problem 1: A bank plans to open a single server drive in banking facilities at a specific center. It is estimated that 20 customers will arrive each hour on an average. If, on an average, it required 2 minutes to process a customer’s transaction, find out:

a) The proportion of time which the system will be idle.
b) On an average how long a customer will have to wait before reaching the server?
c) Traffic intensity of Bank?

problem 2: Workers come to a tool store room to enquiry regarding the special tools (needed by them) for a particular job. The average time between the arrivals is 60 seconds and the arrivals are supposed to be in Poisson distribution. The average service time is 40 seconds. Determine:

a) Average queue length.
b) Average length of non-empty queue.

problem 3:

a) Describe about pure birth and death process with illustrations.
b) Describe about categorization of queuing models.

problem 4: A maintenance service facility has poisson arrival rates, negative exponential service time and operates and first come first served queue discipline. Breakdowns take place on an average of three per day with a range of zero to eight. The maintenance crew can service on an average six machines per day with arrange 0 to 7 Determine:

a) Utilization factor of the service acility.
b) Mean time in the system.
c) Mean number in the system in breakdown (or) repair.
d) Mean waiting time in the queue.
e) Probability of finding two machines in the system.
f) Expected number in the queue.