Q7 A company has a single service station which has the following characteristics: the mean arrival rate of customers and the mean service time are 6.2 minutes and 5.5 minutes respectively. The time between an arrival and its services varies from one minute to seven minutes. The arrival and service time distribution are given below: Time (minutes) Arrival (probability) Service (probability) 1-2 0.05 0.10 2-3 0.20 0.20 3-4 0.35 0.40 4-5 0.25 0.20 5-6 0.10 0.10 6-7 0.05 The queuing process starts at 8 am and closes at 9 am. An arrival moves immediately into the service facility if it is empty. On the other hand, if the service station is busy, the arrival will wait in the queue. Customers are served on the first come, first served basis. Determine: a) Average queue length b) Average waiting time of customers before service. c) Average service time d) Time a customer spends in the system. Simulate the process for 6 trials, Using Monte-Carlo simulations technique. Use the following random numbers for arrival and service (left to right) Random numbers for Arrival 64 04 02 70 03 60 Random numbers for Service 30 75 38 24 57 09 3