Traffic greater than number of devices

[vadb]

Hi, I'm new around here :).

I was checking the Erlang-B table and I noticed that with very high B it is possible to have more traffic than the number of devices, for example, according to ErlangB table, if N = 8 and B = 40, you can have 11.42 Erlangs. As I understand, if I have N devices, the maximum traffic that can be carried is N.

Is this really possible?. I don't know if I misunderstood something.

Thanks in advance for your comments.

[RF engineer]

Hi, I'm new around here :).

I was checking the Erlang-B table and I noticed that with very high B it is possible to have more traffic than the number of devices, for example, according to ErlangB table, if N = 8 and B = 40, you can have 11.42 Erlangs. As I understand, if I have N devices, the maximum traffic that can be carried is N.

Is this really possible?. I don't know if I misunderstood something.

Thanks in advance for your comments.

IF you check ErlangB formula it is not dependent only on N you have also time which you have less user but they generate more traffic due to long time spend.

Erl=N*MHT/3600.


BR

[vadb]

Hi,

Yes, but in an hour, the maximum value of MHT should be 3600s, so, the previous formula would become:

Erl=N*MHT/3600 = N*3600/3600 = N

If this is true, the max traffic value would be equal to the number of devices, right?

Regards,
Victor

[dekili]

Hi,

Yes, but in an hour, the maximum value of MHT should be 3600s, so, the previous formula would become:

Erl=N*MHT/3600 = N*3600/3600 = N

If this is true, the max traffic value would be equal to the number of devices, right?

Regards,
Victor


No, Victor, it is not true.
Definition of 1 Erlang is to have connection for one hour during one hour. So, for N lines, you can have N parallel (instantaneous) users which is not equal to the available capacity (traffic). Also, you need to make difference between offered and achieved traffic because you use (probably) 2% of blocking probability. This will make the difference in the number of users and traffic supported.
cheers,

[vadb]

Hi dekili,

I understand that I have a capacity below the number of devices if I use Erlang B with 2% of GOS, and the maximum simultaneaos users will be given by the number of devices. However, I don't understand how is possible to "occupy" more channels than the existing, for example, in the next table, you can see that is possible to carry 9,79 Erlangs with only 7 devices if we have 40% of GOS:

http://www.wirelesstechie.com/wp-content/uploads/2010/11/erlangB_calc1.png

When I use 7 lines during the whole hour, the traffic would be 7 Erlangs, right?

Regards.

[Philippe]

I think you are confusing traffic and capacity.
N (=7) is the number of lines or channels in your system.
2.935 is the average Erlang traffic you can support to have no more than 2% blocking when trying to access the 7 lines.
9.7998 is the average Erlang traffic you can support to have no more than 40% blocking when trying to access the 7 lines. 9.7998 is the AVERAGE Erlang traffic generated: part of the time, it is less than 7 simultaneous calls and the Erlang-B law guarantees you that statistically it will be more than 7 simultaneous calls in less than 40% of the cases.
Moreover 9.7998 Erl is the offered traffic. The carried traffic (the average traffic not rejected) is 9.7998 * (1-40%) = 5.9Erl is well below the number of 7 lines.

[rkdrkd]

About Erlang B (lost calls Cleared) Distribution.

Please make it clear that Erlang B table shows that offered traffic to a system of N servers or channels with a particular grade of service or blocking.

so offered traffic can be more than the no of servers if the blocked calls are cleared from the system.

i hope it clears



Hi dekili,

I understand that I have a capacity below the number of devices if I use Erlang B with 2% of GOS, and the maximum simultaneaos users will be given by the number of devices. However, I don't understand how is possible to "occupy" more channels than the existing, for example, in the next table, you can see that is possible to carry 9,79 Erlangs with only 7 devices if we have 40% of GOS:

http://www.wirelesstechie.com/wp-content/uploads/2010/11/erlangB_calc1.png

When I use 7 lines during the whole hour, the traffic would be 7 Erlangs, right?

Regards.

[rkdrkd]

Hi dekili,

When I use 7 lines during the whole hour, the traffic would be 7 Erlangs, right?

Regards.

Yes if you use 7 lines during the whole hour the traffic would 7 Erlangs in the loss-less systems where the calls are not blocked/lost. Loss-less sytem is possible only in the case where no of servers/channels available is less than or equal to the number of subscribers. But in the ERlang-B model the numbers of subscribers to the system is considered as infinite or much much greater than available servers/channels

I hope it clears

[vadb]

Thank you all!! Finally, I got it!

[hoamanlau]

Thanks, I learnt one or two things from these formula.