Question: A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow Poisson distribution at the rate of three per minute. In serving themselves, customers take about 20 seconds, exponential distributed.
Requried: 1. What average number of customers would you expect to see in line?
2. What average number of customers can be expected to be in the system?
3. What is the average amount of time that a person can expect to spend in line?
4. How long do you expect to take getting a cup of coffee?
5. What percentage of time is the urn used?
Model 1: Single Channel, Poisson Arrival, Exponential Service Time
| Arrival rate |
l = |
3 |
| Service rate |
m = |
4 |
| Interarrival Time |
1/l = |
0.3333 |
| Service time |
1/m = |
0.2500 |
| System Utilization |
r = |
0.7500 |
| Probability system is empty |
P0 = |
0.2000 |
| Average number in line |
Lq = |
2.1500 |
| Average number in system |
Ls = |
3.0000 |
| Average time in line |
Wq = |
0.8500 |
| Average time in system |
Ws = |
1.0000 |