During this talk I will present a queuing model for database locking systems, where jobs represent user requests for simultaneous access to a set of files in a large database.

While files are in use, their content can change, so to preserve consistency throughout the database files currently in use are locked, creating blocking and idleness in the system. This model is known as a writer-only system, and can also be thought of as a queuing network where jobs are split into pieces to be served in parallel by randomly assigned servers, with the condition that their service must be synchronized. Assuming a FCFS service discipline for each file (server), we model the stationary waiting time distribution of a job, i.e., the amount of time a request needs to wait before it can access its target files, under a many-servers limit. Our model leads to a so-called high-order Lindley equation whose attracting endogenous solution can be analyzed asymptotically.

Bio:

Dr. Olvera-Cravioto received her bachelor’s degree is in Applied Mathematics from the “Instituto Tecnológico Autónomo de México (ITAM)”. She obtained her Ph.D. at Stanford University. From 2006 to 2016 she worked in the Department of Industrial Engineering and Operations Research at Columbia University. Prior to coming to UNC she was a Visiting Associate Professor in the IEOR Department at UC Berkeley.
Mariana does research in Applied Probability, in particular, she works on problems involving heavy-tailed phenomena. Her current work is focused on the analysis of information ranking algorithms and their large-scale behavior, which is closely related to the study of the solutions to certain stochastic recursions constructed on weighted branching processes. She is also interested in the analysis of complex networks.