Don't you put me on hold!

You realize that you're being ripped off by your internet service provider, so you call them to cancel your service. All customer service calls are handled by the same call center, which has \(N\) representatives. The average call to the center lasts for \(\langle t \rangle\) minutes, and calls arrive at random at a rate of \(\lambda\) calls per minute. What is the probability that you'll get put on hold when you call?

Assumptions and Details

  • Customers who call when all representatives are busy are put on hold and end their calls immediately.
  • \(N=10 \text{ representatives}\).
  • \(\lambda = 0.7\text{ calls per min} \)
  • \(\langle t \rangle = 10\text{ min}\)

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