What is the resolution of this exercise below: Consider a queuing model with two attendants and a waiting position operating under steady-state conditions. Suppose that if a customer arrives and finds both agents busy and the waiting position unoccupied, then the customer will wait as long as necessary for service. If the customer finds both attendants busy and the waiting position also occupied, he leaves immediately. Customers access the system according to a Poisson process with a rate of 2 customers per hour and that service follows an exponential distribution with a mean of 1 hour. The proportion of customers who arrive at the system and will not be served is: a)2/5 b)1/8 c)2/3 d)2/7 e)1/6
W= 3 days per Order L = 5 orders are waiting in Queue λ= ? According to Little's law L= λW λ=L/W = 5/3 =1.6 orders per unit Time Substituting the values in Little's law we can find the average number of orders the system can produce per week. L = Wλ = 3 * 1.6 = 4.6 orders by week We can't have orders produced in fractions, Therefore we round up to the nears whole number 5. I hope I am correct.
Thanks for the comment. FIFO service patterns are quite prominent than you think, and you have perhaps witnessed this recently. Example of FIFO queues are waiting in line to use the ATM, board a bus, or to get vaccinated. Customers arriving to these queues are attended to on a first come first serve basis (FIFO). For LIFO, a typical example is when you respond to the emails in your inbox from the top. The first email that is usually visible is the last one received. Scrolling down to the first received email quickly changes the email service pattern to FIFO. You could also choose to ignore certain emails and select the ones you would rather respond to in no particular order. When you do this, you are using a RANDOM ORDER. As for service patterns based on PRIORITY, this is commonly used in hospitals, particularly in the A&E department. Where you have a patient with a knife stuck in their head and another patient suffering from constipation from excessive eating on the same queue, a service pattern based on priority is imperative here. Irrespective of the patients’ arrival time, priority will be given to patients with more serious health issues (i.e. the patient with a knife stuck in their head). I hope this makes these service patterns clearer. Thanks for watching again. Please remember to share the videos. Will be grateful. 🙂
@@DrOgunseyin3940 One thing that I would like tell you is that please, please keep your video lecture on your areas no matter how much you get less number of followers. You are so sound for it. I always prefer your lectures to any other. Hope, 1day u'll be a leader of all of virtual Academicians.
Awesome. No simpler way to illustrate this subject.
Loved the explanation. This video definitely deserves more views.
Thanks so much for such a kind and encouraging comment. Appreciate this a lot!
Awesome video! Thank you and God bless!
What is the resolution of this exercise below:
Consider a queuing model with two attendants and a waiting position operating under steady-state conditions. Suppose that if a customer arrives and finds both agents busy and the waiting position unoccupied, then the customer will wait as long as necessary for service. If the customer finds both attendants busy and the waiting position also occupied, he leaves immediately.
Customers access the system according to a Poisson process with a rate of 2 customers per hour and that service follows an exponential distribution with a mean of 1 hour. The proportion of customers who arrive at the system and will not be served is:
a)2/5 b)1/8 c)2/3 d)2/7 e)1/6
W= 3 days per Order
L = 5 orders are waiting in Queue
λ= ?
According to Little's law L= λW
λ=L/W = 5/3 =1.6 orders per unit Time
Substituting the values in Little's law we can find the average number of orders the system can produce per week.
L = Wλ = 3 * 1.6 = 4.6 orders by week
We can't have orders produced in fractions, Therefore we round up to the nears whole number 5.
I hope I am correct.
Thank you for this very useful video!
Congratulations ! Continue the work !
Was really helpful
Nicely summarized
Is the Kendall notation commonly used? Is like (a/b/c):(d/e/f)
Yes it is! A video explaining Kendall's Notation will soon be released.
Thank you very much!
You are most welcome!
Answer for last question
Wow, so nice.
Can you give us real world examples for each service pattern types (FIFO, LIFO, Random, Order and Priority)?
Thanks for the comment. FIFO service patterns are quite prominent than you think, and you have perhaps witnessed this recently. Example of FIFO queues are waiting in line to use the ATM, board a bus, or to get vaccinated. Customers arriving to these queues are attended to on a first come first serve basis (FIFO).
For LIFO, a typical example is when you respond to the emails in your inbox from the top. The first email that is usually visible is the last one received. Scrolling down to the first received email quickly changes the email service pattern to FIFO. You could also choose to ignore certain emails and select the ones you would rather respond to in no particular order. When you do this, you are using a RANDOM ORDER.
As for service patterns based on PRIORITY, this is commonly used in hospitals, particularly in the A&E department. Where you have a patient with a knife stuck in their head and another patient suffering from constipation from excessive eating on the same queue, a service pattern based on priority is imperative here. Irrespective of the patients’ arrival time, priority will be given to patients with more serious health issues (i.e. the patient with a knife stuck in their head).
I hope this makes these service patterns clearer.
Thanks for watching again. Please remember to share the videos. Will be grateful. 🙂
@@DrOgunseyin3940 Just speechless to express my gratitude Dr. I thanks again. Sure, I will share it. 👏
@@gsiyoum You are most welcome my friend. Its a pleasure!
@@DrOgunseyin3940 One thing that I would like tell you is that please, please keep your video lecture on your areas no matter how much you get less number of followers. You are so sound for it. I always prefer your lectures to any other. Hope, 1day u'll be a leader of all of virtual Academicians.
@@gsiyoum Thank you so much for such kind words. Very encouraging. Not to worry, I will keep the videos coming. Thanks so much again 🙂
thank you for the effort. good explanation
- I think L=5*3=15 days
thankyouuuu
You're welcome 😊
Please remove the background music
Will do mate and will upload an alternative version.
@@DrOgunseyin3940 Awesome, thanks!
The no background music version:👇
th-cam.com/video/JF8-Ha2APyA/w-d-xo.html
@@DrOgunseyin3940 Awesome, thank you very much!
You are most welcome my friend 😊. I get the other one sorted for you too. 👍