I am working to model some queuing systems and running into a challenge answering a specific question.
I am looking to be able to graph the probability of different wait times. Example: probability a customer will wait between 0 and 1 minute, probability a customer will wait between 1 and 2 minutes, etc.
I have been unable to find an equation to answer this. My statistics isn't as good as it used to b, so if someone can help me work through an example it would be helpful.
Below is an example of single queue single server. Additional question on any answers, would I be able to apply to same to the results of a single queue, multi server analysis?
Time Unit hour
Arrival Rate (lambda) 5 customers/hour Service Rate (mu) 10 customers/hour
Average Time Between Arrivals 0.20 hour Average Service Time 0.10 hour
Average Utilization (Rho) 50% Probability of empty system (P0) 50% Average Customers in System (L) 1 customers Average Customers in Line (Lq) 0.5 customers Average Time in System (W) 0.2 hour Average time in Queue (Wq) 0.10 hour
Probability of customer wait time
0-1 min ? 1-2 min ? 2-3 min ? etc