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61
Fluid stochastic Petri nets: Theory applications and solution techniques
 European Journal of Operational Research
, 1998
"... In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold uid rather than discrete tokens. We de ne a class of uid stochastic Petri nets in such awaythat the discrete and continuous portions may a ect each other. Following this de nition we provide equation ..."
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Cited by 67 (11 self)
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In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold uid rather than discrete tokens. We de ne a class of uid stochastic Petri nets in such awaythat the discrete and continuous portions may a ect each other. Following this de nition we provide equations for their transient and steadystate behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.
Discreteevent simulation of Fluid Stochastic Petri Nets
 IEEE Transactions on Software Engineering
, 1999
"... The purpose of this paper is to describe a method for simulation of recently introduced fluid stochastic Petri nets. Since such nets result in rather complex set of partial differential equations, numerical solution becomes a formidable task. Because of a mixed, discrete and continuous state space, ..."
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Cited by 36 (6 self)
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The purpose of this paper is to describe a method for simulation of recently introduced fluid stochastic Petri nets. Since such nets result in rather complex set of partial differential equations, numerical solution becomes a formidable task. Because of a mixed, discrete and continuous state space, simulative solution also poses some interesting challenges, which are addressed in the paper. 1
Queueing Analysis of Resource Dispatching and Scheduling in MultiMedia Systems
, 1991
"... In multimedia systems, we have a number of different resources being used exclusively and simultaneously to satisfy the requirements of an arriving customer. We consider two classes of resources and a Poissonstream of customers. Each customer needs one resource from both classes at the beginning o ..."
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Cited by 20 (6 self)
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In multimedia systems, we have a number of different resources being used exclusively and simultaneously to satisfy the requirements of an arriving customer. We consider two classes of resources and a Poissonstream of customers. Each customer needs one resource from both classes at the beginning of its treatment. Both resources are released independently from each other after a negative exponentially distributed amount of time where the releaserate can be class as well as statedependent. Therefore, the resources of both classes are occupied synchronously but released asynchronously. For the resulting queueing model no product form solution can be obtained. By the application of a dimensionreduction algorithm, we derive the stateprobabilities and related performance measures by solving a twodimensional Markov chain. Numerical examples show that the performance of the queueing system depends mainly on the different number of resources in each class. All numerical results have been validated by simulation. At last, we briefly take a look at the case that the resources are occupied and released synchronously.
Performance Evaluation for Parallel Systems: A Survey
, 1997
"... Performance is often a key factor in determining the success of a parallel software system. Performance evaluation... ..."
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Cited by 12 (0 self)
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Performance is often a key factor in determining the success of a parallel software system. Performance evaluation...
Towards an EndtoEnd Delay Analysis of Wireless Multihop Networks
 Elsevier Ad Hoc Networks
, 2009
"... We employ discretetime queueing theory to analyze the endtoend (e2e) delay of wireless multihop networks for two MAC schemes, mphase TDMA and slotted ALOHA. Unlike general twodimensional networks where there exists sucient trac multiplexing that would permit the arrival processes to be approxi ..."
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Cited by 11 (0 self)
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We employ discretetime queueing theory to analyze the endtoend (e2e) delay of wireless multihop networks for two MAC schemes, mphase TDMA and slotted ALOHA. Unlike general twodimensional networks where there exists sucient trac multiplexing that would permit the arrival processes to be approximated as independent, in linear networks with multihop communication, the arrival processes are correlated due to the lack of trac multiplexing. This paper studies an extreme scenario, a linear network fed with a single
ow. A decomposition approach is used to decouple the whole network into isolated nodes. Each node is modeled as a GI/Geo/1 queueing system. We derive the complete pernode delay distribution, Preprint submitted to Elsevier 5 June 2007 accounting for both the queueing delay and access delay. Additionally, we characterize the departure processes by a correlated and bursty ono trac model. The pernode analysis provides the e2e delay mean while for the e2e delay variance, the strong correlations between the arrival processes need to be considered. Our study shows that the sign of the correlation coecients depends on both the MAC scheme and the trac burstiness, both of which determine the relative burst size of the source
ow compared to a Bernoulli process, which constitutes an \eigentrac" process. There is a wide gap in the e2e delay variances for the source
ows with dierent burst sizes even if they have identical average rates. The relative burst size also determines from which direction and at which rate the departure processes converge to the eigentrac process after traversing multiple relay nodes.
Accurate computation of the smallest eigenvalue of a diagonally dominant Mmatrix
 Math. Comp
, 2002
"... Abstract. If each offdiagonal entry and the sum of each row of a diagonally dominant Mmatrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we dev ..."
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Cited by 11 (3 self)
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Abstract. If each offdiagonal entry and the sum of each row of a diagonally dominant Mmatrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision. Rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms. 1.
Optimal Divisible Load Scheduling and Markov Chain Models
 Hopkins University
, 2003
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Quo Vadis  A Framework for Intelligent Routing in Large Communication Networks
 DEPARTMENT OF COMPUTER SCIENCE, IOWA STATE UNIVERSITY
, 1994
"... This paper presents Quo Vadis, an evolving framework for intelligent traffic management in very large communication networks. Quo Vadis is designed to exploit topological properties of large networks as well as their spatiotemporal dynamics to optimize multiple performance criteria through cooperat ..."
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Cited by 7 (6 self)
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This paper presents Quo Vadis, an evolving framework for intelligent traffic management in very large communication networks. Quo Vadis is designed to exploit topological properties of large networks as well as their spatiotemporal dynamics to optimize multiple performance criteria through cooperation among nodes in the network. It employs a distributed representation of network state information using local load measurements supplemented by a less precise global summary. Routing decisions in Quo Vadis are based on parameterized heuristics designed to optimize various performance metrics in an anticipatory or proactive as well as compensatory or reactive mode and to minimize the overhead associated with traffic management. The results of simulation experiments within a grid network clearly demonstrate the ability of Quo Vadis to avoid congestion and minimize message delay under a variety of network load conditions.