GOS vs blocking probability; E.164 plan

GoS and blocking probability in a loss system

• Grade of Service (GoS): ratio of calls lost to calls offered in the busy hour, $GoS = \dfrac{\text{calls lost}}{\text{calls offered}}$. It is the quality target set for a route or for the end-to-end connection (e.g. 0.01).
• Blocking probability ($P_B$): probability, given by a traffic model, that all N servers are busy when a call arrives. For Poisson traffic, Erlang B: $P_B = \dfrac{A^N/N!}{\sum_{k=0}^{N}A^k/k!}$.

For infinite Poisson sources, call congestion = time congestion, so GoS = $P_B$ for a single group; for links in tandem GoS ≈ $\sum P_{B,i}$.

National numbering plan (ITU-T E.164 format)

A numbering plan gives every subscriber a unique number so that calls can be routed and charged. ITU-T E.164 sets the international format, with at most 15 digits (excluding prefixes):

 |<------------ max 15 digits ------------->|
 +------+----------+--------------------------+
 |  CC  |   NDC    |           SN             |
 +------+----------+--------------------------+
 1-3 dig  |<----- national (significant) no. ----->|

• CC – Country Code: 1 to 3 digits, given by ITU (Nepal 977, India 91, USA 1). First digit is the world zone.
• NDC – National Destination Code: area/trunk code or mobile network code (Kathmandu valley 1; Nepal Telecom mobile 984/985/986, Ncell 980/981/982).
• SN – Subscriber Number: identifies the line within the NDC area.
• NSN (National Significant Number) = NDC + SN; its length is fixed by the national plan (maximum 15 − length of CC).

Prefixes (not part of the number):

• Trunk (national) prefix: dialled before the NSN for calls inside the country, usually 0 (e.g. 01-4xxxxxx in Nepal).
• International prefix: dialled before CC for outgoing international calls, ITU recommends 00.
• Short codes for emergency and services (100 police, 101 fire, 102 ambulance in Nepal).

Example: a Kathmandu fixed line: international format +977 1 4xxxxxx; national format 01-4xxxxxx; local format 4xxxxxx. A Nepali mobile: +977 98X XXXXXXX.

Requirements of a good national plan: unique numbers, enough spare capacity for growth (planned for 30–50 years), easy routing and charging from the leading digits, uniform length where possible, compatibility with E.164 and with number portability.