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lecture18
Course: ENGR 320, Fall 2009School: Wisconsin
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18 Queueing Lecture Theory Announcements HW 5 due today Exam Appeals deadline today Queueing Theory notes on Wendt Course Reserve 2 Project 1 Overall good job Please see me if I made comments you do not understand Average score ~ 93 3 Project 2 Get started on Project 2 NOW, if you haven't already! Ask early if you need help, you don't want extra work at the end of the semester...
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18
Queueing Lecture Theory
Announcements
HW 5 due today Exam Appeals deadline today Queueing Theory notes on Wendt Course Reserve
2
Project 1
Overall good job Please see me if I made comments you do not understand Average score ~ 93
3
Project 2
Get started on Project 2 NOW, if you haven't already! Ask early if you need help, you don't want extra work at the end of the semester
4
Last Time
Queueing Theory
Definitions Terminology
, ? Utilization? L, Lq? W, Wq? M/M/1? Little's Law?
5
Today
Queueing Theory
Airport example continued (hopefully) BirthDeath process
6
Queueing Theory
Example in ProModel
1 server a runway (it takes 8 minutes to take off, exponentially distributed) 1 entity type a plane (arriving every 10 minutes, exponentially distributed)
7
Airport Example
If I told you that W = 40 minutes Utilization = L = Wq = Lq =
8
Airport Example
Verify the results with simulation
9
BirthDeath Process
10
BirthDeath Process
Birth = Arrivals Death = Departure State system of is # of customers in system Assumptions
Remaining time until next birth is exponential Remaining time until next death is exponential Birth and death are mutually independent
Special case of continuous time Markov chain! Rate In = Rate Out (Balance Equations)
11
Example
Two onebarber shops sit side by side. Each can hold a max of 4 people, and any potential customer who finds a shop full will not wait for a haircut. Barber 1 charges $11 per haircut and takes an average of 15 minutes to complete a haircut. Barber 2 charges $7 per haircut and takes an average of 10 minutes to complete a haircut. An average of 10 potential...
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