USE R programming A bank manager wants to investigate the congestion at the bank’s automated tellermachine (ATM). Upload the ATM_times.csv data set into R. This contains data that has beencollected on 10 customers which includes their interarrival times in the variableIT_times. Also given are two sets of service times, S_times1 and S_times2. (all times are inseconds)One assumption to using an M/M/1 queuing model is that the interarrival times andservice times be exponentially distributed. 2(a). Investigate if the interarrival and service times are exponentially distributed.Do this by plotting a histogram for each and overlaying an exponential density curve on thehistogram to see how close the data set matches the distribution. (Hint: to overlay thecurve, you will need a value for the rate of the exponential distribution. How could youestimate this from the data?) Comment on each plot as to how closely each data set matches an 2(b). Of the two sets of service times, S_times1 and S_times2, which has anapproximate service rate that would not allow for the use of a M/M/1 queuing model.Explain why IA_times S_times1 S_times2 1 55.396 95.856 3.268 2 51.817 8.006 14.782 3 11.782 29.419 7.839 4 2.404 4.184 3.929 5 55.008 25.857 7.317 6 16.604 75.649 33.875 7 42.444 69.821 50.998 8 47.86 61.922 3.192 9 8.583 26.505 17.646 10 3.806 29.066 39.215
USE R programming
A bank manager wants to investigate the congestion at the bank’s automated teller
machine (ATM). Upload the ATM_times.csv data set into R. This contains data that has been
collected on 10 customers which includes their interarrival times in the variable
IT_times. Also given are two sets of service times, S_times1 and S_times2. (all times are in
seconds)
One assumption to using an M/M/1 queuing model is that the interarrival times and
service times be exponentially distributed.
2(a). Investigate if the interarrival and service times are exponentially distributed.
Do this by plotting a histogram for each and overlaying an exponential density curve on the
histogram to see how close the data set matches the distribution. (Hint: to overlay the
curve, you will need a value for the rate of the exponential distribution. How could you
estimate this from the data?)
Comment on each plot as to how closely each data set matches an
2(b). Of the two sets of service times, S_times1 and S_times2, which has an
approximate service rate that would not allow for the use of a M/M/1 queuing model.
Explain why
| IA_times | S_times1 | S_times2 | |
| 1 | 55.396 | 95.856 | 3.268 |
| 2 | 51.817 | 8.006 | 14.782 |
| 3 | 11.782 | 29.419 | 7.839 |
| 4 | 2.404 | 4.184 | 3.929 |
| 5 | 55.008 | 25.857 | 7.317 |
| 6 | 16.604 | 75.649 | 33.875 |
| 7 | 42.444 | 69.821 | 50.998 |
| 8 | 47.86 | 61.922 | 3.192 |
| 9 | 8.583 | 26.505 | 17.646 |
| 10 | 3.806 | 29.066 | 39.215 |
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