Sumários
Aula 27
24 maio 2016, 13:00 • Ana Maria Santos Ferreira Gorjão Henriques
Presentation of Work 12 - Queueing systems, including discussion of the M/M/1 (Section 4.82) system.
Birth and death queueing systems in equilibrium, 4 performance measures Ls, Lq, Ws and Wq, Little´s law (Theorem 4.58, Remark 4.59), PASTA property. Review of distributional properties of the 4 performance measures in the queueing systems: M/M/m, M/M/m/m, M/M/infinity.
Exercise 4.72, Teste Recurso 2013/06/24 G3.2.
Aula 26
23 maio 2016, 08:00 • Ana Maria Santos Ferreira Gorjão Henriques
Continuation of birth and death processes: rate diagrams, the M/M/s queueing system as an example; classification of states in CTMC (Definition 4.37, Proposition 4.40, Remark 4.41); Limit behavior of CTMC (Proposition 4.44 and Theorem 4.45, Remark 4.46, Theorem 4.47 and Remark 4.48, balance equations, Proposition 4.50, Remark 4.53 - ergodicity condition)
Examples and exercises: M/M/s queueing system,
TPC: Exercises 4.52, 2nd test Recurso 2014/07/01 G3. Obtain the limiting probability for the number of customers in the system in the M/M/1 queueing system discussing the ergodicity condition.
Aula 25
17 maio 2016, 13:00 • Ana Maria Santos Ferreira Gorjão Henriques
Presentation of W9 - Branching processes, which included Definition 3.99, Propositions 3.100, 3.102, 3.104, 3.107, and Exercises 3.105, 3.108.
Discussion of Exercise 3.109 (TPC).
Continuous Time Markov chains: Definition 4.2, properties of Transition Probability Matrix (Proposition 4.7), Marginal and Joint probabilities (natural extensions from DTMC); Kolmogorov´s backward and forward equations (Proposition 4.14), rate matrix and Kolmogorov´s backward and forward equations in matrix form (Proposition 4.16) and brief comments on computing the TPM.
Birth and death processes: Definition 4.21 and Remark 4.22.
TPC: Exercises 4.9, 4.23,Kolmogorov´s backward and forward equations for birth and death processes (Proposition 4.26).
Aula 24
16 maio 2016, 08:00 • Ana Maria Santos Ferreira Gorjão Henriques
Presentation of W11 `Hypo and Hyper Exponential Random Variables'.