Question

Five administrative assistants use an office copier. The average time between arrivals for each assistant is 41 minutes, which is equivalent to an arrival rate 1/41 of arrivals per minute. The mean time 41 each assistant spends at the copier is 8 minutes, which equivalent to a service rate of 1/8 per minute. Use the M/M/1 model with a finite calling population to determine the following. (a) The probability that the copier is idle. (Round your answer to four decimal places.) (b) The average number of administrative assistants in the waiting line. (Round your answer to four decimal places.) (c) The average number of administrative assistants at the copier. (Round your answer to four decimal places.) (d) The average time (in minutes) an assistant spends waiting for the copier. (Round your answer to two decimal places.) min (e) The average time (in minutes) an assistant spends at the copier. (Round your answer to two decimal places.) min (f) During an 8-hour day, how many minutes does an assistant spend at the copier? How much of this time is waiting time? (Round your answers to two decimal places.) total time min min waiting time

(g) Should management consider purchasing a second copier? Explain. (Round your answer to two decimal places.) A total of the administrative team's time is spent waiting for the office copier. If the sole objective of management were to reduce non-productive waiting management --Select--- consider purchasing second copier

Answer 1

We lack sufficient information to accurately calculate the probabilities and averages requested for the M/M/1 queuing model with a finite calling population. Correct data is required to apply the M/M/1 queuing theory formulas.

Step-by-step explanation:

We do not have enough information to calculate the probability that the copier is idle or the other detailed statistics requested. The M/M/1 queuing model formulas generally require knowing the arrival rate (λ) and the service rate (μ), but also the number of servers (which is 1 in this case), and crucially for a finite population, the actual population size. The data given implies an infinite source of customers, which contradicts the statement that there are five administrative assistants (finite calling population). The numbers provided (30 arrivals per hour from solution 5.11, and the time between arrivals and service times in your question) do not align to provide a consistent set of data to use for the calculations. With the correct data, we would use equations from the M/M/1 queuing theory to find the probability that the copier is idle, the average number of administrative assistants in the waiting line, and so on.