GOS and blocking probability in a loss system

Grade of Service (GoS)

In a loss system (blocked calls cleared, no queue), GoS is the proportion of calls offered in the busy hour that are lost:

$$GoS = \frac{\text{calls lost}}{\text{calls offered}} = \frac{A_o - A_c}{A_o}$$

It is a measured value or design target set by the operator, e.g. 0.01 for trunk routes, and it describes the service seen by users over the whole network or a route.

Blocking probability

Blocking probability $P_B$ is the probability, calculated from a traffic model, that all N servers are busy when a call arrives. For Poisson traffic A offered to N trunks (Erlang B):

$$P_B = E_{1,N}(A) = \frac{A^N/N!}{\sum_{k=0}^{N}A^k/k!}$$

It has two forms: time congestion (fraction of time all servers are busy) and call congestion (fraction of calls lost). With infinite Poisson sources they are equal, so $GoS = P_B$; with finite sources (Engset), call congestion is less than time congestion.

Use in design and evaluation

1. Dimensioning: forecast the busy-hour traffic A, choose the GoS (e.g. 0.01), then find N from Erlang B tables. Example: A = 5 E with GoS 0.01 gives N = 11 trunks.
2. End-to-end budget: a call through several links in tandem has a total GoS ≈ $B_1 + B_2 + \dots$, so the overall target is split among the links (e.g. 0.002 per switch, 0.005 per trunk).
3. Cost trade-off: a lower GoS needs more circuits; designers pick the GoS that balances cost and customer satisfaction.
4. Routing design: high-usage direct routes are dimensioned for a high blocking value (large GoS) and overflow to a final route dimensioned for a low GoS.
5. Evaluation: measured lost calls in the busy hour are compared with the target; if the target is exceeded, trunks are added or traffic is re-routed.
6. Cellular planning: the number of channels per cell is chosen for 2% blocking.