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- 1. P13ITE05 High Speed Networks UNIT - II Dr.A.Kathirvel Professor & Head/IT - VCEW
- 2. UNIT - II Queuing Analysis and models Single server queues Effects of congestion & congestion control Traffic management Congestion control in packet switching networks Frame relay congestion control
- 3. Basic concepts Performance measures Solution methodologies Queuing system concepts Stability and steady-state Causes of delay and bottlenecks
- 4. Performance Measures Delay Delay variation (jitter) Packet loss Efficient sharing of bandwidth Relative importance depends on traffic type (audio/video, file transfer, interactive) Challenge: Provide adequate performance for (possibly) heterogeneous traffic
- 5. Solution Methodologies Analytical results (formulas) Pros: Quick answers, insight Cons: Often inaccurate or inapplicable Explicit simulation Pros: Accurate and realistic models, broad applicability Cons: Can be slow Hybrid simulation Intermediate solution approach Combines advantages and disadvantages of analysis and simulation
- 6. Examples of Applications Analytical Modeling Discrete-Event Simulation Hybrid DES Decomposition with Explicit with Kleinrock DES only with and Independence Explicit Traffic Background Assumption Traffic M/G/./. & G/G/./. FIFO Analysis M/G/./. & G/G/./. Priority Analysis Best Effort Service for Standard Data Traffic Yes N/A N/A Yes Yes Best Effort Service for LRD/Self-Similar Behavior Traffic Yes N/A N/A Yes Yes "Chancing It" with Best Effort Service for Voice, Video and Data Yes N/A N/A Yes Yes Using QoS to differentiate service levels for the same type of traffic N/A Yes (loss of accuracy) N/A Yes Yes Using QoS to support different requirements for different application types given as a detailed study of setting Cisco Router queueing parameters N/A Highly approximate N/A Yes Yes N/A Hop-by-hop Analysis (loss of accuacy) Yes (some loss of Yes (Run time a accuracy - e.g., traffic function of network shaping) complexity) Yes [Fast with minimal loss of accuracy] N/A Hop-by-hop Analysis (loss of accuacy) Yes (Run time a function of network complexity) Yes [Fast with minimal loss of accuracy] Analysis Scenarios Single Link with FIFO Service Single Link with QoS-Based Queueing Network of Queues General network model extending the previous QoS queueing model Reduction of the general model to a representative end-to-end path N/A
- 7. Queuing System Concepts Queuing system Data network where packets arrive, wait in various queues, receive service at various points, and exit after some time Arrival rate Long-term number of arrivals per unit time Occupancy Number of packets in the system (averaged over a long time) Time in the system (delay) Time from packet entry to exit (averaged over many packets)
- 8. Stability and Steady-State A single queue system is stable if packet arrival rate < system transmission capacity For a single queue, the ratio packet arrival rate / system transmission capacity is called the utilization factor Describes the loading of a queue In an unstable system packets accumulate in various queues and/or get dropped For unstable systems with large buffers some packet delays become very large Flow/admission control may be used to limit the packet arrival rate Prioritization of flows keeps delays bounded for the important traffic Stable systems with time-stationary arrival traffic approach a steady-state
- 9. Little’s Law For a given arrival rate, the time in the system is proportional to packet occupancy N=T where N: average # of packets in the system : packet arrival rate (packets per unit time) T: average delay (time in the system) per packet Examples: On rainy days, streets and highways are more crowded Fast food restaurants need a smaller dining room than regular restaurants with the same customer arrival rate Large buffering together with large arrival rate cause large delays
- 10. ExplanationofLittle’sLaw Amusement park analogy: people arrive, spend time at various sites, and leave They pay $1 per unit time in the park The rate at which the park earns is $N per unit time (N: average # of people in the park) The rate at which people pay is $T per unit time (: traffic arrival rate, T: time per person) Over a long horizon: Rateofparkearnings=Rateofpeople’spayment or N = T
- 11. Delay is Caused by Packet Interference If arrivals are regular or sufficiently spaced apart, no queuing delay occurs Regular Traffic Irregular but Spaced Apart Traffic
- 12. Burstiness Causes Interference Note that the departures are less bursty
- 13. Burstiness Example Different Burstiness Levels at Same Packet Rate
- 14. Packet Length Variation Causes Interference Regular arrivals, irregular packet lengths
- 15. High Utilization Exacerbates Interference Time Queuing Delays As the work arrival rate: (packet arrival rate * packet length) increases, the opportunity for interference increases
- 16. Bottlenecks Types of bottlenecks At access points (flow control, prioritization, QoS enforcement needed) At points within the network core Isolated (can be analyzed in isolation) Interrelated (network or chain analysis needed) Bottlenecks result from overloads caused by: High load sessions, or Convergence of sufficient number of moderate load sessions at the same queue
- 17. Bottlenecks Cause Shaping The departure traffic from a bottleneck is more regular than the arrival traffic The inter-departure time between two packets is at least as large as the transmission time of the 2nd packet
- 18. Bottlenecks Cause Shaping Incoming traffic Outgoing traffic Exponential inter-arrivals gap Bottleneck 90% utilization
- 19. Incoming traffic Outgoing traffic Small Medium Bottleneck 90% utilization Large
- 20. Variable packet sizes Histogram of inter-departure times for small packets # of packets Variable packet sizes Peaks smeared Constant packet sizes sec
- 21. Queuing Models Widely used to estimate desired performance measures of the system Provide rough estimate of a performance measure Typical measures Server utilization Length of waiting lines Delays of customers Applications Determine the minimum number of servers needed at a service centre Detection of performance bottleneck or congestion Evaluate alternative system designs 21
- 22. Kendall Notation A/S/m/B/K/SD A: arrival process S: service time distribution m: number of servers B: number of buffers(system capacity) K: population size SD: service discipline 22
- 23. Service Time Distribution Time each user spends at the terminal IID Distribution model Exponential Erlang Hyper-exponential General cf. Jobs = customers Device = service centre = queue Buffer = waiting position 23
- 24. Number of Servers Number of servers available Single Server Queue Multiple Server Queue 24
- 25. Service Disciplines First-come-first-served(FCFS) Last-come-first-served(LCFS) Shortest processing time first(SPT) Shortest remaining processing time first(SRPT) Shortest expected processing time first(SEPT) Shortest expected remaining processing time first(SERPT) Biggest-in-first-served(BIFS) Loudest-voice-first-served(LVFS) 25
- 26. Example M/M/3/20/1500/FCFS Time between successive arrivals is exponentially distributed Service times are exponentially distributed Three servers 20 buffers = 3 service + 17 waiting After 20, all arriving jobs are lost Total of 1500 jobs that can be serviced Service discipline is first-come-first-served 26
- 27. Default Infinite buffer capacity Infinite population size FCFS service discipline Example G/G/1 G/G/1/ 27
- 28. Little’sLaw Waiting facility of a service center Mean number in the queue = arrival rate X mean waiting time Mean number in service = arrival rate X mean service time 28
- 29. Example A monitor on a disk server showed that the average time to satisfy an I/O request was 100msecs. The I/O rate was about 100 request per second. What was the mean number of request at the disk server? Solution: – Mean number in the disk server = arrival rate X response time = (100 request/sec) X (0.1 seconds) = 10 requests 29
- 30. Stochastic Processes Process : function of time Stochastic process process with random events that can be described by a probability distribution function A queuing system is characterized by three elements: A stochastic input process A stochastic service mechanism or process A queuing discipline 30
- 31. Types of Stochastic Process Discrete or continuous state process Markov processes Birth-death processes Poisson processes Markov process Birth-death process Poisson process 31
- 32. Discrete/Continuous State Processes Discrete = finite or countable Discrete state process Number of jobs in a system n(t) = 0,1,2,… Continuous state process Waiting time w(t) Stochastic chain : discrete state stochastic process 32
- 33. Markov Processes Future states are independent of the past Markov chain : discrete state Markov process Not necessary to know how log the process has been in the current state State time : memory less(exponential) distribution M/M/m queues can be modelled using Markov processes The time spent by a job in such a queue is a Markov process and the number of jobs in the queue is a Markov chain 33
- 34. M/M/1 Queue The most commonly used type of queue Used to model single processor systems or individual devices in a computer system Assumption Interarrival rate of exponentially distributed Service rate of exponentially distributed Single server FCFS Unlimited queue lengths allowed Infinite number of customers Need to know only the mean arrival rate() and the mean service rate State = number of jobs in the system* 34
- 35. M/M/1 Operating Characteristics Utilization(fraction of time server is busy) ρ = / Average waiting times W = 1/( - ) Wq = ρ/( - ) = ρ W Average number waiting L = /( - ) Lq = ρ /( - ) = ρ L 35
- 36. Flexibility/Utilization Trade-off Must trade off benefits of high utilization levels with benefits of flexibility and service High utilization Low ops costs Low flexibility Poor service L Lq W Wq Low utilization High ops costs High flexibility Good service = 0.0 Utilization = 1.0 36
- 37. M/M/1 Example On a network gateway, measurements show that the packets arrive at a mean rate of 125 packets per seconds(pps) and the gateway takes about two milliseconds to forward them. Using an M/M/1 model, analyze the gateway. What is the probability of buffer overflow if the gateway had only 13 buffers? How many buffers do we need to keep packet loss below one packet per million? 37
- 38. Arrival rate = 125pps Service rate = 1/.002 = 500 pps Gateway utilization ρ = / = 0.25 Probability of n packets in the gateway (1- ρ) ρ n = 0.75(0.25)n Mean number of packets in the gateway ρ/(1- ρ) = 0.25/0.75 = 0.33 Mean time spent in the gateway (1/ )/(1- ρ) = (1/500)/(1-0.25) = 2.66 milliseconds Probability of buffer overflow P(more than 13 packets in gateway) = ρ13 = 0.2313 =1.49 X 10-8 ≈ 15 packets per billion packets To limit the probability of loss to less than 10-6 ρ n < 10-6 n > log(10-6)/log(0.25) = 9.96 Need about 10 buffers 38
- 39. Effects of congestion Congestion occurs when number of packets transmitted approaches network capacity Objective of congestion control: keep number of packets below level at which performance drops off dramatically 39
- 40. Queuing Theory Data network is a network of queues If arrival rate > transmission rate then queue size grows without bound and packet delay goes to infinity 40
- 41. 41
- 42. At Saturation Point, 2 Strategies Discard any incoming packet if no buffer available Saturated node exercises flow control over neighbours May cause congestion to propagate throughout network 42
- 43. Figure 10.2 43
- 44. Ideal Performance i.e., infinite buffers, no overhead for packet transmission or congestion control Throughput increases with offered load until full capacity Packet delay increases with offered load approaching infinity at full capacity Power = throughput / delay Higher throughput results in higher delay 44
- 45. Figure 10.3 45
- 46. Practical Performance i.e., finite buffers, non-zero packet processing overhead With no congestion control, increased load eventually causes moderate congestion: throughput increases at slower rate than load Further increased load causes packet delays to increase and eventually throughput to drop to zero 46
- 47. Figure 10.4 47
- 48. Congestion Control Backpressure Request from destination to source to reduce rate Choke packet: ICMP Source Quench Implicit congestion signaling Source detects congestion from transmission delays and discarded packets and reduces flow 48
- 49. Explicit congestion signaling Direction Backward Forward Categories Binary Credit-based rate-based 49
- 50. Traffic Management Fairness Quality of Service Last-in-first-discarded may not be fair Voice, video: delay sensitive, loss insensitive File transfer, mail: delay insensitive, loss sensitive Interactive computing: delay and loss sensitive Reservations Policing: excess traffic discarded or handled on best-effort basis 50
- 51. Figure 10.5 51
- 52. Frame Relay Congestion Control Minimize frame size Maintain QoS Minimize monopolization of network Simple to implement, little overhead Minimal additional network traffic Resources distributed fairly Limit spread of congestion Operate effectively regardless of flow Have minimum impact other systems in network Minimize variance in QoS 52
- 53. 53
- 54. Traffic Rate Management Committed Information Rate (CIR) Aggregate of CIRs < capacity For node and user-network interface (access) Committed Burst Size Rate that network agrees to support Maximum data over one interval agreed to by network Excess Burst Size Maximum data over one interval that network will attempt 54
- 55. 55
- 56. Figure 10.7 56
- 57. Congestion Avoidance with Explicit Signaling 2 strategies Congestion always occurred slowly, almost always at egress nodes forward explicit congestion avoidance Congestion grew very quickly in internal nodes and required quick action backward explicit congestion avoidance 57
- 58. 2 Bits for Explicit Signaling Forward Explicit Congestion Notification For traffic in same direction as received frame This frame has encountered congestion Backward Explicit Congestion Notification For traffic in opposite direction of received frame Frames transmitted may encounter congestion 58
- 59. Questions ? 59

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