4.

(a) For a single server queuing model, the average service time is 3 minutes and service is idle for 25% of the time. The inter-arrival time of customers for such a system will be:

(i) 12 minutes (ii) 4.5 minutes (iii) 4 minutes (iv) indeterminate

(b) For a single server queuing model, the average service time is 15 minutes and the inter-arrival time of customers is 20 minutes. What is the average waiting time of a customer in the queue?

(

c) If on an average, 10 customers join a queue in one hour and the average service time per customer is 6 minutes, then the average waiting time of a new arrival in a MIM/1 (single server) queuing system is one hour.

(i) True, (ii) False, (iii) Cannot say.

(

d) In a single server queuing situation, the service system is occupied 7 5% of the time and the interarrival time of customers is 4 minutes. For this, the average service time will be:

(i) 4.5 minutes (ii) 4 minutes (iii) 3 minutes (iv) 2 minutes

(e) Customers arrive at a sales counter manned by a single person according to a Poisson process with a mean rate of 20 per hour. The time required to serve a customer has an exponential distribution with a mean of 100 seconds. What is the average waiting time of a customer?