Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2011)

Reconstructing Model Parameters in Partially-Observable Discrete Stochastic Systems (Statistics Inference) (Analytical and Stochastic Modeling) Part 1

Abstract The analysis of partially-observable discrete stochastic systems reconstructs the unobserved behavior of real-world systems. An example for such a system is a production facility where indistinguishable items are produced by two machines in stochastically distributed time intervals and are then tested by a single quality tester. Here, the source of each defective item can […]

Reconstructing Model Parameters in Partially-Observable Discrete Stochastic Systems (Statistics Inference) (Analytical and Stochastic Modeling) Part 2

Symbolic Polynomial Analysis The iterative analysis is a simple algorithm that usually finds accurate estimates for unknown model parameter values, but does not give any guarantees about time-to-convergence and optimality of the values found. In those cases where all unknown probabilities can be expressed as polynomials in a single common variable, this problem can be […]

Performance Evaluation of a Kitting Process (Queueing Theory) (Analytical and Stochastic Modeling) Part 1

Abstract Nowadays, customers request more variation in a company’s product assortment leading to an increased amount of parts moving around on the shop floor. To cope with this tendency, a kitting process can be implemented. As it gathers the necessary parts into a container prior to assembly, kitting enables a more cost-efficient and qualitative production. […]

Performance Evaluation of a Kitting Process (Queueing Theory) (Analytical and Stochastic Modeling) Part 2

Methodology: The Sparse Matrix Techniques Queueing models for kitting processes are rather complicated. Indeed, the modelled kitting process has a multidimensional state space. Even for relative moderate buffer capacity, the multidimensionality leads to huge state spaces; this is the so-called state-space explosion problem. For many queueing systems, infinite-buffer assumptions may mitigate this problem. Given some […]

Perfect Sampling of Phase-Type Servers Using Bounding Envelopes (Queueing Theory) (Analytical and Stochastic Modeling) Part 1

Abstract In queueing models, phase-type servers are very useful since they can be used to approximate any service distributions of real-life telecommunication networks. However, the corresponding Markov chains are in most cases very large and hard to solve without the help of an efficient simulation model. A simulation framework, based on perfect sampling, had already […]

Perfect Sampling of Phase-Type Servers Using Bounding Envelopes (Queueing Theory) (Analytical and Stochastic Modeling) Part 2

Coupling of Phase-Type Systems Envelopes This section is dedicated to the analysis of the coupling time of the envelopes for networks of phase type servers The main features can actually be seen in the simplest network: two queues in tandem with a phase-type server on the first queue. This case is considered first. The general […]

Monotone Queuing Networks and Time Parallel Simulation (Queueing Theory) (Analytical and Stochastic Modeling) Part 1

Abstract We show how we can make more efficient the time parallel simulation of some queueing networks. We had previously introduced some improvements of two classical time parallel simulation approaches: the precomputation of states at specific time instants and the fix-up computations. We have proved that we can obtain more parallelism using monotonicity on input […]

Monotone Queuing Networks and Time Parallel Simulation (Queueing Theory) (Analytical and Stochastic Modeling) Part 2

Monotone Networks of Queues For the sake of readability we begin with a simple result to show how we can prove hv-monotonicity and then we generalise the results with more sophisticated routing strategies and more complex service time distributions. Finally we show with an example that G-networks of queues with positive and negative customers are […]

Traffic-Centric Modelling by IEEE 802.11 DCF Example (Telecommunication Networks) (Analytical and Stochastic Modeling) Part 1

Abstract Probably no protocol has been analysed as much as the various versions of the IEEE 802.11 Distributed Coordination Function (DCF). In this paper, we show how to describe a typical DCF analytic model as a semi-Markov process (SMP) by taking a new approach to performance modelling, called Traffic-Centric Modelling (TCM). TCM is therefore explained […]

Traffic-Centric Modelling by IEEE 802.11 DCF Example (Telecommunication Networks) (Analytical and Stochastic Modeling) Part 2

Verification of the SMP Analysis From the observed convergence behaviour of the solver, illustrated in Table 2, it is clear that the SMP is already in steady-state after 2 x 107 x N state changes, where N nodes are contending to access the channel. As a verification of the resulting performance model, we decided that […]

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