Instructions:

1. Late submission will be accepted but will be mark 5% absent.
2. Assignment submission will only be accepted through assignment link.
3. Submit the Assignment carefully once I mark the assignment then I will not change the marks again.
4. Solve the Questions completely with formulas and all calculations.
5. This Assignment is given from chapter 3.

Question 1: At Al rajhi bank, on an average 7 customers arrive per hour. The teller takes 6 minutes per customer on an average for service. It can be assumed that arrivals follow Poisson distribution and the tellers service time follows an exponential distribution. Determine the following:

(i) percent of times a customer can walk right inside teller cabin without having to wait. (0.25 mark)

(ii) The average number of customers waiting for their turn (0.25 mark)

(iii) The average time a customer spends in the bank. (0.25 mark)

(iv) Expected Idle time of teller in a day. (0.25 mark)

2. The arrivals at an ATM booth are assumed to be exponentially distributed. The arrival rate is 6 per hour and the service rate is 14 per hour. Determine the following:

i) Average number of customers in the system (0.25 mark)

ii) Average number of customer waiting to be served or average queue length (0.25 mark)

iii) Average time a customer spends system (0.25 mark)

iv) Average waiting time of a customer before being served. (0.25 mark)