Question 1 A large hotel maintains a customer service number staffed by 3 operat

Question

Question 1

A large hotel maintains a customer service number staffed by 3 operators. If you call and all 3 operators are currently busy, you get disconnected. Assume that arrivals are Poisson and arrive at an average rate of 12 per hour. The average length of a call is 3 minutes and service times are exponentially distributed. For simplicity, do not consider call retry in case you get disconnected.

What formula is used to calculate blocking probability for this system (either name the formula or write it out)?

Question 2

For the queuing system in Question 1, assume that the blocking probability (P3) = 0.02. On average, how many calls would be served per hour by this call center (specify to 2 decimal places)?

Explanation / Answer

Solution:

1)

We will be using Poisson distribution formula here which says

P(x; ) = (e-) (x) / x!

where is the average rate of successes that can occur in a specified region and x is the actual success which can occur in a specified region

So on an hour 20 slots of 3 minutes are there and

arrivals are 12 per hour which means that the number of success that can occur is 8

2)

So ut of 20

0.02 are blocked,

this means that

0.98 gets through

so the success number of calls would be 0.98*20= 19.60

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

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