This presentation was prepared by Ishara Amarasekera and Prabath Weerasinghe based on the paper, Feedback Queueing Models for Time Shared Systems by Edward G. Coffman and Leonard Kleinrock. This presentation contains a summary of the content provided in this research paper and was presented as a paper discussion for the course, Advanced Operating Systems in Computer Science.

1. Present By : Ishara Amarasekera
Prabath Weerasinghe
By
Edward G. Coffman and Leonard Kleinrock

2. • Stochastic Process – A process that describes the data of
a random process.
• Markov Property - The memory less characteristic of
stochastic process.
• Memory less - Future state can be predicted without
knowing the previous states
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3. What is Scheduling?
Scheduling is the method by which threads, processes or
data flows are given access to system resources.
Why need Scheduling?
To load balance and share system resources effectively or
achieve a target quality service.
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4. P
QUEUEA(t)
PROCESS
OR
B(r)
q
• Units arrive from infinite source
• Units take the end of the queue immediately on their arrival
• Served a fixed amount of service (q) on FCFS basis
• If a unit being served completely within q, it exits the system
• If not, is removed from the processor and put back to the end of
the queue
How it works
3

5. • Once all units ahead are served, the interrupted unit is again
served. –Preemptive Resume
• The same will continue for all the units in the queue
How it works
P
QUEUEA(t)
PROCESS
OR
B(r)
q
4

6. • Average service time B(r) and Average arrival time A(r) is constant
• Q = Total Capacity or No. of instructions can be processed per
second
• n= No of units per second
• Therefore, Q/n = Amount of capacity shared among each unit per
second.
.
Consider RR system in which q 0
Q
PROCESSOR
q 0n
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7. • Thus the processor is being shared among all units with Q/n
amount.
This leads to a Processor Shared Model
By making all units in the system receive service concurrently and
experience no waiting time in the queue.
Consider RR system in which q 0
Q
PROCESSOR
q 0n
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8. • Input traffic is broken into P separate priority groups.
• Service Time given to a unit with priority p when q = 0 = gpq
• when q = 0
Service Time given to a unit with priority p = gp/ ∑ gini
f1
f1
.
.
f1
f2
f2
.
.
f2
.
.
fp
fp
.
fp
.
.
ƛp
N1 PRIORITY
UNITS
N2 PRIORITY
UNITS
NP PRIORITY
UNITS
• Unit with priority p might get a service time which is > Q/n due
to it’s priority
• A generalization of the processor shared model.
gp = Priority group
ni = number of members
from the group I present in
the system
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9. How it works
PROCESSOR
q
ƛ
N
2
1
:
:
P
• Unit at the service point at any given queue level will not be
serviced unless all tower level queues are empty
•Unit at service is given a quantum (q) of service like in the RR
model
•If q is not enough, the unit will be subsequently placed at the end
of the next higher level queue 8

10. When q 0 and N is finite it gives a FCFS Model
When q 0 and N is infinite it gives a RR Model
i + 1
i
:
PROCESSOR
q
ƛ
N
1
P
:
9

11. i +
1
i
:
PROCESSOR
q
ƛ1
1
P
:
ƛ2
ƛp
• Different quantum sizes for different levels and different mean
times for different priory-level units are given.
• Units can come from outside.
•Until the Lowest level is the highest priority queue is processed
they need to wait.
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12. • For all the models no overhead or swap time is
associated with the process of unloading and loading
units from the processor .
• Therefore the results may be viewed as upper bound of
system performance.
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13. • Process with smallest time will be processed first
• Waiting time in the queue W(t).
• Non pre emptive, therefore this results slow response
time to new jobs.
t - service time
λ - Arrival rate
µ - Service rate
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14. RR – Round Robin
Processor-Shared Models(q -> 0)
Priority Processor-Shared Model
Multiple Level FB Model
Priority Based Multiple Level FB Model
Shortest Job First
FCFS
When q limits to zero q -> 0
With priorities assigned – gp
With priorities assigned – gp
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15. • Performances differ on each model.
• So need to analysis before recommending.
• Using Average Waiting Time W(t) is a good choice.
Wait.. define Average
Waiting Time.
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16. “Average wait time for a given model is the sum of the
time spent in queues and the service.”
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17. • Considering q ≠ 0 and time in service as negligible,
only the time in queue is taken to calculate the
average wait time.
• In FBN N -> α
• Wk = W(t) – t
• A graph is drawn with the average waiting time Wk
against the load ƿ.
• Load ƿ can be considered as the number if arrivals
per service.
ƿ = λ/μ 16

18. 17

19. •FCFS is used as a reference.
•With respect to that;
o The average waiting time behavior of FN and RR
models at low load values.
o Which one is better for short service time units ?
o Which one is better for longer service time units ?
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20. • When q ≠ 0, N -> α, λ = 0.5 sec,
μ = 1.0 sec
• Two separate graphs for both RR and FBα with two
events.
• 2 seconds service time event and 0.5 sec service time
event.
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21. What is this ?
Why is this saw
tooth shape ?
What explains the
upper envelope
slope…..
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22. Same questions can
be asked as of the
RR model
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23. • Why those serrations ?
• What makes the increasing slopes ?
• What makes the decreasing slopes ?
• Reasoning the behavior between two
discontinuities ?
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24. Unit with 2 sec service time.
System with 1 sec average service time.
Model A : q = 2.0 – ε
Model B : q = 1.0 – ε
What would contribute to the wait time the most ?
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25. •Number of levels = 4
•Below 2/3 sec quantum size -> Sends the unit to level 4
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26. •Processor-Shared Model
•Preemptive Processor-Shared Model
•Shortest Job First
All the above get analyzed in two graphs.
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27. 26

28. 27

29. • Round Robin Model : Late – Arrival Systems Average
Wait Time
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30. • There’s one in all kind of scheduling model.
• All are different in their own ways and usage differs
with the applications
• According to the Conservation Law :
- Any favors to some units would result in a
discrimination of some others.
• This is because of having a constant CPU capability.
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