A Theory of QoS for Wireless

I-Hong Hou

Vivek Borkar

P.R. Kumar

University of Illinois,

Urbana-Champaign

Background: Wireless Networks

There will be increasing use of wireless networks for serving traffic with QoS constraints:

– VoIP

– Video Streaming

– Real-time Monitoring

– Networked Control

1/19

Challenges

How to formulate a relevant and tractable framework for QoS?

Relevant – Jointly deal with three criteria:– Deadlines– Delivery ratios– Channel unreliabilities

Tractable – Provide solutions for QoS support:– Admission control policies for flows– Scheduling policies for packets

2/19

Client-Server Model

A system with N wireless clients and one AP

Time is slotted

One packet transmission in each slot– successful with probability pn

– failed with probability 1-pn

Non-homogeneous link qualities– p1,p2,…,pN may be different

AP

12

3

N

slot length = transmission duration

p1 p2

p3

pN

3/19

Protocol for Operation

AP indicates which client should transmit in each time slot

Uplink– Poll (ex. CF-POLL in 802.11 PCF)DataNo need for ACKpn = Prob( both Poll/Data are delivered)

DownlinkDataACKpn = Prob( both Data/ACK are delivered)

AP

n

CF-POLL

4/19

Protocol for Operation

AP indicates which client should transmit in each time slot

Uplink– Poll (ex. CF-POLL in 802.11 PCF)– DataNo need for ACKpn = Prob( both Poll/Data are delivered)

DownlinkDataACKpn = Prob( both Data/ACK are delivered)

AP

nData

4/19

Protocol for Operation

AP indicates which client should transmit in each time slot

Uplink– Poll (ex. CF-POLL in 802.11 PCF)– Data– No need for ACK– pn = Prob( both Poll/Data are delivered)

DownlinkDataACKpn = Prob( both Data/ACK are delivered)

AP

n

4/19

Protocol for Operation

AP indicates which client should transmit in each time slot

Uplink– Poll (ex. CF-POLL in 802.11 PCF)– Data– No need for ACK– pn = Prob( both Poll/Data are delivered)

Downlink– DataACKpn = Prob( both Data/ACK are delivered)

AP

n

Data

4/19

Protocol for Operation

AP indicates which client should transmit in each time slot

Uplink– Poll (ex. CF-POLL in 802.11 PCF)– Data– No need for ACK– pn = Prob( both Poll/Data are delivered)

Downlink– Data– ACK– pn = Prob( both Data/ACK are delivered)

AP

nACK

4/19

QoS Model

time slot

Timeline of the system

5/19

QoS Model

Clients generate packets with fixed period τDeadline = PeriodPackets expire and are dropped if not delivered by the

deadlineDelay of successfully delivered packet is at most τDelivery ratio of packets that meet deadline for client n

should be at least qn

arrival arrival arrival arrivalτ

5/19

QoS Model

Clients generate packets with fixed period τ Deadline = Period Packets expire and are dropped if not delivered by the

deadlineDelay of successfully delivered packet is at most τDelivery ratio of packets that meet deadline for client n

should be at least qn

arrival deadline

5/19

QoS Model

Clients generate packets with fixed period τ Deadline = Period Packets expire and are dropped if not delivered by the

deadline Delay of successfully delivered packet is at most τDelivery ratio of packets that meet deadline for client n

should be at least qn

arrival deadlineτ

5/19

QoS Model

Clients generate packets with fixed period τ Deadline = Period Packets expire and are dropped if not delivered by the

deadline Delay of successfully delivered packet is at most τ Delivery ratio of packets that meet deadline for client n

should be at least qn

#delivered packets in periodsliminf , a.s., nn

K

Kq

K

delivered delivered

dropped

5/19

Problem Formulation

Admission control– Decide whether a set of clients is feasible

Scheduling policy– Design a policy that fulfills every feasible set of

clients

6/19

The proportion of time slots needed for client n is

Work Load

1 nn

n

qw

p τ

7/19

The proportion of time slots needed for client n is

Work Load

1 nn

n

qw

p τ

expected number of time slots needed for a successful transmission

7/19

The proportion of time slots needed for client n is

Work Load

1 nn

n

qw

p τ

number of required successful transmissions in a period

7/19

The proportion of time slots needed for client n is

Work Load

1 nn

n

qw

p τ

normalize by period length

7/19

The proportion of time slots needed for client n is

We call wn the “work load”

Work Load

1 nn

n

qw

p τ

7/19

Necessary Condition for Feasibility of QoS Requirements

Necessary condition from classical queuing theory:

But the condition is not sufficient Packet drops by deadline misses cause more

idleness than in queuing theory

11

N

nnw

AP

1 2

S XS X

forced idleness

8/19

Let I be the expected proportion of idle time

Stronger necessary condition

Sufficient?

Stronger Necessary Condition

1

1N

nn

w I

Still NO!

9/19

Even Stronger Necessary Condition

Let IS = Expected proportion of the idle time when the set of clients is S– IS decreases as S increases

Theorem: the condition is both necessary and sufficient

1, {1,2,..., }n Sn S

w I S N

10/19

Largest Debt First Scheduling Policies

Give higher priority to client with higher “debt”

AP

1 2

3

SF FF

SF

11/19

Two Definitions of Debt

The time debt of client n – time debt = wn – actual proportion of transmission time

given to client n

The weighted delivery debt of client n– weighted delivery debt = (qn – actual delivery ratio)/pn

Theorem: Both largest debt first policies fulfill every feasible set of clients

– Feasibility Optimal Policies

12/19

Tractable Policy for Admission Control

Admission control consists of determining feasibility

Apparently, we need to check:

2N tests, so computationally complex

Theorem: Can be made into N tests– Polynomial time algorithm for admission control– Order clients by qn

1, {1,2,..., }n Sn S

w I S N

13/19

Simulation Setup

Implement on IEEE 802.11 Point Coordination Function (PCF)

Application: VoIP standard

Deadline miss ratio (DMR) = shortfall in delivery ratio

64 kbp data rate 20 ms period

160 Byte packet 11 Mb/s transmission rate

610 μs time slot 32 time slots in a period

14/19

Evaluated Four Policies

DCF

PCF with randomly assigned priorities

Time debt first policy

Weighted-delivery debt first policy

15/19

Test at Edge of Feasibility

Two groups of clients:– Group A requires 99% delivery ratio– Group B requires 80% delivery ratio– The nth client in each group has (60+n)% channel

reliability Feasible set: 6 group A clients and 5 group B

clients Infeasible set: 6 group A clients and 6 group

B clients

16/19

Results for a Feasible Set

0

1

2

3

4

5

6

0 1 2 3 4 5

Time (sec)

DM

R

Weighted-delivery

17/19

Results for a Feasible Set

0

1

2

3

4

5

6

0 1 2 3 4 5

Time (sec)

DM

R

Weighted-deliveryTime-based

fulfilled

17/19

Results for a Feasible Set

0

1

2

3

4

5

6

0 1 2 3 4 5

Time (sec)

DM

R

Weighted-deliveryTime-based

Random

17/19

Results for a Feasible Set

0

1

2

3

4

5

6

0 1 2 3 4 5

Time (sec)

DM

R

Weighted-deliveryTime-based

Random

DCF

17/19

Results for an Infeasible Set

0

1

2

3

4

5

6

0 1 2 3 4 5

Time (sec)

DM

R

Weighted-delivery

18/19

Results for an Infeasible Set

0

1

2

3

4

5

6

0 1 2 3 4 5

Time (sec)

DM

R

Weighted-deliveryTime-based

small DMR

18/19

Results for an Infeasible Set

0

1

2

3

4

5

6

0 1 2 3 4 5

Time (sec)

DM

R

Weighted-deliveryTime-based

Random

18/19

Results for an Infeasible Set

0

1

2

3

4

5

6

0 1 2 3 4 5

Time (sec)

DM

R

Weighted-deliveryTime-based

Random

DCF

18/19

Conclusion

Formulate a framework for QoS that deal with deadlines, delivery ratios, and channel unreliabilities

Characterize when QoS is feasible

Provide efficient scheduling policy

Provide efficient admission control policy

Address implementation issues

19/19

Backup Slides

An example:– Two clients, τ = 3– p1=p2=0.5– q1=0.876, q2=0.45– w1=1.76/3, w2=0.3– I{1}=I{2}=1.25/3, I{1,2}=0.25/3

w1+I{1}=3.01/3 > 1 However, w1+w2+I{1,2}=2.91/3 < 1