Georgia Institute of Technology College of Sciences

Consider a series of n single-server queues each with unlimited waiting space and FIFO discipline. At first the system is empty, then m customers are placed in the first queue. The service times of all the customers at all the queues are iid. We are interested in the exit time of the last customer from the last server and that's when queues meet random matrices and GUEs. If the number of customers is a small fractional power of the number of servers, and as such customers stay within a tube, that's when queues encounter Tracy and Widom. This talk will be self contained and accessible to graduate students.