Procesos Estocásticos

Procesos estocasticos

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Procesos Estocásticos 2016-2 Resultado de imagen para javeriana cali logo

Juan David Arciniegas Jurado

Fabián Marín Buritica

Juan Sebastián Maldonado Morón

Every day from the start of the student's day at 7am and at every moment of rush hour either 9am, 11am and 2pm, there are high levels of congestion at the entrance of the parking lot to the University, which use a system of porter's lodge and index cards for each one of the vehicles, in some situations the students and teachers have presented complaints of the system being this little efficient.

As students of the course Stochastic processes our objectives are to find the rate of arrival of the cars and the rate of parking service; Identify the model to use, so that the analysis can be performed and demonstrate if the system needs improvement, such as include another porter's lodge or other doorman in order to improve the service or otherwise corroborate that the system is good and does not need improvements, to be able to do this we will need to calculate queuing times and service times as well as number of cars in queue and in the system.

The system of entrance of cars to the university counts on a young worker who is in charge of checking that the cars that enter belong to the community Javeriana, located to 20 meters of the porter's lodge, in the course of time while the car is corroborated As a member of the community and in travel the 20 meters, the porter ready the index card to deliver to the vehicle, sometimes when there was a lot of congestion the porter took more than one index card in hand to make the process more agile, the entry of cars Manages a PEPS system since the first car that enters is the first one to which the index card is given and exit.

To measure the times within the system, it starts from the moment when the car is identified as belonging to the community, until the doorman delivers the index card. To take these times were used two stopwatches, one of them took the times of entry (once identified the car) and the other the times of departure (once delivered the index card)

Exponential distribution adjustment test:

The actual model that presents the system according to the Kendall-Lee definition is (M / M / 1) :( PEPS / α / α) Where M represents that the times between arrival are independent random variables and identically distributed, whose distribution is exponential, In the same way for the second M that specifies the nature of the service times, the third (1) represents the number of servers, in this case only a single doorman, PEPS system because since the first car to enter is The first to receive the index card, the number of cars that can enter