For a single-channel waiting line where the mean arrival time is 17 per hour and the mean service rate for the channel is 22 per hour:

Calculate the probability that at least one customer will be waiting correct to 3 decimal places.

A fast food outlet opened up a drive-in window for customers who are too busy to come into the building. The mean arrival time is 11 per hour and the mean service rate for the channel is 19 per hour. It was so popular that it decided to open up a second window to service the queue of customers.

Calculate the probability that the queue will be empty. 

For a single-channel waiting line where the mean arrival time is 9 per hour and the mean service rate for the channel is 40 per hour:

Calculate the expected time it takes, in minutes, for service to be completed. 

Your answer should be correct to two decimal places.

Two computers are connected by a 512 Kbps link. There are 3 concurrent  sessions between the computers. 

Packets have a mean size of 6 kilobits.  Each session generates data at a mean rate of 6 packets per second. 

 Find the mean response time (seconds) of the whole system,

In a particular organization it has been determined that in any given day the probability of a working computer crashing is 0.01 and the probability of a broken computer being fixed in the same time period is 0.93

Assuming that initially all computers are working, calculate the expected probability that a computer chosen at random will not be working at the start of day four.

Two computers are connected by a 512 Kbps link. There are 7 concurrent  sessions between the computers. 

Packets have a mean size of 2 kilobits.  Each session generates data at a mean rate of 5 packets per second. 

 Calculate the probability that the system is busy, correct to three decimal places.,

Three airlines operate on the Dublin to London route and a passenger survey gave the following results.

92% of Aer Lingus customers were happy to fly with the airline on their next trip, 6% said they would choose Ryanair and 2% would fly with British Airways.

94% of Ryanair customers were happy to fly with the airline on their next trip, 3% said they would choose Aer Lingus and 3% would fly with British Airways.

3% of British Airways customers would change to Aer Lingus and 9% would change to Ryanair the rest would remain loyal to British Airways.

Calculate the steady state percentage of customers that Ryanair can expect to carry. Give your answer to the closest integer value.

In a particular organization it has been determined that in any given day the probability of a working computer crashing is 0.03 and the probability of a broken computer being fixed in the same time period is 0.87

Calculate the steady state probability that a computer will be working.

With regard to the network diagram below, calculate the effective arrival rate for queue 1 (Q1) where the probabilities are given by P1 = 0.6 and P2 = 0.21.

Give your answer correct to one decimal place.

A fast food outlet opened up a drive-in window for customers who are too busy to come into the building. The mean arrival time is 22 per hour and the mean service rate for the channel is 26 per hour. It was so popular that it decided to open up a second window to service the queue of customers.

Calculate the probability that there is exactly two customers in the queue .