Telecommunication Network
The summer vacation scholorship by looking at loss systems gave an explicit expression for blocking probability and is also known as Erlang's Formula.
Abstract
1 Loss System For a background review, I started the summer vacation scholorship by looking at loss systems. In a telecommunication context, this means that a new coming call is blocked (or lost) if there is no free circuits for that call. First of all, I made myself familiar with the notations. In a loss system, let C be the total number of circuits available, n be the number of circuits in use, ν be the arrival rate of new call and µ be the departure rate of an existing call. Then, this stochastic process can be defined by transition rates: If˜π = (π(0), π(1),. .. , π(C)) is the stationary distribution of the process, then it satisfies C n=0 π(n) = 1 and π n = λ 0 λ 1 · · · λ n−1 µ 1 · · · µ n−1 µ n π 0. Then, it is easy to show that π(C) = φ C /C! C n=0 φ n /n! (1) where φ = ν µ As π(C) is the probability that the process stays in the state that the system is full, it approximates the probability that a call is blocked. Then, equation (1) gives an explicit expression for blocking probability and is also known as Erlang's Formula.