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QUESTION 5 (a) Briefly discuss two important applications of queuing theory. (2 marks) (b) Explain the meaning of the following: (i) M/M/5/FCFS/00/queuing model. (2 marks) (ii) Traffic intensity. (1 mark) (c) A self-service store employs one cashier at its counter. 8 customer arrive on an average every 5 minutes while the cashier can serve 10 customers in the same time. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, determine: (i) the util zation factor of the cashier. (1 mark) (ii) the average number of customers in queue. (1 mark) (iii) the average time a customer spends in the system. (1 mark) (iv) the probability that there is no customer at the counter. (1 mark) (v) the probability of having exactly two customers in the store. (1 mark) (vi) the probability of having less than 3 customers in the store at any time. (2 marks)