Queueing theory and production processes: general characteristics of queuing systems. Notation and examples. Probability density functions: random variables, memoryless and stochastic processes. Basic queuing models (e.g. M/M/1, M/M/c, models with limited capacity) and application to real cases. Little's law. Queuing models with general distributions (M/G/1, GI/M/1, GI/G/1).
Resources in networks: open queuing networks (tandem queues, Jackson’s networks). Closed queuing networks (Solberg model). Petri Nets: notation, general properties of Petri Nets, applications and examples in productive and service systems.
Markov Chains: discrete and continuous time. Birth and death processes (BD); ergodic and absorbing states. Classification of Markov chins and relevant properties. Examples of applications in production contexts and services.
Decision making in multicriteria environments: the Analytic Hierarchic Process (AHP).
Discrete-event simulation of productive systems: model assessment, random number generation, performance indices. Model validation. Simulation runs and truncation. Program coding and reporting assessment. Continuous simulation. Hybrid simulation. Applicative cases. Simulation and optimization problems: formulating the optimization problem (local optimum, discrete local optimum, global optimum, problem instances). Hints on computational complexity and the performance measurement of algorithms.
Applications in productive-service environments.