Question: Waiting Line Model

In a waiting line situation, unit arrivals occur around the clock at a rate of five per day, and the service (there is only one server running for 24 hours per day) completes on average at one unit every four hours. Assume arrivals follow a Poisson distribution and service time follows an exponential distribution.

(Note: This is a \(\mathrm{M} / \mathrm{M} / 1\) queuing system. You must show the formulas and steps you used for answering the questions.)

1. What is \(\lambda\) ? What is \(\mu\) ? Find probability of no units in the system.
2. Find average number of units in the system.
   (Note: It's not the average number of units waiting in the line).
3. Find average time spent in the waiting line.
4. Find probability that there is only one person waiting to be serviced.

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