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

2. What, Why, How? Admission control based on measurements rather than source modeling Why MBAC? Source modeling is difficult (peak rate, average rate) Network utilization is low with descriptors like peak rate and average rate. High utilization can be achieved if we can weaken the reliability of the delay bound Applications like vat, vic and nv are tolerant How? Initial crude source characterizations (peak rates) Analytical modeling of memoryless and memory-based models Timescale-based analysis and simulation

3. 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.

4. Service Categories Gauranteed Service Gaurantees a worst-case delay bound for a flow by reserving bandwidth at the network elements along the path Lower network Utilization(acceptable only for smooth flows, not burst flows) Predictive Service Takes initial traffic descriptor, but then adapts according to effective bandwidth, allowing occasional delay violations Improves Network utilization

5. MBAC in Integrated Services Packet Networks (Jamin et. Al) a priori source characterizations only for incoming flows (token bucket filters) Measurements to characterize flows that are currently in place Utilization does not suffer significantly if the source descriptors are not tight (y?) Ability to occasionally incur delay violations Used only with predictive service and other more relaxed service commitments (y?) Useful only when there is a high-degree of statistical multiplexing (y?)

6. 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

7. Worst Case Delay: Predictive Service : Worst-case delay of priority queue level The worst-case class j delay, with FIFO discipline within the class and assuming infinite peak rates for the sources, is the following for each class j b: bucket depth of a flow r: token generation rate µ: link capacity : token bucket parameters for all flows of class j

8. Effect of a new predictive flow on traffic When a new flow α is added at the same priority level: When a new flow α is added at a lower priority level:

9. Effect of a new gauranteed flow on predictive traffic Effect of new gauranteed flow on predictive traffic:

10. 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 predictive class with an equivalent token bucket filter with parameters determined from traffic measurement.

11. 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:

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

13. Measurement mechanism To measure: Experienced delay & Utilization Queueing delay for each packet Usage rate for guaranteed service Usage rate for each predictive class j Measurement window Updating delay: Updating bandwidth:

14. Performance Tuning Knobs Utilization target, to keep utilization below certain levels Delay backoff estimate, (2) Averaging period (atleast 100 packet transmission times) Measurement window

26. 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

27. 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

28. 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 letbe 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 Letaccording as at time t the system is in a backoff or not is then a Markov Chain with off-diagonal transition rates:

29. 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

33. a model of two traffic classes with time-varying offered loads. Explicit priorities are assigned to connections by extending the state space to 0, 1 and 2.The precise description of the off-diagonal transition rates for the Markov chain are as follows

35. 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.

36. MBAC Issues Estimation Error Certainty Equivalence Dynamics and Separation of time scale Flow arrival and departure dynamics Flow and Burst timescale dynamics Memory Can improve quality of estimators Large memory window can reduce adaptability to non-stationarities in the statistics

37. Unified Model Goal: make QoS guarantees in the presence of measurement uncertainty, without requiring the tuning of system parameters Heavy Traffic regime System size is large Can use statistical regularity by increasing utilization, but keeping QoS constant Allows Gaussian approximations and use of first and second order statistics of the traffic processes

39. 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

40. 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

41. 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,

42. 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:

43. 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

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

46. 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.

47. 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

48. To get overflow probability in steady state, set Is independent of The difference is a Gaussian RV with mean 0 and variance Thus, In the exact case, the bw fluctuation comes from fluctuations in individual flows, but in the estimated bw case, the fluctuations come from both the number of flows and the measurement of each flow.

49. Therefore, we adjust, Using the approximation, Q(x) ~ Φ(x)/x for small Q(x), where Φ(x) Is the pdf of N(0,1). = ifThe loss of utilization: Universal result, since performance in the certainty equivalence scheme is independent of the stationary distribution of the flow and its mean and variance. Difference between actual and measured value of µ,

50. 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: The Continuous Load Model

51. 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:

52. 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 functionand 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

54. 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

55. 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

56. Taking and using stationarity of

57. Analysis of Overflow Probability Since is stationary and symmetrically distributed around 0, Can be interpreted as the hitting probability of a Gaussian process on a moving boundary Define: to be the variance of Assuming that the single-sided derivatives ofat exist and are finite, letbe the right derivative of Then the hitting probability is approximated by: where is the N(0,1) probability density function.

58. Consider a specific auto-correlation function : governs the exponential drop-off rate of the correlation function. natural correlation time scale for burst dynamics now becomes the well-known Ornstein-Uhlenbeck process Further,

59. Making a time-scale assumption (γ >> 1) Comparing with the result for impulsive load model Much worse. In the impulsive model, errors can happen at 0 In the continuous model, errors happen upto roughly to have an impact on the load at time t.

60. Smaller Faster fluctuation in memoryless mean bandwidth estimates larger the probability in estimation at some time in the interval Since decreases aswhere is the actual mean Holding time, the overflow probability decreases roughly as Thus

62. 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

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

64. 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

65. 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:

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

67. Robust MBAC Chooseandsuch that Thus the average bandwidth utilization: For known

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

75. Questions???