Post on 13-Jan-2016
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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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
New application enables new ways of using the internet but also adds challenges…
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
A key requirement of Real-time applications is short network delay
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Well-ordered sequence of packets
The packets must be ’clocked’ at the same rate on both sides
Constant network delay
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Well-ordered sequence of packets
delay is no longer constant
When demand exceeds the capacity queues build up in routers
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
When demand exceeds the capacity queues build up in routers
Queue of packets
Varying network delay
Packets received with jitter
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
When demand exceeds the capacity queues build up in routers
Queue of packets
Varying network delay jitter buffer
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Packets that do not make it on time will be discarded
Queue of packets
Varying network delay jitter buffer
too late
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Queue of packets
Varying network delay jitter buffer
Admission control to prevent network congestion
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Internet flows representing real-time applications and a singel network link with limited capacity
The exhibition venue
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
The exhibition venue has limited space and it is popular
Venue passes are expensive
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition Venue
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition VenueYESYES
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition Venue
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition Venue
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition Venue
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition Venue
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition Venue
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition Venue
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition VenueNONO
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition VenueNONO
Exhibition room with capacity c
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Exhibition Venue
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Every person represents 1 Mbps while in the exhibition room
R(t)
t
Aggregate raten passes sold
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
Every person represents 1 Mbps while in the exhibition room
R(t)
t
c = 1000Mbpsc
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admission Control
How many passes can you sell?
R(t)
t
c = 1000Mbpsc
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Probability that all passholders are at the expo simultaneously is very very very small
Sell more than 1000 passes
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Sell as many passes as you can
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
1) Maximize utilization2) P(people at venue > 1000) = small
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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:
Observationestimate:
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
MBAC
window
R(t)
t
< uc
Admit if:
1000
uc is the maximum average rate
But how accurate are these estimates?
Observationestimate:
Observationestimate:
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
MBAC
window
R(t)
t
< uc
Admit if:
1000
uc is the maximum average rate
How long do we need to observe to judge the accuracy of the measurement?
Observationestimate:
Observationestimate:
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
There is an uncertainty in the admission decision
Admit too many Not enough
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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:
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Network link with limited capacity c
MBACR(t) = aggregate rate of accepted flows
t
new flows
Leavingflows
blocked flows
uc is the maximum average rate
Tuning = u, 0<u <1
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
= average rate over the window
window
average max = uc
Admit at most one flow per window
Accepted flows
R(t) = aggregate rate
Video mean
New flows
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
= average rate over the window
window
average max = uc
MBAC knows when a flow comes but not when a flow leaves
Accepted flows
R(t) = aggregate rate
Video mean
New flows
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
= average rate over the window
window
average max = uc
The performance of the MBAC admission decision is determined analytically
Accepted flows
R(t) = aggregate rate
Video mean
New flows
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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:
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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^
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Accepting a flow: False Acceptance
Consider the critical state: The system is in state
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Accepting a flow: False Acceptance
Consider the critical state: The system is in state
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Accepting a flow: False Acceptance
Consider the critical state: The system is in state
Safeguard
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
(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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Admit too many Not enough
What should be the safeguard size?
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Flows arrive following a Poisson process
MBAC R(t)
t
Leavingflows
blocked flows
Poissonλ
Flow lifetime distribution: negExp, μ
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Flows arrive following a Poisson process
MBAC R(t)
t
A=λ/μ
APB
A(1-P )B
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Ideal admission controller the Psychic controller
The ideal controller is a controller that always makes a correct decision
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
OFF
ON r = 2Mbps
2 s-1 2 s
-1
= 50
Two state MMRP Source Model
Case study:
(Erlang load)
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Carried useful traffic can be maximized by choosing the right safeguard (in terms of levels)
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Carried useful traffic can be maximized by choosing the right safeguard (in terms of levels)
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
The effect of multiple arrivals, a simulation study
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
= 50
A = 100 erlang
OFF
ON r = 2Mbps
2 s-1 2 s
-1Two state MMRP Source Model
Case study:
= 50
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
= 50
A = 100 erlang
OFF
ON r = 2Mbps
2 s-1 2 s
-1Two state MMRP Source Model
Case study:
= 50
Peak rate strategy
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
To simplify analyis, we introduce the concept of similar flows.Similar flows share a common correlation structure (t)
Similar flows
For class i
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Similar flows simplify the determination of the variance of the time average
Similar flows
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Two dimensional state space. Ideal admission control.
n2
n15 10 15 20 2500
1
2
5
4
3
Ideal: E(R) uc = 25 Mbps
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Two dimensional state space. MBAC.
n2
n15 10 15 20 2500
1
2
5
4
3
Ideal: E(R) uc = 25 Mbps
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
n2
n15 10 15 20 2500
1
2
5
4
3
Rejection region for video 1
P(False acceptance|rejection region) 1
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Rejection region for video 2
n2
n15 10 15 20 2500
1
2
5
4
3
1
0
25Mpbs
4 s1 s-1 -1
mean: 5Mpbs
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Rejection region for video 2
n2
n15 10 15 20 2500
1
2
5
4
3
P(False acceptance|rejection region) 2
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Consider a state in the rejection region for class i, i = 1,2
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Consider a state in the rejection region for class i, i = 1,2
safeguard
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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)
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Probability of false acceptance given that the system is in the rejection region
Safeguard size
requirement
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
Similar flows simplify the analyses if the auto-correlation structure is known
Similar flows
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
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
Anne Nevin, The Uncertainty of Decisions in Measurement Based Admission Controlwww.q2s.ntnu.no
• 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