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# GATE 2023 || Industrial Engineering || Quiz 54

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Question 1

The cost of providing service in a queuing system increases with

Question 2

If λ and μ are the arrival rate and service rate in a single server queuing model, then the average waiting time in the system is __________.

Question 3

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?

Question 4

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

Question 5

At a work station, 5 jobs arrive every minute. The mean time spent on each job in the work station is 1/8 minute. The mean steady state number of jobs in the system is ______

Question 6

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.
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