary research in the field of probabilistic performance modelling of parallel applications. The work was carried out as part of the ProcMod (Processor Modelling) subproject of the parTool project. The ProcMod subproject aims at the development of a perfo ..."
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Cited by 7 (2 self)
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This report describes the results of preliminary research in the field of probabilistic performance modelling of parallel applications. The work was carried out as part of the ProcMod (Processor Modelling) subproject of the parTool project. The ProcMod subproject aims at the development of a performance modelling technique and associated tool support which, based on a generic machine modelling paradigm, predicts parallel application performance at different hierarchical levels. In this way, performance feedback is available at all modelling levels, enabling the use of performance information during all stages of the application development process. The application of this technique is twofold: on the one hand, performance can be optimised by means of feedback to the user (or parallelising compiler) for a given target machine (or machine class); on the other hand, a comparative analysis of target machine performance can be made given a parallel application (or application class). In an earlier report the emphasis was on the description of parallel computer architectures [18]. This report, on the other hand, concentrates on the performance modelling and prediction techniques