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Measurement-based Admission Control
CS 8803NTM Network Measurements
Parag Shah
Papers covered
• 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
: aggregate bandwidth utilization for flows of class j: experienced packet queueing delay for class j
Describe existing aggregate traffic of each predictiveclass with an equivalent token bucket filter with parametersdetermined from traffic measurement.
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:• Extreme measurement errors allow too many sources • Extreme behaviour by admitted sources
• They are analyzed at the following timescales: • 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 jMean 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 connectionand the time when the first connection then in progress ends
Let according as at time t the system is in a backoff or notis 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 timesτ : shorter time period, typically time before a packet buffer overflow
A Framework for Robust Measurement-Based 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 largestinteger 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. offlows 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 certaintyEquivalence, 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 flowsAdmitted, 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
Exponentially distributed holding time for which a flowStays in the system
Assumption: [Worst Case] There are always flows waiting to enter the system(admitted)
The auto-correlation function of the flow:
The Continuous Load Model
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 withunit variance and autocorrelation function and can be
interpreted as the scaled aggregate bandwidth fluctuation aroundThe 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].
• 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
As converges in distribution to
and the overflow probability
converges to
Taking and using stationarity of
Smaller Faster fluctuation in memoryless mean bandwidth estimateslarger the probability in estimation at some time in the interval
Since decreases as where is the actual mean 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
Choose and such that
Thus the average bandwidth utilization:
For known
Robust MBAC For unknown
Choose on the order of the critical timescale
Suppose
Suppose critical time scale is much longer than memory timescale, then