Question 1: Customers arrive at a reception counter at an average rate of 15 minutes and the receptionist takes an avera

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Question 1: Customers arrive at a reception counter at an
average rate of 15 minutes and the receptionist takes an average of
10 minutes for each customer. Determine the average queue
length.
Question 2: Cars arrive at a service station according to
Poison's distribution with a mean rate of 7 per hour. The service
time per car is exponential with a mean of 10 minutes. At steady
state, the average waiting time in the queue is ____?
Question 3: Jobs arrive at a facility at an average rate of 8 in
an 8 hour shift. The arrival of the jobs follows Poison
distribution. The average service time of a job on the facility is
1 hour. The service time follows exponential distribution. Idle
time (in hours) at the facility per shift will be____?
Question 4: At a workstation, 7 jobs arrive every minute. The
mean time spent on each job in the workstation is 1/10 minute. The
mean steady state number of jobs in the system is____?
Question 5: The arrival of customers over fixed time intervals
in a bank follow a Poison distribution with an average of 40
customers/hour. The probability that the time between successive
customer arrivals is between 2 and 5 minutes is____?
Question 6: Customers arrive at a ticket counter at a rate of 60
per hour and tickets are issued in the order of their arrival. The
average time taken for issuing a ticket is 1.5 min. Assuming that
customer arrivals form a Poison process and service times are
exponentially distributed, the average waiting time in queue in
minutes is____?
Question 7: Shopkeeper handles only 1 person in 8 minute while
customer is arriving in every 10 minutes. Average queue length will
be____?
Question 8: In a single-channel queuing model, the customer
arrival rate is 15 per hour and the serving rate is 25 per hour.
The expected time that a customer is in queue is___?
Question 9: Consider a single machine workstation to which jobs
arrive according to a Poison distribution with a mean arrival rate
of 10 jobs/hour. The process time of the workstation is
exponentially distributed with a mean of 5 minutes. The expected
number of jobs at the workstation at any given point of time
is____?
Question 10: At a production machine, parts arrive according to
a Poison process at the rate of 0.25 parts per minute. Processing
time for parts has an exponential distribution with a mean of 1.5
minutes. What is the probability that a random part arrival finds
that there are already 10 parts in the system (in machine + in the
queue