A conference is being held at a centre that has three different entrances. A reg

Question

A conference is being held at a centre that has three different entrances. A registration desk is being set up at each entrance. Assume that each desk will have its own queue and will see an equal portion of the expected 125 total customers per hour arriving at the conference (assume Poisson arrivals), and that customers will not line jockey between registration desks since they are significant distances apart. If each registration desk can serve one customer at a time, and the average time to serve a customer is 0.75 minutes, then what will be the average time that a customer waits in a line (in minutes) before being able to register?

0.13 mins

0.47 mins

0.82 mins

2.41 mins

4.98 mins

a.

0.13 mins

b.

0.47 mins

c.

0.82 mins

d.

2.41 mins

e.

4.98 mins

Explanation / Answer

Option C is the correct answer

s = 3 = 125 per hour, ' = 125/3 = 41.67 µ = 80 per hour ( 1 per 0.75 minutes) Average Utilization of the system = p = ' /µ = 41.67/80 = 52.0833% Average time a customer is in the system = Ws = 1 /µ- ' = 1 / 80 - 41.67 = 0.026087 hours Average time a customer is in the queue = Wq = pWs = 0.520833 * 0.026087 = 0.013587 hours = 0.82 minutes

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