Post on 07-Oct-2020
Queueing & Pythonpip install ciw
Geraint Ian Palmer@GeraintPalmer @CiwPython
PyCon UK 2016
CiwCiw
What is a Queue?
µΛ
What is a Queue?
n1 µ1
µ2
µ2
Λ1
Λ2
r12r21
r11
r22
Distributions
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.60.0
0.1
0.2
0.3
0.4
0.5
Priority Queues
µ
Λ?
Λ
Baulking
µΛ Too long?
P(baulk | x in queue) = b(x)
b(x) =
x20 if x ≤ 2x
x+3 if 2 < x ≤ 10
1 otherwise
0 2 4 6 8 10 12 14 16
x
0.0
0.2
0.4
0.6
0.8
1.0
b(x)
Server Schedules
Λ
µ
µ
µ
Server Schedules
Λ µ
Server Schedules
Λ
Server Schedules
Λ
µ
µ
Server Schedules
Λ
µ
µ
µ
Server Schedules
Λ µ
Server Schedules
Λ
Server Schedules
Λ
µ
µ
On duty, not busy On duty, busy Off duty, busy
0 40 65 110 150
Server 1 for (−40, 0)
Server 2 for (−40, 0)
Server 3 for (−40, 0)
Server 1 for (0, 40)
Server 1 for (65, 110)
Server 2 for (65, 110)
Server 1 for (110, 150)
Server 2 for (110, 150)
Server 3 for (110, 150)
Server 1 for (150, 190)
Academic Uses
Theoretical WorkInvestigating deadlock in queueing networks.(Geraint Palmer, Prof. Paul Harper, Dr. Vincent Knight)
Practical WorkModelling an ophthalmology clinic to strategise scheduling.(Lieke Holscher, Dr. Jennifer Morgan)
Investigating Deadlock
A1
B1
B2
C1
C2
B1
C1
A1
B2
A1
B1
B2
C1
C2
B1
A1
B2
A1
B1
B2
Investigating Deadlock
A1
B1
B2
C1
C2
B1
C1
A1
B2
A1
B1
B2
C1
C2
B1
A1
B2
A1
B1
B2
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
µ
0
5
10
15
20
25Ti
me
to D
eadl
ock
from
(0)
Expected Time to Deadlock From State (0)Analytical MeanSimulation Results
Modelling Ophthalmology Clinic
12
3
4567
8
9
1011 12
12
3
4567
8
9
1011 12
12
3
4567
8
9
1011 12
Thank you!
@GeraintPalmer@CiwPython
http://ciw.readthedocs.io
https://github.com/geraintpalmer/Ciw
https://ciwpython.github.io/CiwVis/
CiwCiw