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Measurement-based Admission Control. CS 8803NTM Network Measurements Parag Shah. Papers covered.

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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

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:
- 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 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 connectionand 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 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 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

be the random number of flows admitted under MBAC

Let

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

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

be the aggregate load time at time t

Let

be the overflow probability at time t

converges in distribution to

As

and the overflow probability

converges to

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

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:

Robust MBAC

For unknown

Choose

on the order of the critical timescale

Suppose

Suppose critical time scale is much longer than memory

timescale, then

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