On a Photographic Transit Circle

Covering on a Circle

Modeling Based on Photographic Data

Photography is a 2-dimensional medium which represents 3-dimensional space, as a central projection on a plane. As it is possible to represent 3D space by a photograph, it is also possible, using mathematical methods, to obtain data about 3-dimensional structures from the data registered on photographs. We used two methods to obtain spatial data from photographs: restitution of perspective imag...

Queuing on a continuous circle

In this thesis we analyze a queueing model on a continuous circle. The model is motivated by an application in optical data transport. A processor moves with constant speed on this circle. Jobs arrive at the current location of the processor, according to a Poisson process of fixed intensity. If the server is not occupied, it immediately takes the new job into service and releases it after comp...

A TAXICAB VERSION OF A TRIANGLE' S APOLLONIUS CIRCLE

One of the most famous problems of classical geometry is the Apollonius' problem asks construction of a circle which is tangent to three given objects. These objects are usually taken as points, lines, and circles. This well known problem was posed by Apollonius of Perga ( about 262 - 190 B.C.) who was a Greek mathematician known as the great geometer of ancient times after Euclid and Archimede...

Queueing systems on a circle

Consider a ring on which customers arrive according to a Poisson process. Arriving customers drop somewhere on the circle and wait there for a server who travels on the ring. Whenever this server encounters a customer, he stops and serves the customer according to an arbitrary service time distribution. After the service is completed, the server removes the client from the circle and resumes hi...