Assignment:
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.
Q1. What average number of customers would you expect to see in line?
Q2. What average number of customers can be expected to be in the system?
Q3. What is the average amount of time that a person can expect to spend in line?
Q4. How long do you expect to take getting a cup of coffee?
Q5. 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
Provide complete and step by step solution for the question and show calculations and use formulas.