Question

Consider an M/M/2/3 capacitated queueing system with the arrival rate of 3 customers per hour and...

Consider an M/M/2/3 capacitated queueing system with the arrival rate of 3 customers per hour and the service rate of 2 customers per hour.

a. Calculate the steady-state distribution of the number of customers in the system.

b. Calculate L, Lq, Effective arrival rate, W and Wq.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
in an M/M/1 queueing system, the arrival rate is 9 customers per hour and the service...
in an M/M/1 queueing system, the arrival rate is 9 customers per hour and the service rate is 14 customers per hour. What is the utilization? (Round your answer to 3 decimal places.) What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.) What is the expected waiting time in the system (W)? (Express the waiting time in hours, round your answer to 3 decimal places.) What is the expected number of...
n an M/M/1 queueing system, the arrival rate is 9 customers per hour and the service...
n an M/M/1 queueing system, the arrival rate is 9 customers per hour and the service rate is 14 customers per hour. What is the utilization? (Round your answer to 3 decimal places.) What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.) What is the expected waiting time in the system (W)? (Express the waiting time in hours, round your answer to 3 decimal places.) What is the expected number of...
A simple queueing system has an arrival rate of 6 per hour and a service rate...
A simple queueing system has an arrival rate of 6 per hour and a service rate of 10 per hour. For this system the average time in line has been estimated to be 20 minutes. Using Little’s Law estimate the following: Average time in the queueing system Average number of customers in the queueing system Average number of customers in the queue Average number of customers in service.
1.) A system has 5 servers. Customers arrive at a rate of 6 per hour and...
1.) A system has 5 servers. Customers arrive at a rate of 6 per hour and service time is 20 minutes. What is the service rate of the system? 2.) A system has 5 servers. Customers arrive at a rate of 6 per hour and service time is 20 minutes. What is the system utilization? (Show answer as a decimal.) 3.)Suppose that this system has 3 servers instead of 5. What is the probability there are no customers in the...
Consider a system that can be modelled as an M/M/3 queuing system with an arrival rate...
Consider a system that can be modelled as an M/M/3 queuing system with an arrival rate of 8 parts per hour (on the average) and a processing time of 10 minutes (on the average). a.) Draw the steady state rate diagram for this system (you can stop at 5 or 6 nodes). Label the arrival and service rates on the diagram as is customary. b) Is it a problem that the arrival rate is greater than the service rate? Why...
Consider an M / M / 1 queueing system with capacity N = 2. Suppose that...
Consider an M / M / 1 queueing system with capacity N = 2. Suppose that customers arrive at the rate of λ per hour and are served at the rate of 8 per hour. a. What should the arrival rate be so that an arriving potential customer has a 50% chance of joining the queue? b. With λ chosen to satisfy the requirement of part a, what percentage of the customers who actually enter the system get served immediately?
For an M/M/1/GD/∞/∞ queuing system with arrival rate λ = 16 customers per hour and service...
For an M/M/1/GD/∞/∞ queuing system with arrival rate λ = 16 customers per hour and service rate μ = 20 customers per hour, on the average, how long (in minutes) does a customer wait in line (round off to 3 decimal digits)?
State Bank always has two tellers on duty. Customers arrive to receive service from a teller...
State Bank always has two tellers on duty. Customers arrive to receive service from a teller at a mean rate of 40 per hour. A teller requires an average of 2 minutes to serve a customer. When both tellers are busy, an arriving customer joins a single line to wait for service. Experience has shown that customers wait in line an average of 1 minute before service begins. (a) Describe why this is a queueing system. (b) Determine the basic...
Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate...
Speedy Oil provides a single-server automobile oil change and lubrication service. Customers provide an arrival rate of 4 cars per hour. The service rate is 5 cars per hour. Assume that arrivals follow a Poisson probability distribution and that service times follow an exponential probability distribution. A) What is the average number of cars in the system? If required, round your answer to two decimal places L = B) What is the average time that a car waits for the...
With an average service rate of 15 customers per hour and an average customer arrival rate...
With an average service rate of 15 customers per hour and an average customer arrival rate of 12 customers per hour, calculate the probability that actual service time will be less than or equal to five minutes.