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

• 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

2. Time-Sharing Models

A. Round – RobinB. Processor-shared modelC. Multiple level FB modelD. 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 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

2. Both A(t) and B(r) follows Poisson process exponentially distributed

Markov Assumptions (Ctd.)

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 levels2. Different mean service time for different priority units

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

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.