This is a presentation created to facilitate a research paper discussion on 'Feedback queuing models for time shared systems' for a final year undergraduate course. This includes a summary of the concepts presented with the paper, excluding their statistical proofs.

1. Feedback Queuing Models for Time-
Shared Systems (Paper Discussion)
-Cited by 93 related articles-
EDWARD G. COFFMAN
Princeton University, Princeton, New Jersey
AND
LEONARD KLEINROCK
University of California, Los Angeles, California
Published in 1968
This presentation is a summary of the paper content,
that is used to provide the foundation of the paper
discussion

2. Eefficiently serve the user queue
• Main Concern : Extending the analysis on time
shared processor operations
• Main assumption : User’s service time is a not
known priori

3. 2. Time-Sharing Models
A. Round – Robin
B. Processor-shared model
C. Multiple level FB model
D. Multiple level FB model with priorities

4. A. Round – Robin

5. Assumptions
• Preemptive resume
• No swap time  upper bounds on system
performance
• inter- arrival time distribution - A (t)
• The service requirements of arriving units -B(r)

6. Markov Assumptions
1. Input process has a discrete time parameter t =
nq, n is distributed according to the geometric
distribution. Then,
Mean inter-arrival period = q/1-€ sec
Mean arrival rate = 1-€ /q per sec
Similarly,
Mean servicing time = q/1-£ sec
Where q is the time quantum(the basic time
interval) ,
1-€ - probability of arrival of a new unit
1-£ - probability of receiving service

7. Markov Assumptions (Ctd.)
2. Both A(t) and B(r) follows Poisson process 
exponentially distributed

8. Assumption at the End of Time Interval
• Late arrival
– Eject the unit in service
• Allow to join end of queue
– Instantly new unit arrive (under probability)
• Early arrival
– Vice versa

9. B. Processor-shared Models
• Round-robin system in which q  0
• All units in the system receive service
concurrently
• No waiting time in queue
• Program speed = 1/k the speed from processor
alone speed if k-1 processes running

10. Generalization  priority processor-
shared model
• q !=0  member of
p priority group goes
in a queue
• q 0 reduced to a
processor shared
model

11. C. Multiple level FB model (FBN)
• N th level is quantum
controlled , FCFS
• Lower level unit comes
N th level unit is
preempted after the
quantum in progress
• q  0 implies in the limit
a FCFS
• FB1  FCFS
 Possible Starvation at last
level??

12. D. Multiple level FB model with
priorities
• Assign external priorities to
arriving units
• Within a group FCFS
• Arrival queue level low 
in the front of queue
A proposed step :
1. Different quantum size for different levels
2. Different mean service time for different priority units

13. 4. Shortest-Job-First Model
• Service the unit with shortest service time
• No preemption at new arrival
 Possible starvation for long service required
units??
A proposed step :
1. Improvements to get the information on total service time
required by the unit at arrival

14. 5. Examples and Discussion
• RR, FBN, SJF favor short service time
• RR implicit discrimination on past service
• FBN explicitly based on past service
We can have a discussion comparing the
presented models

15. Compare FB and RR
• Shorter service
requirement  shorter
wait than in FCFS for
both FB and RR
• RR is better for long
service requirements
• FB1 and FB 7
comparison

16. RR waiting times FB waiting times
• Waiting time increase without a change in the number of
levels as q increase
• What more can we observe?

17. Summary
• Superior treatment given certain units
inferior treatment to some other units
• Paper provides system designers with several
options, presenting the behavior of each
model

18. Thank You!
All the diagrams are from the research paper itself and from the internet. I am grateful to
all those resources.