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.

enter image description here

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

  • \$\begingroup\$ 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. \$\endgroup\$ – Jacob Garby Oct 11 '18 at 21:48
  • \$\begingroup\$ It is related to the fundamentals of mobile communication. Do you know a better SE for this topic? \$\endgroup\$ – Chirag Arora Oct 11 '18 at 21:52
  • \$\begingroup\$ Probability of what? What is A? Does it make physical sense to have A > c? \$\endgroup\$ – The Photon Oct 11 '18 at 22:00
  • \$\begingroup\$ Probabilities are [0, 1] by definition. You are misinterpreting something. \$\endgroup\$ – vicatcu Oct 11 '18 at 22:09
  • \$\begingroup\$ @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. \$\endgroup\$ – 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\$.


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