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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 …

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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  • 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
  • The shorter waiting times at FB1 is in the expense of long waiting times for longer service units
  • Transcript

    • 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 ModelsA. Round – RobinB. Processor-shared modelC. Multiple level FB modelD. 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 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. 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 toall those resources.

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