Erlang B Table

[islam wagih]

Dear Expersts,
In Erlang B table, why with increasing "Blocking Probability", the "Erlang" traffic increases ?

[Nyquist]

Simple, allowing more blocking time the system can manage more calls i.e. more traffic

[islam wagih]

Simple, allowing more blocking time the system can manage more calls i.e. more traffic

sorry, I didn't get the point; could you clear more please :)

[Nyquist]

Hi. Sure.

Erlang is a system based on blocking, that is with queues and losses.
Blocking is the time when two different calls are trying to get the same resource. These calls have being manage by the system but they cannot use the network at that time. After a random time that two calls try again and one of them could get the resource at the end.
The blocking probability can be seen as a window of time when two o more calls are blocked due to a lack of resources.
If you increase this time window, i.e. you increase the blocking probability, the system can manage a higher amount of calls (all the calls using all the resources + all the calls in the queue waiting to get the resources).
Sorry for my english. I hope it is clear enough now.

[Nyquist]

A little bit of theory:

The Unit of Traffic
In telephony, one way to define traffic is the average number of calls in progress during a specific period of time, often one hour. A circuit or path that carries its usage for one traffic call at a time is referred to as a trunk. Telephone traffic, although it is a dimensionless quantity, is expressed either in erlang (named after Agner Krarup Erlang, a Danish pioneer of traffic theory) or in hundred-call-seconds (CCS), the latter being commonly used in North America. One erlang equals 36 CCS. A simple way to understand this unit is to look at a bicycle. In one hour, the most that you can ride this bicycle is 36 hundred seconds. Two or more people can ride, or occupy, or hold this bicycle one at a time, but they cannot exceed a total of 36 hundred seconds (or 36 hundred-ride-seconds) in a period of one hour. A group of ten bicycles for rent, while it has a theoretical capacity of 360 hundred-ride-seconds, may sometimes be used only for an average of 36 hundred-ride-seconds on a Monday morning, but on a Sunday this same group of ten bicycles may not be enough, so “congestion” occurs.
Some lose interest, others wait for the next available bicycle, and some try again later. Telephone trunks are arranged in groups. The traffic capacity of a group of trunks depends on the nature or distribution of call durations or holding time. Widely distributed call holding times tend to reduce traffic handling capacity. Traffic carried by a group of trunks may, therefore, be stated as follows:

A = C x H / T

where A = traffic in erlangs
C = average number of calls in progress during a period of time
H = average holding time of each call
T = 3,600 seconds (1 hour).

Congestion
Congestion occurs when calls are unable to reach their destination as a result of excess demand for system capacity. Getting a busy tone instead of a ringback tone because the called subscriber station is busy is not congestion by definition. Rather, congestion can occur because, while the central offi ce has sufficient equipment installed to provide terminal access for all subscribers, most likely it does not have sufficient facilities to handle the peak volume of calls encountered during the busy hour. Some calls are allowed to be lost during this time to meet the economic objectives of providing service. It is highly costprohibitive to provide sufficient trunks to carry all traffi coffered to a system with no calls lost at all. The measure of calls lost during a busy hour period is known as grade of service.
In the dimensioning of a telephone network, traffic engineers look at grade of service in the following ways:
1. The probability that a call will be lost as a result of congestion
2. The probability of congestion
3. The proportion of time during which congestion occurs
Grade of service, B , is designed into the system by traffic engineers. After the system is put into service, it is observed and verified using traffic scanning devices. Traffic observation and measurement show how many calls are offered, carried, and lost in the system.
Grade of service, B , is then determined as:

B = number of calls lost / number of calls offered

or

B = traffic lost / traffic offered

The lower this number, the higher the grade of service.