the uncertainty of decisions in measurement based admission control

Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no

The Uncertainty of Decisions in Measurement Based Admission Control

Anne Nevin

Centre for Quantifiable Quality of Service in Communication Systems (Q2S)

Thesis for the degree of

Philosophia Doctor


Presentation Outline:• Introduction and thesis contribution• Homogeneous flows, probability of false acceptance and

provisioning• Flow dynamics and performance measures• Multiple arrivals within a measurement window, a

simulation study• Non homogeneous flows and the Similar flow concept• Conclusion


New application enables new ways of using the internet but also adds challenges…


A key requirement of Real-time applications is short network delay


Well-ordered sequence of packets

The packets must be ’clocked’ at the same rate on both sides

Constant network delay


Well-ordered sequence of packets

delay is no longer constant

When demand exceeds the capacity queues build up in routers



Queue of packets

Varying network delay

Packets received with jitter



Queue of packets

Varying network delay jitter buffer


Packets that do not make it on time will be discarded

Queue of packets


too late


Queue of packets


Admission control to prevent network congestion


Internet flows representing real-time applications and a singel network link with limited capacity

The exhibition venue


The exhibition venue has limited space and it is popular

Venue passes are expensive


Admission Control

Exhibition Venue

Exhibition room with capacity c


Admission Control

Exhibition VenueYESYES



Admission Control

Exhibition Venue



Admission Control

Exhibition VenueNONO



Admission Control

Exhibition Venue


Admission Control

Exhibition Venue

The number of people at the venue will vary with time

N (t)

t

only one pass sold

time in system


Admission Control

Aggregate rate

Mbp

s1

One person represents 1 Mbps while in the exhibition room

R (t)

t

only one pass sold

time in system


Admission Control

Every person represents 1 Mbps while in the exhibition room

R(t)

t

Aggregate raten passes sold


Admission Control

Every person represents 1 Mbps while in the exhibition room

R(t)

t

c = 1000Mbpsc


Admission Control

How many passes can you sell?

R(t)

t

c = 1000Mbpsc


Probability that all passholders are at the expo simultaneously is very very very small

Sell more than 1000 passes


Sell as many passes as you can


1) Maximize utilization2) P(people at venue > 1000) = small


MBAC

Measurement Based Admission Control, MBAC

window

R(t)

t

< uc

Admit if:

1000

uc is the maximum average rate

Tuning = u, 0<u <1

Observationestimate:



MBAC

window

R(t)

t

< uc

Admit if:

1000


But how accurate are these estimates?




MBAC

window

R(t)

t

< uc

Admit if:

1000


How long do we need to observe to judge the accuracy of the measurement?




There is an uncertainty in the admission decision

Admit too many Not enough


This thesis defines a theoretical framework to study the uncertainty of the admission decision

Probability of false rejection Carried useful traffic

Probability of false acceptance Carried useless traffic

New performance measures:


This thesis answers some of the shortcomings with the state of the art method of analyzing MBAC performance

• In the literature, simulation has been used to carry out the performance analysis over an infinite time scale, thus ”hiding” what happens when the actual admission decision is made

• The work in this thesis is fundamentally different from previous work in that it considers what happens at a short time-scale governed by measurement updates

• The thesis defines new flow level performance measures specifically targeting the MBAC decision process

• Performance of MBAC is carried out using mathematical analysis and performance measures can be stated up front

• The concept of Similar flows is introduced which simplifies the analysis when flows are non-homogeneous


Presentation Outline:• Introduction and thesis contribution• Homogeneous flows, probability of false acceptance

and provisioning• Flow dynamics and performance measures• Multiple arrivals within a measurement window, a



Network link with limited capacity c

MBACR(t) = aggregate rate of accepted flows

t

new flows

Leavingflows

blocked flows


Tuning = u, 0<u <1


Video

= average rate over the window

window

mean

New flows

MBAC Algorithm to be studied: The measured sum

Accepted flows

R(t) = aggregate rate

average max = uc



window

average max = uc

Admit at most one flow per window

Accepted flows


Video mean

New flows



window

average max = uc

MBAC knows when a flow comes but not when a flow leaves

Accepted flows


Video mean

New flows



window

average max = uc

The performance of the MBAC admission decision is determined analytically

Accepted flows


Video mean

New flows


General assumptions when doing the mathematical analysis:

• A.1: The flows are independent• A.2: The auto-covariance function of the rate process is

known• A.3: The lost traffic due to previous arrivals within a

window can be ignored• A.4: The probability of a flow leaving within a

measurement window is small • A.5: The correlation at arrival points can be neglected


Consider the case when flows are homogeneous

r1

K (t) 2

K (t)n

K (t) 1

t

peak rate: r auto-covariance: ρ(t)

mean rate:


r1

K (t) 2

K (t)n

K (t) 1

t

peak rate: r auto-covariance: ρ(t)

mean rate:

System state: N=n (number of flows) = maximum number of flows

Consider the case when flows are homogeneous


r1

K (t) 2

K (t)n

K (t) 1

Flows areindependent

i

K (t)iR (t) =

Measurement Process

R(t)

twindow

w

estimated average rate when N=n:

variance of the estimated average rate:R^


Accepting a flow: False Acceptance

Consider the critical state: The system is in state


Accepting a flow: False Acceptance

Consider the critical state: The system is in state

Safeguard


For a given quantile and window size, we can determine l

Provision the system to reduce the probability of false acceptance

Assumption: sum of the time averages is Normally distributed


(number of levels = 0) (window size = 5 s)

OFF

ON r = 2Mbps

2 s-1 2 s

-1Two state MMRP Source Model

Case study:

= 50


Admit too many Not enough

What should be the safeguard size?


Flows arrive following a Poisson process

MBAC R(t)

t

Leavingflows

blocked flows

Poissonλ

Flow lifetime distribution: negExp, μ


Flows arrive following a Poisson process

MBAC R(t)

t

A=λ/μ

APB

A(1-P )B


Ideal admission controller the Psychic controller

The ideal controller is a controller that always makes a correct decision


i ... ... ∞

λqi-1 λqi

nmaxμiμ (i+1)μ

nmax

λqnmax

nmax-1 nmax+1

λqnmax+1

(nmax+1)μ (nmax+2)μ

λqnmax-1

...Acceptance Region Rejection Region

MBAC will make erroneous admission decisions


Probability of False acceptance is the probability that an arriving flow is accepted when it should have been rejected

Probability of False rejection is the probability that an arriving flow is rejected when it should have been accepted

Blocking probability is the probability that an arriving flow is lost


Carried useful traffic is the expected number of flows in the acceptance region

Carried useless traffic is the expected number of flows in the rejection region


OFF

ON r = 2Mbps

2 s-1 2 s

-1

= 50

Two state MMRP Source Model

Case study:

(Erlang load)


Carried useful traffic can be maximized by choosing the right safeguard (in terms of levels)


The effect of multiple arrivals, a simulation study


arrival time

MBAC decision

t

t

w

flow1

flow1

flow2

wR

Rejected

Block All: Additional flows are blocked: flow2 is blocked.

Accept All: The MBAC does not keep track of flows and all flows within a window will be treated the same

Peak rate: The MBAC artificially increases the aggregate measurement with the peak rate of the arriving flow. The MBAC algorithm will accept a flow if


= 50

A = 100 erlang

OFF

ON r = 2Mbps

2 s-1 2 s


Case study:

= 50


= 50

A = 100 erlang

OFF

ON r = 2Mbps

2 s-1 2 s


Case study:

= 50

Peak rate strategy




simulation study• Non homogeneous flows and the Similar flow

concept• Conclusion


The non-homogeneous flows are grouped into classes

K (t)ij

rate process, peak rate, rauto covariance, covKmean rate,

K (t)ij

ri

i

ij

i

For class i

1

0

class 1

class k

r1

rk

n1

11

0

1

2

1

0

11

0

1

2

b1a1

n k

ak bk

t


The flows are grouped into classes

1

0

class 1

class k

r1

rk

n1

11

0

1

2

1

0

11

0

1

2

b1a1

n k

ak bk

r1

K (t)12

K (t)1n

K (t)11

rk

K (t) k2

K (t)kn

K (t)k1

Flows are independent

t

t


We observe the rate process continuously over the window1

0

class 1

class k

r1

rk

n1

11

0

1

2

1

0

11

0

1

2

b1a1

n k

ak bk

r1

K (t)12

K (t)1n

K (t)11

rk

K (t) k2

K (t)kn

K (t)k1

Flows are independent

R(t)

twindow

w

t

t


We observe the rate process continuously over the window

estimated average rate:

variance of the estimated average rate:

1

0

class 1

class k

r1

rk

n1

11

0

1

2

1

0

11

0

1

2

b1a1

n k

ak bk


To simplify analyis, we introduce the concept of similar flows.Similar flows share a common correlation structure (t)

Similar flows

For class i


Similar flows simplify the determination of the variance of the time average

Similar flows


Example with two classes:

MBAC

video 1

1

0

1

0

video 2

2 Mbps

25 Mbps

2.5 s-1 2.5 s-1

1 s-1 4 s-1

mean: 1Mpbs

mean: 5Mpbs

uc = 25Mbps


MBAC

Example with two classes and the flows are similar

video 1

1

0

1

0

video 2

2 Mbps

25 Mbps

2.5 s-1 2.5 s-1

1 s-1 4 s-1

r =1

r =2

mean: = 1Mpbs

mean: = 5Mpbs

uc = 25Mbps

1

2


Two dimensional state space. Ideal admission control.

n2

n15 10 15 20 2500

1

2

5

4

3

Ideal: E(R) uc = 25 Mbps


Two dimensional state space. MBAC.

n2

n15 10 15 20 2500

1

2

5

4

3

Ideal: E(R) uc = 25 Mbps


Rejection region for video 1

n2

n15 10 15 20 2500

1

2

5

4

3

mean = 1Mbps

2Mbps1

0

2.5 s-1-12.5 s


n2

n15 10 15 20 2500

1

2

5

4

3


P(False acceptance|rejection region) 1



n2

n15 10 15 20 2500

1

2

5

4

3

1

0

25Mpbs

4 s1 s-1 -1

mean: 5Mpbs



n2

n15 10 15 20 2500

1

2

5

4

3

P(False acceptance|rejection region) 2


Consider a state in the rejection region for class i, i = 1,2


Consider a state in the rejection region for class i, i = 1,2

safeguard


Most critical are the boundary states

n2

n15 10 15 20 2500

1

2

5

4

3

1

0

25Mpbs

4 s1 s-1 -1

mean: 5Mpbs


n2

n15 10 15 20 2500

1

2

5

4

3

Use the stochastic knapsack to find the state probabilities in the rejection region for the ideal case.

P(False acceptance|rejection region)


Probability of false acceptance given that the system is in the rejection region

Safeguard size

requirement


The probability of false acceptance can be stated up front for analytically tractable sources with a known covariance function

If the covariance is unknown it must be estimated


Similar flows simplify the analyses if the auto-correlation structure is known

Similar flows


• This is a theoretical framework to study how measurement errors impact the performance of the MBAC admission decision

• With some analytically tractable sources we can state the defined performance measures up front

• Performance is affected by– Source rate characteristics, window size and flow dynamics

• The concept of Similar flows simplifies the error analysis with non-homogeneous flows

• The defined methodology and framework can be used to study a variety of cases to gain insight into MBAC behavior

• The ultimate goal is to design robust MBAC algorithms

Conclusions

the uncertainty of decisions in measurement based admission control

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