Mixed criteria packet scheduling
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Mixed Criteria Packet Scheduling. Eric Torng and Chad Meiners Department of Computer Science and Engineering Michigan State University. Motivation. Simplified View. S 1. ?. A. B. S 2. A processor. Unit Size Jobs Arriving Over Time. Buffer. Scheduling Interpretation. S 1. A. B.

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Mixed Criteria Packet Scheduling

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Mixed criteria packet scheduling

Mixed Criteria Packet Scheduling

Eric Torng and Chad Meiners

Department of Computer Science and Engineering

Michigan State University


Motivation

Motivation


Simplified view

Simplified View

S1

?

A

B

S2


Scheduling interpretation

A processor

Unit Size Jobs Arriving Over Time

Buffer

Scheduling Interpretation

S1

A

B

S2


Packet weights

Buffer

Packet Weights

S1

4

1

5

A

B

2

S2

3

7


Single criterion packet scheduling

FIFO buffer, bounded capacity

20

4

50

1

8

7

10

3

NOT FIFO, but deadlines

20,1

4,2

50,2

1,3

8,4

7,5

10,5

3,6

Single Criterion Packet Scheduling

Maximize weight of transmitted packets


Where do weights come from

Where do Weights Come From?

  • Price per packet

    • Corresponds to maximizing network’s profit

    • But there may not be prices

  • Weights should then correspond to users’ needs

    • Problem: users have different needs


Weights

Weights?

Skype video call

iTunes song download

What are the user’s needs?

How do they measure success?


User s goals

User’s Goals

  • Skype video call

    • Each packet must be delivered in a timely manner to avoid jitter

    • Each packet has a deadline

  • iTunes song download

    • Goal is to have entire file downloaded as quickly as possible

    • User wants to minimize flow time/completion time of entire download


Weights1

Weights?

Skype video call

iTunes song download

If iTunes download does not hurt Skype call, give priority to iTunes packets.


Weights2

Another skype

call

Weights?

Skype video call

iTunes song download

If iTunes download will cause one or both calls to have poor performance, prioritize skype calls.


Mixed criteria packet scheduling1

Another skype

call

Mixed Criteria Packet Scheduling

Skype video call

iTunes song download

Rather than use weights, measure each client’s goal exactly.

Skype packets have deadlines.

iTunes user worries about final packet arrival time.


Deadflow problem

DeadFlow Problem

  • Input I = Id union If

    • Id: Real time jobs with deadlines

      • Goal: meet all deadlines (assuming this is possible)

    • If: Flow time jobs without deadlines

      • Goal: minimize average flow time

  • We assume preemption is allowed

  • Jobs are not all unit size

    • Model entire flow, not individual packets


Single criterion problems

Single Criterion Problems

  • Each set of jobs can be handled if alone

    • Given only flow jobs: SRPT is optimal

    • Given only deadline jobs: EDF, LLF, and several other algorithms are optimal


Related work

Related Work

  • Some work on mixed criteria scheduling that focuses on non-preemptive setting

    • Baker & Smith, 2003

    • Agenetis, Mirchandani, & Pacciarelli, 2004

  • Real-time scheduling with hard periodic jobs and soft aperiodic tasks

    • Chetto and Chetto, 1989

    • Lehoczky and Ramos-Thuel, 1992

    • Spuri and Buttazo, 1996


Our results

Our Results

  • DeadFlow is weakly NP-hard

    • Reduction from Partition/Knapsack

  • Unit DeadFlow where the flow jobs have unit size is solvable in polynomial time

    • Schedule deadline jobs as late as possible

    • Move up only to fill holes unused by flow jobs (and possibly speed up later flow jobs)


Hardness proof

Hardness Proof

  • Selection instances

  • Canonical schedules for selection instances

  • Knapsack model


Selection instances

SRPT(If)

0

d

Selection Instances

  • Flow jobs do not overlap (ignoring deadline job)

    • ri + pi ≤ ri+1

One deadline job: release time is 0, deadline is d, processing time is p


Canonical schedules

OK:

SRPT(If)

x

x

NOT OK:

0

d

Canonical Schedules

  • In interval [0,d), a flow job j runs only during [rj,rj + pj).

  • If not finished by rj + pj,it completes after d.


Knapsack interpretation

SRPT(If)

0

d

cost of this job

value of this job

Knapsack Interpretation

  • Deadline job

    • Let p be processing time of deadline job after all gaps between flow jobs have been filled

    • Goal: Choose p units of flow jobs to displace of minimum total cost


Polynomial time algorithm

Polynomial Time Algorithm

  • Unit Deadflow Problem

    • All flow jobs are unit size

    • Deadline jobs may have different deadlines and different sizes

  • Slacker Algorithm

    • Schedule deadline jobs as late as possible

      • Use EDF on “reversed” input instance

    • Move up jobs into holes not used by flow jobs


Open problems

Open Problems

  • Lots!

  • Online algorithms

    • Need to consider maximization problems for deadline jobs

      • Maximize value of jobs that complete by their deadlines (still need to compute values)

      • Maximize number of jobs that complete by their deadlines


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