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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
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
2. Time-Sharing Models
A.   Round – Robin
B.   Processor-shared model
C.   Multiple level FB model
D.   Multiple level FB model with priorities
A. Round – Robin
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)
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
Markov Assumptions (Ctd.)

2. Both A(t) and B(r) follows Poisson process 
  exponentially distributed
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
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
Generalization  priority processor-
            shared model
• q !=0  member of
  p priority group goes
  in a queue

• q 0 reduced to a
  processor shared
  model
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??
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
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
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
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
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?
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
Thank You!




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

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Feedback queuing models for time shared systems

  • 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.

Editor's Notes

  1. Earlier has mentioned that low priority queues are considered only when higher priorities are empty. Input traffic is separated into P priority groups. But no information on how it is done
  2. The shorter waiting times at FB1 is in the expense of long waiting times for longer service units