1) The automobile service center has three related service points each of which can service the average of 5 automobiles per hour. Average of ten automobiles arrive each hour at service center. Arrivals are Poisson and service is exponentially distributed with parking facilities being unlimited. Find out the following:

(a) Expected number of automobiles in the system

(b) Expected time spent by an automobile waiting for service

(c) Expected time of the automobile  spent in the system.

2) Describe the criteria used in decision making under uncertainty.

3) Customers arrive at the milk book for required service. Suppose that inter arrival and service time are constants and given by 1.5 and 4 minutes respectively. Simulate the system by hand computations for 14 minutes

(a) Determine the waiting time per customer

(b) Determine the percentage idle time for the facility?

(Suppose that the system starts at t = 0)

4) Create a sequence of 6 three digit random numbers by employing mixed congruential method defined by r_i+1 =  217 r_i+ 725( mod 1000) with r_o =  437.