Queueing Theory??
Can someone help me with this please? it's do with queueing theory in Quantitative Methods to Data Analysis
Question 2
An electronics company retains a pool of technicians to repair machine breakdowns that occurat an average rate of 3 per day. The pattern of breakdowns is assumed to follow a Poissondistribution. The team of technicians repair the machines at average rate of one machine perhour. It is assumed that this repair rate resembles the Exponential distribution and that thetechnicians work 8 hours per day.
a) What is the probability that a broken machine has to wait to be repaired?
b) What is the probability that a broken machine can be repaired immediately?
c) What is the average downtown (the average waiting time) for a machine that is broken?
d) How many machines are waiting to be serviced at any given time?
e) What is the probability that there is one machine in the queue at any given time?
f) What is the probability that there is more than one machine in the queue at any giventime?
g) What is the probability that a machine can be serviced in less than 1 hour?State and discuss any assumptions made in your calculations.
Question 2
An electronics company retains a pool of technicians to repair machine breakdowns that occurat an average rate of 3 per day. The pattern of breakdowns is assumed to follow a Poissondistribution. The team of technicians repair the machines at average rate of one machine perhour. It is assumed that this repair rate resembles the Exponential distribution and that thetechnicians work 8 hours per day.
a) What is the probability that a broken machine has to wait to be repaired?
b) What is the probability that a broken machine can be repaired immediately?
c) What is the average downtown (the average waiting time) for a machine that is broken?
d) How many machines are waiting to be serviced at any given time?
e) What is the probability that there is one machine in the queue at any given time?
f) What is the probability that there is more than one machine in the queue at any giventime?
g) What is the probability that a machine can be serviced in less than 1 hour?State and discuss any assumptions made in your calculations.
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