# Ma6453 Question Bank PROBABILITY AND QUEUEING THEORY

## Sample Ma6453 Question Bank:

1. (a) Derive Pollaczck – Khintchine formula for the average number of customers in the M/G/I queuing system (16)
Or
(b) (i) Write a short note on open queueing network. (8)
(ii) Patients arrive at a clinic in a poisson fashion at the rate of 3 per hour. Each arriving patients has to pass through two sections. The assistant in the first section take 15 minutes per patient and the doctor in the second section takes nearly 6 minutes per patient. It the service times in the two sections are approximately exponential, find the probability that there are 3 patients in the first sections and 2 patients in the second section. Find also average number of patients in the clinic and the average waiting time of a patient. (8)

2. (a) (i) Explain Markovian Birth Death process and obtain the expressions for steady state probabilities. (8)
(ii) A supermarket has two girls attending to sales at the counters. If the service time for each customer is exponential with mean 4 min and if people arrive in poisson fashion at the rate of 10 per hour. What is the probability that a customers has to wait for service? (8)
Or
(b) (i) A small mail – business has one telephone line and a facility for call waiting for two additional customers. Orders arrive at the rate of one per minute and each order requires 2 minutes and 30 seconds to take down the particulars.
What is the expected number of calls waiting in the queue? What is the mean waiting time I n the queue? (8)

 Subject Name PROBABILITY AND QUEUEING THEORY Subject code MA6453 Regulation 2013