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Feedback queuing models for time shared systems

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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.

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Feedback queuing models for time shared systems

  1. 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. 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. 3. 2. Time-Sharing ModelsA. Round – RobinB. Processor-shared modelC. Multiple level FB modelD. Multiple level FB model with priorities
  4. 4. A. Round – Robin
  5. 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. 6. Markov Assumptions1. Input process has a discrete time parameter t = nq, n is distributed according to the geometric distribution. Then,Mean inter-arrival period = q/1-€ secMean arrival rate = 1-€ /q per secSimilarly,Mean servicing time = q/1-£ secWhere q is the time quantum(the basic time interval) ,1-€ - probability of arrival of a new unit1-£ - probability of receiving service
  7. 7. Markov Assumptions (Ctd.)2. Both A(t) and B(r) follows Poisson process  exponentially distributed
  8. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 18. Thank You!All the diagrams are from the research paper itself and from the internet. I am grateful toall those resources.

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