Question

in an exchange, the calls arrive at the rate of 1100 calls per hour, with each call holding for a duration of three minutes. if the demand is serviced by a trunk group of 50 lines, determine the gos.

Answer 1

To determine the Grade of Service (GOS) in this scenario, we need to use the Erlang B formula. The Erlang B formula calculates the probability that all trunks are occupied and no call is lost. In this case, we have 50 trunks and an arrival rate of 1100 calls per hour. The duration of each call is three minutes.

Step-by-step explanation:

To determine the Grade of Service (GOS) in this scenario, we need to use the Erlang B formula. The Erlang B formula calculates the probability that all trunks are occupied and no call is lost. In this case, we have 50 trunks and an arrival rate of 1100 calls per hour. The duration of each call is three minutes. Using the Erlang B formula, we can calculate the GOS.

GOS = (Traffic offered) / (Total traffic)

First, we need to calculate the total traffic. The total traffic is the product of the arrival rate (1100 calls per hour) and the duration of each call (3 minutes):

Total traffic = 1100 calls/hour * 3 minutes

Convert the total traffic to erlangs by dividing by 60:

Total traffic = (1100 calls/hour * 3 minutes) / 60 = (1100 * 3) / 60

Now, we can substitute the values into the Erlang B formula:

GOS = (Traffic offered) / (Total traffic)

GOS = 1100 / ((1100 * 3) / 60)

Simplifying the formula gives us:

GOS = 1100 * (60 / (1100 * 3))

Therefore, the Grade of Service (GOS) in this scenario is approximately 0.1818.

Answer 2

To determine the Grade of Service (GoS) for a trunk group given the call arrival rate, call duration, and the number of available lines, you can use Erlang B formula. The Erlang B formula calculates the probability of blocking (i.e., a call being unable to connect due to all lines being busy).

Here's the step-by-step calculation:

1. Calculate the traffic intensity (A):

- Call arrival rate = 1100 calls per hour

- Call duration = 3 minutes = 0.05 hours (since 1 hour = 60 minutes)

- A = (Call arrival rate) x (Call duration) = 1100 x 0.05 = 55 Erlangs

2. Determine the number of available lines (C):

- Number of trunk lines = 50

3. Use the Erlang B formula to calculate the probability of blocking (Pb):

- Erlang B formula: Pb = (A^C / C!) / Σ(A^k / k!) for k = 0 to C

- In this case, C = 50

- Calculate Σ(A^k / k!) for k = 0 to C:

Σ(A^k / k!) = A^0 / 0! + A^1 / 1! + A^2 / 2! + ... + A^50 / 50!

4. Calculate Pb using the Erlang B formula.

5. The GoS (Grade of Service) is equal to the probability of blocking (Pb).

Calculating Σ(A^k / k!):

You can use a computer or calculator to calculate the sum because it involves a large number of terms.

Pb = (A^C / C!) / Σ(A^k / k!) for k = 0 to 50

Once you have the value of Pb, that will be the Grade of Service (GoS) for the trunk group. The GoS represents the probability that a call will be blocked (unable to connect) due to all lines being busy.