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