A developing apparatus includes a toner collection apparatus having a waste toner accommodation chamber that temporarily accommodates waste toner removed from a photosensitive medium. The module is entirely located outside that machine. The apparatus further comprises a distal section with a lumen in communication with a port in a distal end of the catheter and with the first lumen and the second lumen. A square operator performs square operations on results of the calculation of differences. Furthermore, the method may include rendering, in response to the received request, the determined set of resources and the cost factor with respect to the determined set of resources.