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# Erlang Problem

1. A company needs to provide sufficient private trunks between two switches to accommodate 90% of call attempts among employees during the busy hour. Assume that there will be 560 callers at random times during that hour, and that call duration averages 3 minutes. Employees are instructed to attempt to call using a trunk; if blocked, callers will use a more expensive company-issued calling card. How many trunks will be needed?

2. In order to eliminate the cost of calling cards, the company in the above problem is considering a new policy that requires blocked callers to redial over and over until they get a trunk. Assuming the same number of callers and the same call duration, what is the new level of blockage, and about how long is the average total call time including both dialing and talking?

#### Solution Preview

1. A company needs to provide sufficient private trunks between two switches to accommodate 90% of call attempts among employees during the busy hour. Assume that there will be 560 callers at random times during that hour, and that call duration averages 3 minutes. Employees are instructed to attempt to call using a trunk; if blocked, callers will use a more expensive company-issued calling card. How many trunks will be needed?

I have provided some theory, background, examples and then indicated the solution approach for your learning pleasure!

This is the Erlang B problem

Erlang B, a formula developed by A.K. Erlang, is widely used to determine the number of trunks required to handle a known calling load during a one hour period. The formula assumes that if callers get busy signals, they go away forever, never to retry ('lost calls cleared'). Since some callers retry, Erlang B can underestimate trunks required. However, Erlang B is generally accurate in situations with few busy signals.

The data you will require includes the number of calls, the average talk and after call work time to first determine the number of erlangs of telephone traffic you have ...

#### Solution Summary

This solution is provided in 905 words. It describes the Erlang B and C formula and provides examples using the erlang unit to further learning. It also discusses the Erlang equation in relation to blocking probability.

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