Question

In the service department of the Glenn-Mark Auto Agency, mechanics requiring parts for auto repair or service present their request forms at the parts department counter. The parts clerk fills a request while the mechanic waits. On average everyday around 210 mechanics arrive in a random fashion over 10-hour working period. It takes the clerk average 2 minutes to fill a request. Assuming the service time and inter-arrival time is random and exponentially distributed. a) What is the average time mechanics spend waiting and having requests filled under the current system

Answer 1

the average time spend is 0.111

Explanation:

The computation of the average time spend is as follows;

Arrival rate is

= 210 ÷ 10

= 21 per hour

Now the service rate is

= 60 ÷ service time

= 60 ÷ 2 minutes

= 30 per minute

And, finally the average time spend is

= 1 ÷ (service rate - arrival rate)

= 1 ÷ (30 - 21)

= 0.111

Hence, the average time spend is 0.111