We take it for granted that someone in America can make a phone call to Japan. Almost every home has its own telephone line which is connected to a series of exchanges that span the globe. The reliable and efficient operation of telephone networks is of vital importance to both personal and commercial users.
Mathematicians have developed ingenious ways of routing calls which can cope with unpredictable events that could disrupt telephone service.
Where C is the number of lines, with an average of v calls starting per minute, and that the average length of a call is one minute. E(v,C) represents the proportion of callers that find all the lines already full, and so would not be able to make their call until later.