# ORG - Operations Research Group

The group is directed by Prof. Juan A. Carrasco and is composed by himself and Prof. Víctor Suñé. Unfortunately, the group does not have currently any way to support prospective PhD students. They must support themselves. The cv of Prof. Juan A. Carrasco can be found at https://eel.upc.edu/ca/personal/pagines-personals/Juan_Antonio_Carrasco. Prospective PhD students have to have a good level of mathematics, specially the theory of continuous-time Markov chains and numerical methods for continuous-time Markov chains, a good level of programming using a high-level programming language for which there is a free compiler running on any variant of UNIX allowing to measure CPU times or using MATLAB, a good level of latex, and a very good level of american english. They must also have their own laptop. All this will be tested presentialy in a process that will last about two or three weeks. No expenses related to that process will be covered. In order not to loose tehir time and money, prospective PhD students are strongly advised to look at all the papers of our group, which can be found in the Researchgate entry of Prof. Juan A. Carrasco. Only after that test, the group will be allowed to apply for a PhD in Electronic Engineering under the supervision of members of the group.

Note that Prof. Juan A. Carrasco will be in a sabbatical leave at the Mathematics Department of University of California at Berkeley to finish his promising preliminary research work about the computation of singular values and associated rihgt singular vectors of large and sparse complex matrices under the supervision of Prof. Beresford N. Parlett, a very well-known authority in the field. That sabbatical leave will cover the period September 1st 2021 to September 1st 2022.

A practical outset of the research group is the Markovian modeling tool METFAC. That tool is offered either with a free licence or a licence of 5000 € depending on the usage and the applicant. For more information follow the hyperlink

https://eel.upc.edu/ca/recerca/carpeta-grups/metfac/metfactool

An example of current activities of the research group is the development of new general-purpose numerical methods to compute both the distribution of the proportion of time that a system modelled by an arbitrary finite continuous-time Markov chain (CTMC) is in subset of states in a time interval and the distribution of the reward accumulated by a system modelled by an arbitrary finite CTMC with reward rates associated to states during a time interval. Both methods are expected to cover CTMCs with large state spaces in reasonable CPU times, which is not the case of currently available methods covering arbitrary finite CTMCs with reward rates associated with states in the case of the distribution of the reward accumulated by a system. Another example is the enhancement of a method developed by the research group to compute the interval availability complementary distribution and the complementary distribution of cumulative reward, or bounds for them, of failure/repair CTMC models of fault-tolerant systems with exponential failure and repair time distributions and repair in every state with failed components, an increasing structure function in the case of the interval availability distribution or bounds for it, and some mild conditions on how the reward rates associated with the states of the CTMC vary with the number of failed components. Another example is the analysis of the accuracy of efficient methods to compute individual Poisson probabilities.