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Problem 3. A service facility consists of one server who can serve an average of 2 customers per hour( service times are exponential). An average of 3 customers per hour arrive at the facility (interarrival times are assumed exponential). The system capacity is three customers. Complete the following items listed below: 1. Define the states 2. Define the events and the rates associated with the events. 3. Construct the state transition diagram for this model. 4. Set up flow balance equations using your state transition diagram. 5. Solve for the steady state probabilities. 6. On average, how many potential customers enter the system each hour? 7. What is the probability that the server will be busy? 8. How do we know a steady state probability distribution exists for a queueing system? If the arrival rate is bigger than the service rate what does this imply?

Problem 3. A service facility consists of one server who can serve an average of 2 customers per hour( service times are exponential). An average of 3 customers per hour arrive at the facility (interarrival times are assumed exponential). The system capacity is three customers. Complete the following items listed below: 1. Define the states 2. Define the events and the rates associated with the events. 3. Construct the state transition diagram for this model. 4. Set up flow balance equations using your state transition diagram. 5. Solve for the steady state probabilities. 6. On average, how many potential customers enter the system each hour? 7. What is the probability that the server will be busy? 8. How do we know a steady state probability distribution exists for a queueing system? If the arrival rate is bigger than the service rate what does this imply?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Problem 3. A service facility consists of one server who can serve an average of 2 customers per hour( service times are exponential). An average of 3 customers per hour arrive at the facility (interarrival times are assumed exponential). The system capacity is three customers. Complete the following items listed below: 1. Define the states 2. Define the events and the rates associated with the events. 3. Construct the state transition diagram for this model. 4. Set up flow balance equations using your state transition diagram. 5. Solve for the steady state probabilities. 6. On average, how many potential customers enter the system each hour? 7. What is the probability that the server will be busy? 8. How do we know a steady state probability distribution exists for a queueing system? If the arrival rate is bigger than the service rate what does this imply?
Transcribed Image Text:Problem 3. A service facility consists of one server who can serve an average of 2 customers per hour( service times are exponential). An average of 3 customers per hour arrive at the facility (interarrival times are assumed exponential). The system capacity is three customers. Complete the following items listed below: 1. Define the states 2. Define the events and the rates associated with the events. 3. Construct the state transition diagram for this model. 4. Set up flow balance equations using your state transition diagram. 5. Solve for the steady state probabilities. 6. On average, how many potential customers enter the system each hour? 7. What is the probability that the server will be busy? 8. How do we know a steady state probability distribution exists for a queueing system? If the arrival rate is bigger than the service rate what does this imply?
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