Measurement-based
Admission Control
CS 8803NTM
Network Measurements
Parag Shah
Papers covered
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Sugih Jamin, Peter B. Danzig, Scott Shenker, Lixia Zhang, "A
Measurement-based Connection Admission Control Algorithm for
Integrated Services Networks", IEEE/ACM Transactions on Networking,
5(1):56-70. February 1997.
R.J. Gibbens and F.P.Kelly, "Measurement-based connection
admission control". In International Teletraffic Congress Proceedings,
June 1997.
Matthias Grossglauser, David N. C. Tse, "A Framework for Robust
Measurement-based Admission Control", IEEE/ACM Transactions on
Networking, 7(3):293-309, June 1999.
MBAC in Integrated Services Packet Networks
(Jamin et. Al)
•Admission control algorithm done under CSZ
scheduling algorithm
•Multiple levels of predictive service with per-delay
bounds that are order of magnitude different from
each other
•Approximate worst-case parameters with measured
quantities (Equivalent Token Bucket Filter)
•Gauranteed services use WFQ and Predictive
services use Priority queueing
Equivalent Token Bucket Filter
Describe existing aggregate traffic of each predictive
class with an equivalent token bucket filter with parameters
determined from traffic measurement.
: aggregate bandwidth utilization for flows of class j
: experienced packet queueing delay for class j
The admission control algorithm
For a new predictive flow α:
1. Deny if sum of current and requested rates exceeds
targeted link utilization levels
2. Deny of new flow violates delay bounds at same or lower priority
levels:
The admission control algorithm
(ctd…)
For a new guaranteed service flow:
1. Deny of bandwidth check fails
2. Deny when delay bounds are violated
Measurement-based connection
admission control (Gibbens et.al)
• Performance of MBAC depends upon statistical interactions
between several timescales (packet, burst, connection
admission, connection holding time)
• Buffer overflow happens when:
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Extreme measurement errors allow too many sources
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Extreme behaviour by admitted sources
• They are analyzed at the following timescales:
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Admission decision and holding times
•
Timescales comparable to busy period before overflow
The Basic Model
as the load produced by a connection of class j at time t.
No. of connections at class j
Peak rate of class j
Mean rate of class j
Resource capacity
rate of load lost at a resource of capacity C
The Basic Model (ctd…)
Let connections of class j arrive in a Poisson stream of rate
Let holding times of accepted connections be independent and
exponentially distributed with parameter
Let
and let
be a subset of
Suppose a connection arriving at time t is accepted if
and is rejected otherwise.
Back-off period: Period between the rejection of a connection
and the time when the first connection then in progress ends
Let
according as at time t the system is in a backoff or not
is then a Markov Chain with off-diagonal transition rates:
The basic model (ctd…)
is a vector with a 1 in the jth component zeros otherwise
acceptance probability
The proportion of load lost is
where the expectation is taken over the state n of the Markov chain.
t : timescale associated with admission decisions and holding times
τ : shorter time period, typically time before a packet buffer overflow
A Framework for Robust MeasurementBased Admission Control
• Assuming that the measured
parameters are the real ones, can
grossly compromise the target
performance of the system.
• There exists a critical timescale over
which the impact of admission decision
persists.
Impulsive load model
• Bufferless single link with capacity c
• Bandwidth fluctuations are identical stationary and
independent of each other (mean = µ, variance = σ)
• Normalized capacity n – (c/µ)
: Steady-state overflow probability
•Infinite burst of flows arrive at time 0
•After time 0, no more flows are accepted and the
flows stay forever in the system
•Permits study of impact of performance errors on
on the number of flows and on overflow probability
Impulsive Load Model (ctd…)
The number of admissible flows in the system is the largest
integer m such that
: bandwidth of the ith flow at time t
For large n,
If mean and variance are known a priori, then the no. of
flows m* to accept should satisfy
Where Q(.) is the ccdf of a N(0,1) Gaussian RV
Impulsive Load Model (ctd…)
Actual Steady-state Overflow probability:
For reasonably large c
If mean and variance are not known a priori, and if it uses
Estimation from initial bandwidth of flows in certainty
Equivalence, by Central Limit Theorem,
Impulsive Load Model (ctd…)
We want an approximation of average overflow probability
In steady state and for large t and compare it to the target
To find an approximation of the distribution for Mo:
We compare the estimated and actual means:
Can be interpreted as the scaled aggregate
Bandwidth fluctuation at time 0 around the mean
The estimated standard deviation:
is Gaussian
Deviation is of the order of
Distribution of Mo can be approximated by a linearization of
The relationship around a nominal operating point, which is
the operating point under perfect knowledge
Further,
is the order of the estimation error around m* (perfect
knowledge)
Further,
Let
be the random number of flows admitted under MBAC
where capacity is nµ.. Then the sequence of random variables
converges to a distribution to a random variable
Randomness is due to both randomness in the number of flows
Admitted, as well as randomness in the bandwidth demands of
those flows.
The aggregate load at time t can be approximated by
Is the approximation for the scaled aggregate
Bandwidth fluctuation at time t
Further,
For large n, the overflow probability at time t
The Continuous Load Model
Exponentially distributed holding time for which a flow
Stays in the system
Assumption: [Worst Case] There are always flows waiting to
enter the system(admitted)
The auto-correlation function of the flow:
Memoryless MBAC
- Estimates based only on the means and variances of the current
bandwidths and flows
- At any time t, MBAC estimates the admissible number of flows
Mt:
is random and depends only on the current bandwidths
of the flows. It can be approximated as:
A stationary zero-mean Gaussian process with
unit variance and autocorrelation function
and can be
interpreted as the scaled aggregate bandwidth fluctuation around
The mean
Flow departure rate is of the order
Repair Time is of the order
Critical Time scale over which admission errors are repaired
For any s ≤ t,
where A[s,t] is the number of flows admitted during [s,t].
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Flow departures have a repair effect on past mistakes.
Fluctuations around perfect knowledge of no. of flows
is around √n.
• It takes √n flows to depart to rectify past errors in accepting
too many flows.
D[s,t] : Approximated Departure rate
Let
be the aggregate load time at time t
be the overflow probability at time t
converges in distribution to
As
and the overflow probability
converges to
Taking
and using stationarity of
Faster fluctuation in memoryless mean bandwidth estimates
Smaller
larger the probability in estimation at some time in the interval
is the actual mean
decreases as
where
Since
Holding time, the overflow probability decreases roughly as
Thus
MBAC with Estimation Memory
• Problems with memoryless scheme
• Estimation error at a specific time instant is
large
• Correlation timescale is same as that of traffic
causes the probability of under-estimation of mean
Bandwidth during
to be very high
Use more memory in mean and variance estimators
First order auto-regressive filter with impulse response
Thus
Governs how past bandwidths are weighted; measure of
the estimated window length
Relationship between memoryless and memory-based estimators
Where * is the convolution operation
Error in the Filtered estimate of the mean bandwidth of
A flow at time t
The steady-state overflow probability under the MBAC with
Memory can be approximated by
This is the hitting probability if a Gaussian process
on a moving boundary, and can be approximated as:
Under separation of timescales, γ >> 1
Thus
Approximating and writing in terms of
Robust MBAC
For known
Choose
and
such that
Thus the average bandwidth utilization:
Robust MBAC
For unknown
Choose
on the order of the critical timescale
Suppose
Suppose critical time scale is much longer than memory
timescale, then