Measurement-based Admission Control

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

2. 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.

3. 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

4. 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

5. 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:

6. The admission control algorithm (ctd…) For a new guaranteed service flow: 1. Deny of bandwidth check fails 2. Deny when delay bounds are violated

7. 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

8. 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

9. 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:

10. 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

12. 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.

13. 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

14. 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

15. 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,

16. 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:

17. 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

18. Further, is the order of the estimation error around m* (perfect knowledge) Further,

19. 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.

20. 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

21. 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:

22. 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:

23. 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

24. 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

25. 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

26. Taking and using stationarity of

27. 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

28. 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

29. First order auto-regressive filter with impulse response Thus

30. 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

31. 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:

32. Under separation of timescales, γ >> 1 Thus Approximating and writing in terms of

33. Robust MBAC For known Choose and such that Thus the average bandwidth utilization:

38. Robust MBAC For unknown Choose on the order of the critical timescale Suppose Suppose critical time scale is much longer than memory timescale, then