How can Erlang C values be greater than one?

Here is an Erlang C plot I did myself. The x-axis represents the total traffic while the y-axis represents the probability. Each line represents a different total number of channels.

As you can see, the graph has probabilities greater than one. How can this be even possible?

• Correct me if I'm wrong, but I'm not sure if this belongs on electrical engineering. It's likely I just don't understand why it is, however. – Jacob Garby Oct 11 '18 at 21:48
• It is related to the fundamentals of mobile communication. Do you know a better SE for this topic? – Chirag Arora Oct 11 '18 at 21:52
• Probability of what? What is A? Does it make physical sense to have A > c? – The Photon Oct 11 '18 at 22:00
• Probabilities are [0, 1] by definition. You are misinterpreting something. – vicatcu Oct 11 '18 at 22:09
• @ThePhoton 'A' is the total traffic. Whereas 'C' is the total no. of channels. Yes, it makes perfect sense and is, in fact, a real-world case. The number of subscribers can outweigh the total no. of available channels for a telecommunication system. – Chirag Arora Oct 12 '18 at 22:09

You haven't said what event $$\P\$$ measures the probability of.
But you'll notice that your formula gives $$\P>1\$$ when $$\A>c\$$.
So I'll guess $$\P\$$ is something like the probability of a collision on the network, or that a particular channel is occupied with other traffic when a subscriber attempts to connect, or something like that.
Then it would make sense that $$\P=1\$$ when $$\A>c\$$ and the actual formula should be
$$P=\begin{cases} {\rm your\ long\ formula}, & 0 < A < c \\ 1, & A \ge c \end{cases}.$$
Then the formula you used in your program doesn't represent the correct formula for $$\P\$$ for all choices of $$\A\$$ and $$\c\$$.