GATE 2022 ME: Industrial Engineering Quiz - 7

The cost of providing service in a queuing system increases with

A service facility has Poisson arrival rate and negative Exponential service rate on a first come-first server basis queue. Average requests for service  are 5 per day and the rate at which service is provided is 7 per day. Find the probability for exactly 3 machines in the system.

At a production machine, parts arrive according to a Poisson process at the rate of 0.35 parts per minute. Processing time for parts have exponential distribution with mean of 2 min. What is the probability that a random part arrival finds that there are already 8 parts in the system?

Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is