Feedback queuing models for time shared systems
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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
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• Main Concern : Extending the analysis on time shared processor operations
• Main assumption : User’s service time is a not known priori
Eefficiently serve the user queue
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2. Time-Sharing Models
A. Round – RobinB. Processor-shared modelC. Multiple level FB modelD. Multiple level FB model with priorities
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A. Round – Robin
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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)
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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
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2. Both A(t) and B(r) follows Poisson process exponentially distributed
Markov Assumptions (Ctd.)
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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
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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
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Generalization priority processor-shared model
• q !=0 member of p priority group goes in a queue
• q 0 reduced to a processor shared model
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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??
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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 levels2. Different mean service time for different priority units
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4. Shortest-Job-First Model
• Service the unit with shortest service time• No preemption at new arrivalPossible 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
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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
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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
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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?
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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
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Thank You!
All the diagrams are from the research paper itself and from the internet. I am grateful to all those resources.