Copyright © 2002 OPNET Technologies, Inc. 1 Traffic Behavior and Queuing in a QoS Environment Session 1813 Traffic Behavior and Queuing in a QoS Environment.

Presentación del tema: "Copyright © 2002 OPNET Technologies, Inc. 1 Traffic Behavior and Queuing in a QoS Environment Session 1813 Traffic Behavior and Queuing in a QoS Environment."— Transcripción de la presentación:

1 Copyright © 2002 OPNET Technologies, Inc. 1 Traffic Behavior and Queuing in a QoS Environment Session 1813 Traffic Behavior and Queuing in a QoS Environment Networking Tutorials Prof. Dimitri P. Bertsekas Department of Electrical Engineering M.I.T.

2 Copyright © 2002 OPNET Technologies, Inc. 2 Traffic Behavior and Queuing in a QoS Environment Objectives Provide some basic understanding of queuing phenomena Explain the available solution approaches and associated trade-offs Give guidelines on how to match applications and solutions

3 Copyright © 2002 OPNET Technologies, Inc. 3 Traffic Behavior and Queuing in a QoS Environment Outline Basic concepts Source models Service models (demo) Single-queue systems Priority/shared service systems Networks of queues Hybrid simulation (demo)

4 Copyright © 2002 OPNET Technologies, Inc. 4 Traffic Behavior and Queuing in a QoS Environment Outline Basic concepts –Performance measures –Solution methodologies –Queuing system concepts –Stability and steady-state –Causes of delay and bottlenecks Source models Service models (demo) Single-queue systems Priority/shared service systems Networks of queues Hybrid simulation (demo)

5 Copyright © 2002 OPNET Technologies, Inc. 5 Traffic Behavior and Queuing in a QoS Environment 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

6 Copyright © 2002 OPNET Technologies, Inc. 6 Traffic Behavior and Queuing in a QoS Environment 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

7 Copyright © 2002 OPNET Technologies, Inc. 7 Traffic Behavior and Queuing in a QoS Environment Examples of Applications

8 Copyright © 2002 OPNET Technologies, Inc. 8 Traffic Behavior and Queuing in a QoS Environment Queuing System Concepts: Arrival Rate, Occupancy, Time in the System 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)

9 Copyright © 2002 OPNET Technologies, Inc. 9 Traffic Behavior and Queuing in a QoS Environment 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

10 Copyright © 2002 OPNET Technologies, Inc. 10 Traffic Behavior and Queuing in a QoS Environment 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

11 Copyright © 2002 OPNET Technologies, Inc. 11 Traffic Behavior and Queuing in a QoS Environment Explanation of Little’s Law 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: Rate of park earnings = Rate of people’s payment or N =  T

12 Copyright © 2002 OPNET Technologies, Inc. 12 Traffic Behavior and Queuing in a QoS Environment 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

13 Copyright © 2002 OPNET Technologies, Inc. 13 Traffic Behavior and Queuing in a QoS Environment Burstiness Causes Interference Note that the departures are less bursty

14 Copyright © 2002 OPNET Technologies, Inc. 14 Traffic Behavior and Queuing in a QoS Environment Burstiness Example Different Burstiness Levels at Same Packet Rate Source: Fei Xue and S. J. Ben Yoo, UCDavis, “On the Generation and Shaping Self-similar Traffic in Optical Packet-switched Networks”, OPNETWORK 2002

15 Copyright © 2002 OPNET Technologies, Inc. 15 Traffic Behavior and Queuing in a QoS Environment Packet Length Variation Causes Interference Regular arrivals, irregular packet lengths

16 Copyright © 2002 OPNET Technologies, Inc. 16 Traffic Behavior and Queuing in a QoS Environment High Utilization Exacerbates Interference As the work arrival rate: (packet arrival rate * packet length) increases, the opportunity for interference increases

17 Copyright © 2002 OPNET Technologies, Inc. 17 Traffic Behavior and Queuing in a QoS Environment 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

18 Copyright © 2002 OPNET Technologies, Inc. 18 Traffic Behavior and Queuing in a QoS Environment 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

19 Copyright © 2002 OPNET Technologies, Inc. 19 Traffic Behavior and Queuing in a QoS Environment Bottlenecks Cause Shaping Bottleneck 90% utilization Outgoing traffic Incoming traffic Exponential inter-arrivals gap

20 Copyright © 2002 OPNET Technologies, Inc. 20 Traffic Behavior and Queuing in a QoS Environment Bottleneck 90% utilization Outgoing traffic Incoming traffic Large Medium Small

21 Copyright © 2002 OPNET Technologies, Inc. 21 Traffic Behavior and Queuing in a QoS Environment Packet Trains Inter-departure times for small packets

22 Copyright © 2002 OPNET Technologies, Inc. 22 Traffic Behavior and Queuing in a QoS Environment Variable packet sizes Histogram of inter-departure times for small packets sec # of packets Peaks smeared Variable packet sizes Constant packet sizes

23 Copyright © 2002 OPNET Technologies, Inc. 23 Traffic Behavior and Queuing in a QoS Environment Outline Basic concepts Source models –Poisson traffic –Batch arrivals –Example applications – voice, video, file transfer Service models (demo) Single-queue systems Priority/shared service systems Networks of queues Hybrid simulation (demo)

24 Copyright © 2002 OPNET Technologies, Inc. 24 Traffic Behavior and Queuing in a QoS Environment Poisson Process with Rate Interarrival times are independent and exponentially distributed Models well the accumulated traffic of many independent sources The average interarrival time is 1/  (secs/packet), so is the arrival rate (packets/sec)

25 Copyright © 2002 OPNET Technologies, Inc. 25 Traffic Behavior and Queuing in a QoS Environment Batch Arrivals Some sources transmit in packet bursts May be better modeled by a batch arrival process (e.g., bursts of packets arriving according to a Poisson process) The case for a batch model is weaker at queues after the first, because of shaping

26 Copyright © 2002 OPNET Technologies, Inc. 26 Traffic Behavior and Queuing in a QoS Environment Markov Modulated Rate Process (MMRP) Extension: Models with more than two states Stay in each state an exponentially distributed time, Transmit according to different model (e.g., Poisson, deterministic, etc) at each state State 0State 1 OFFON

27 Copyright © 2002 OPNET Technologies, Inc. 27 Traffic Behavior and Queuing in a QoS Environment Source Types Voice sources Video sources File transfers Web traffic Interactive traffic Different application types have different QoS requirements, e.g., delay, jitter, loss, throughput, etc.

28 Copyright © 2002 OPNET Technologies, Inc. 28 Traffic Behavior and Queuing in a QoS Environment Source Type Properties CharacteristicsQoS Requirements Model Voice * Alternating talk- spurts and silence intervals. * Talk-spurts produce constant packet-rate traffic Delay < ~150 ms Jitter < ~30 ms Packet loss < ~1% * Two-state (on-off) Markov Modulated Rate Process (MMRP) * Exponentially distributed time at each state Video * Highly bursty traffic (when encoded) * Long range dependencies Delay < ~ 400 ms Jitter < ~ 30 ms Packet loss < ~1% K-state (on-off) Markov Modulated Rate Process (MMRP) Interactive FTP telnet web * Poisson type * Sometimes batch- arrivals, or bursty, or sometimes on-off Zero or near-sero packet loss Delay may be important Poisson, Poisson with batch arrivals, Two-state MMRP

29 Copyright © 2002 OPNET Technologies, Inc. 29 Traffic Behavior and Queuing in a QoS Environment Typical Voice Source Behavior

30 Copyright © 2002 OPNET Technologies, Inc. 30 Traffic Behavior and Queuing in a QoS Environment MPEG1 Video Source Model Diagram Source: Mark W. Garrett and Walter Willinger, “Analysis, Modeling, and Generation of Self-Similar VBR Video Traffic, BELLCORE, 1994 The MPEG1 MMRP model can be extremely bursty, and has “long range dependency” behavior due to the deterministic frame sequence

31 Copyright © 2002 OPNET Technologies, Inc. 31 Traffic Behavior and Queuing in a QoS Environment Outline Basic concepts Source models Service models –Single vs. multiple-servers –FIFO, priority, and shared servers –Demo Single-queue systems Priority/shared service systems Networks of queues Hybrid simulation (demo)

32 Copyright © 2002 OPNET Technologies, Inc. 32 Traffic Behavior and Queuing in a QoS Environment Device Queuing Mechanisms Common queue examples for IP routers –FIFO: First In First Out –PQ: Priority Queuing –WFQ: Weighted Fair Queuing –Combinations of the above Service types from a queuing theory standpoint –Single server (one queue - one transmission line) –Multiple server (one queue - several transmission lines) –Priority server (several queues with hard priorities - one transmission line) –Shared server (several queues with soft priorities - one transmission line)

33 Copyright © 2002 OPNET Technologies, Inc. 33 Traffic Behavior and Queuing in a QoS Environment Single Server FIFO Single transmission line serving packets on a FIFO (First-In- First-Out) basis Each packet must wait for all packets found in the system to complete transmission, before starting transmission –Departure Time = Arrival Time + Workload Found in the System + Transmission time Packets arriving to a full buffer are dropped

34 Copyright © 2002 OPNET Technologies, Inc. 34 Traffic Behavior and Queuing in a QoS Environment FIFO Queue Packets are placed on outbound link to egress device in FIFO order –Device (router, switch) multiplexes different flows arriving on various ingress ports onto an output buffer forming a FIFO queue

35 Copyright © 2002 OPNET Technologies, Inc. 35 Traffic Behavior and Queuing in a QoS Environment Multiple Servers Multiple packets are transmitted simultaneously on multiple lines/servers Head of the line service: packets wait in a FIFO queue, and when a server becomes free, the first packet goes into service

36 Copyright © 2002 OPNET Technologies, Inc. 36 Traffic Behavior and Queuing in a QoS Environment Priority Servers Packets form priority classes (each may have several flows) There is a separate FIFO queue for each priority class Packets of lower priority start transmission only if no higher priority packet is waiting Priority types: –Non-preemptive (high priority packet must wait for a lower priority packet found under transmission upon arrival) –Preemptive (high priority packet does not have to wait …)

37 Copyright © 2002 OPNET Technologies, Inc. 37 Traffic Behavior and Queuing in a QoS Environment Priority Queuing Packets are classified into separate queues –E.g., based on source/destination IP address, source/destination TCP port, etc. All packets in a higher priority queue are served before a lower priority queue is served –Typically in routers, if a higher priority packet arrives while a lower priority packet is being transmitted, it waits until the lower priority packet completes

38 Copyright © 2002 OPNET Technologies, Inc. 38 Traffic Behavior and Queuing in a QoS Environment Shared Servers Again we have multiple classes/queues, but they are served with a “soft” priority scheme Round-robin Weighted fair queuing

39 Copyright © 2002 OPNET Technologies, Inc. 39 Traffic Behavior and Queuing in a QoS Environment Round-Robin/Cyclic Service Round-robin serves each queue in sequence –A queue that is empty is skipped –Each queue when served may have limited service (at most k packets transmitted with k = 1 or k > 1) Round-robin is fair for all queues (as long as some queues do not have longer packets than others) Round-robin cannot be used to enforce bandwidth allocation among the queues.

40 Copyright © 2002 OPNET Technologies, Inc. 40 Traffic Behavior and Queuing in a QoS Environment Fair Queuing This scheduling method is inspired by the “most fair” of methods: –Transmit one bit from each queue in cyclic order (bit-by-bit round robin) –Skip queues that are empty To approximate the bit-by-bit processing behavior, for each packet –We calculate upon arrival its “finish time under bit-by-bit round robin” assuming all other queues are continuously busy, and we transmit by FIFO within each queue –Transmit next the packet with the minimum finish time Important properties: –Priority is given to short packets –Equal bandwidth is allocated to all queues that are continuously busy

41 Copyright © 2002 OPNET Technologies, Inc. 41 Traffic Behavior and Queuing in a QoS Environment Weighted Fair Queuing Fair queuing cannot be used to implement bandwidth allocation and soft priorities Weighted fair queuing is a variation that corrects this deficiency –Let w k be the weight of the k th queue –Think of round-robin with queue k transmitting w k bits upon its turn –If all queues have always something to send, the k th queue receives bandwidth equal to a fraction w k /  i w i of the total bandwidth Fair queuing corresponds to w k = 1 Priority queuing corresponds to the weights being very high as we move to higher priorities Again, to deal with the segmentation problem, we approximate as follows: For each packet: –We calculate its “finish time” (under the weighted bit-by-bit round robin scheme) –We next transmit the packet with the minimum finish time

42 Copyright © 2002 OPNET Technologies, Inc. 42 Traffic Behavior and Queuing in a QoS Environment Weighted Fair Queuing Illustration Weights: Queue 1 = 3 Queue 2 = 1 Queue 3 = 1

43 Copyright © 2002 OPNET Technologies, Inc. 43 Traffic Behavior and Queuing in a QoS Environment Combination of Several Queuing Schemes Example – voice (PQ), guaranteed b/w (WFQ), Best Effort (Cisco’s LLQ implementation)

44 Copyright © 2002 OPNET Technologies, Inc. 44 Traffic Behavior and Queuing in a QoS Environment Demo: FIFO FIFO Bottleneck 90% utilization

45 Copyright © 2002 OPNET Technologies, Inc. 45 Traffic Behavior and Queuing in a QoS Environment Demo: FIFO Queuing Delay Applications have different requirements Video »delay, jitter FTP »packet loss Control beyond “best effort” needed Priority Queuing (PQ) Weighted Fair Queuing (WFQ)

46 Copyright © 2002 OPNET Technologies, Inc. 46 Traffic Behavior and Queuing in a QoS Environment Demo: Priority Queuing (PQ) PQ Bottleneck 90% utilization

47 Copyright © 2002 OPNET Technologies, Inc. 47 Traffic Behavior and Queuing in a QoS Environment Demo: PQ Queuing Delays FIFO PQ Video PQ FTP

48 Copyright © 2002 OPNET Technologies, Inc. 48 Traffic Behavior and Queuing in a QoS Environment Demo: Weighted Fair Queuing (WFQ) WFQ Bottleneck 90% utilization

49 Copyright © 2002 OPNET Technologies, Inc. 49 Traffic Behavior and Queuing in a QoS Environment Demo: WFQ Queuing Delays FIFO WFQ/PQ Video PQ FTP WFQ FTP

50 Copyright © 2002 OPNET Technologies, Inc. 50 Traffic Behavior and Queuing in a QoS Environment Queuing: Take Away Points Choice of queuing mechanism can have a profound effect on performance To achieve desired service differentiation, appropriate queuing mechanisms can be used Complex queuing mechanisms may require simulation techniques to analyze behavior Improper configuration (e.g., queuing mechanism selection or weights) may impact performance of low priority traffic

51 Copyright © 2002 OPNET Technologies, Inc. 51 Traffic Behavior and Queuing in a QoS Environment Outline Basic concepts Source models Service models (demo) Single-queue systems –M/M/1……M/M/m/k –M/G/1……G/G/1 –Demo: Analytics vs. simulation Priority/shared service systems Networks of queues Hybrid simulation (demo)

52 Copyright © 2002 OPNET Technologies, Inc. 52 Traffic Behavior and Queuing in a QoS Environment M/M/1 System Nomenclature: M stands for “Memoryless” (a property of the exponential distribution) –M/M/1 stands for Poisson arrival process (which is memoryless) –M/M/1 stands for exponentially distributed transmission times Assumptions: –Arrival process is Poisson with rate  packets/sec –Packet transmission times are exponentially distributed with mean 1/  –One server –Independent interarrival times and packet transmission times Transmission time is proportional to packet length Note 1/  is secs/packet so  is packets/sec (packet transmission rate of the queue) Utilization factor:  = /  stable system if  1)

53 Copyright © 2002 OPNET Technologies, Inc. 53 Traffic Behavior and Queuing in a QoS Environment Delay Calculation Let Q = Average time spent waiting in queue T = Average packet delay (transmission plus queuing) Note that T = 1/  + Q Also by Little’s law N =  T and N q =  Q where N q = Average number waiting in queue These quantities can be calculated with formulas derived by Markov chain analysis (see references)

54 Copyright © 2002 OPNET Technologies, Inc. 54 Traffic Behavior and Queuing in a QoS Environment The analysis gives the steady-state probabilities of number of packets in queue or transmission P{n packets} =  n (1-  ) where  = /  From this we can get the averages: N =  /(1 -  ) T = N/ =  / (1 -  ) = 1/(  - ) M/M/1 Results

55 Copyright © 2002 OPNET Technologies, Inc. 55 Traffic Behavior and Queuing in a QoS Environment Example: How Delay Scales with Bandwidth Occupancy and delay formulas N =  /(1 -  )T = 1/(  - )  = /  Assume: –Traffic arrival rate is doubled –System transmission capacity  is doubled Then: –Queue sizes stay at the same level (  stays the same) –Packet delay is cut in half (  and  are doubled  A conclusion: In high speed networks –propagation delay increases in importance relative to delay –buffer size and packet loss may still be a problem

56 Copyright © 2002 OPNET Technologies, Inc. 56 Traffic Behavior and Queuing in a QoS Environment M/M/m, M/M/  System Same as M/M/1, but it has m (or  ) servers In M/M/m, the packet at the head of the queue moves to service when a server becomes free Qualitative result –Delay increases to  as  = /m  approaches 1 There are analytical formulas for the occupancy probabilities and average delay of these systems

57 Copyright © 2002 OPNET Technologies, Inc. 57 Traffic Behavior and Queuing in a QoS Environment Finite Buffer Systems: M/M/m/k The M/M/m/k system –Same as M/M/m, but there is buffer space for at most k packets. Packets arriving at a full buffer are dropped Formulas for average delay, steady-state occupancy probabilities, and loss probability The M/M/m/m system is used widely to size telephone or circuit switching systems

58 Copyright © 2002 OPNET Technologies, Inc. 58 Traffic Behavior and Queuing in a QoS Environment Characteristics of M/M/. Systems Advantage: Simple analytical formulas Disadvantages: –The Poisson assumption may be violated –The exponential transmission time distribution is an approximation at best –Interarrival and packet transmission times may be dependent (particularly in the network core) –Head-of-the-line assumption precludes heterogeneous input traffic with priorities (hard or soft)

59 Copyright © 2002 OPNET Technologies, Inc. 59 Traffic Behavior and Queuing in a QoS Environment M/G/1 System Same as M/M/1 but the packet transmission time distribution is general, with given mean 1/  and variance  2 Utilization factor  = /  Pollaczek-Kinchine formula for Average time in queue = (  2 + 1/  2 )/2(1-  ) Average delay = 1/  + (  2 + 1/  2 )/2(1-  ) The formulas for the steady-state occupancy probabilities are more complicated Insight: As  2 increases, delay increases

60 Copyright © 2002 OPNET Technologies, Inc. 60 Traffic Behavior and Queuing in a QoS Environment G/G/1 System Same as M/G/1 but now the packet interarrival time distribution is also general, with mean and variance  2 We still assume FIFO and independent interarrival times and packet transmission times Heavy traffic approximation: Average time in queue ~ (  2 +  2 )/2(1-  ) Becomes increasingly accurate as 

61 Copyright © 2002 OPNET Technologies, Inc. 61 Traffic Behavior and Queuing in a QoS Environment Demo: M/G/1 Packet inter-arrival times exponential (0.02) sec Capacity 1 Mbps Packet size 1250 bytes (10000 bits) Packet size distribution: exponential constant lognormal What is the average delay and queue size ?

62 Copyright © 2002 OPNET Technologies, Inc. 62 Traffic Behavior and Queuing in a QoS Environment Demo: M/G/1 Analytical Results Packet Size Distribution Delay T (sec)Queue Size (packets) Exponential mean = 10000 variance = 1.0 *10 8 0.021.0 Constant mean = 10000 variance = N/A 0.0150.75 Lognormal mean = 10000 variance = 9.0 *10 8 0.063.0

63 Copyright © 2002 OPNET Technologies, Inc. 63 Traffic Behavior and Queuing in a QoS Environment Demo: M/G/1 Simulation Results Average Delay (sec)Average Queue Size (packets)

64 Copyright © 2002 OPNET Technologies, Inc. 64 Traffic Behavior and Queuing in a QoS Environment Demo: M/G/1 Limitations Application traffic mix not memoryless Video » constant packet inter-arrivals Http »bursty traffic Delay P-K formula Simulation

65 Copyright © 2002 OPNET Technologies, Inc. 65 Traffic Behavior and Queuing in a QoS Environment Outline Basic concepts Source models Service models (demo) Single-queue systems Priority/shared service systems –Preemptive vs. non-preemptive –Cyclic, WFQ, PQ systems –Demo: Simulation results Networks of queues Hybrid simulation (demo)

66 Copyright © 2002 OPNET Technologies, Inc. 66 Traffic Behavior and Queuing in a QoS Environment Non-preemptive Priority Systems We distinguish between different classes of traffic (flows) Non-preemptive priority: packet under transmission is not preempted by a packet of higher priority P-K formula for delay generalizes

67 Copyright © 2002 OPNET Technologies, Inc. 67 Traffic Behavior and Queuing in a QoS Environment Cyclic Service Systems Multiple flows, each with its own queue Fair system: Each flow gets access to the transmission line in turn Several possible assumptions about how many packets each flow can transmit when it gets access Formulas for delay under M/G/1 type assumptions are available

68 Copyright © 2002 OPNET Technologies, Inc. 68 Traffic Behavior and Queuing in a QoS Environment Weighted Fair Queuing A combination of priority and cyclic service No exact analytical formulas are available

69 Copyright © 2002 OPNET Technologies, Inc. 69 Traffic Behavior and Queuing in a QoS Environment Outline Basic concepts Source models Service models (demo) Single-queue systems Priority/shared service systems Networks of queues –Violation of M/M/. assumptions –Effects on delays and traffic shaping –Analytical approximations Hybrid simulation (demo)

70 Copyright © 2002 OPNET Technologies, Inc. 70 Traffic Behavior and Queuing in a QoS Environment Two Queues in Series First queue shapes the traffic into second queue Arrival times and packet lengths are correlated M/M/1 and M/G/1 formulas yield significant error for second queue

71 Copyright © 2002 OPNET Technologies, Inc. 71 Traffic Behavior and Queuing in a QoS Environment Two bottlenecks in series Bottleneck Exponential inter-arrivals Bottleneck No queuing delay Delay

72 Copyright © 2002 OPNET Technologies, Inc. 72 Traffic Behavior and Queuing in a QoS Environment Approximations Kleinrock independence approximation –Perform a delay calculation in each queue independently of other queues –Add the results (including propagation delay) Note: In the preceding example, the Kleinrock independence approximation overestimates the queuing delay by 100% Tends to be more accurate in networks with “lots of traffic mixing”, e.g., nodes serving many relatively small flows from several different locations

73 Copyright © 2002 OPNET Technologies, Inc. 73 Traffic Behavior and Queuing in a QoS Environment Outline Basic concepts Source models Service models (demo) Single-queue systems Priority/shared service systems Networks of queues Hybrid simulation –Explicit vs. aggregated traffic –Conceptual Framework –Demo: PQ and WFQ with aggregated traffic

74 Copyright © 2002 OPNET Technologies, Inc. 74 Traffic Behavior and Queuing in a QoS Environment Basic Concepts of Hybrid Simulation Aims to combine the best of analytical results and simulation Achieve significant gain in simulation speed with little loss of accuracy Divides the traffic through a node into explicit and background –Explicit traffic is simulated accurately –Background traffic is aggregated The interaction of explicit and background is modeled either analytically or through a “fast” simulation (or a combination)

75 Copyright © 2002 OPNET Technologies, Inc. 75 Traffic Behavior and Queuing in a QoS Environment Explicit Traffic Modeled in detail, including the effects of various protocols Each packet’s arrival and departure times are recorded (together with other data of interest, e.g., loss, etc.) along each link that it traverses Departure times at a link are the arrival times at the next link (plus propagation delay) Objective: At each link, given the arrival times (and the packet lengths), determine the departure times

76 Copyright © 2002 OPNET Technologies, Inc. 76 Traffic Behavior and Queuing in a QoS Environment Aggregated Traffic Simplified modeling –We don’t keep track of individual packets, only workload counts (number of packets or bytes) –We “generate” workload counts »by probabilistic/analytical modeling, or »by simplified simulation Aggregated (or background) traffic is local (per link) Shaping effects are complex to incorporate Some dependences between explicit and background traffic along a chain of links are complicated and are ignored

77 Copyright © 2002 OPNET Technologies, Inc. 77 Traffic Behavior and Queuing in a QoS Environment Hybrid Simulation (FIFO Links): Conceptual Framework Given the arrival time a k of the k th explicit packet Generate the workload w k found in queue by the k th packet From a k and w k generate the departure time of the k th packet as Departure Time d k = a k + w k + s k where s k is the transmission time of the k th packet Time a K a K+1 w K w d K = a K + w K + s K Explicit Background ARRIVAL TIMES DEPARTURE TIMES

78 Copyright © 2002 OPNET Technologies, Inc. 78 Traffic Behavior and Queuing in a QoS Environment Simulating the Background Traffic Effects Use a traffic descriptor for the background traffic (e.g., carried by special packets) Traffic descriptor includes: –Traffic volume information (e.g., packets/sec, bits/sec) –Probability distribution of interarrival times –Probability distribution of packet lengths –Time interval of validity of the descriptor Generate w k using one of several ideas and combinations thereof –Successive sampling (for FIFO case) –Steady-state queue length distribution (if we can get it) –Simplified simulation (microsim - applies to complex queuing disciplines)

79 Copyright © 2002 OPNET Technologies, Inc. 79 Traffic Behavior and Queuing in a QoS Environment Hybrid Simulation (FIFO Case) Critical Question: Given arrival times a k and a k+1, workload w k, and background traffic descriptor, how do we find w k+1 ? Note: w k+1 consists of w k and two more terms: –Background arrivals in interval a k+1 - a k –(Minus) transmitted workload in interval a k+1 - a k Must calculate/simulate the two terms The first term is simulated based on the traffic descriptor of the background traffic The second term is easily calculated if the queue is continuously busy in a k+1 - a k Time a 1 a 2 a 3... Arrival times/Workload found w 1 w 2 w 3 d 1 = a 1 + w 1 + s 1 d 2 = a 2 + w 2 + s 2 d 3 = a 3 + w 3 + s 3 Departure times

80 Copyright © 2002 OPNET Technologies, Inc. 80 Traffic Behavior and Queuing in a QoS Environment Short Interval Case (Easy Case) Short interval a k+1 - a k (i.e., a k+1 < d k ) Queue is busy continuously in a k+1 - a k So w k+1 is quickly simulated – Sample the background traffic arrival distribution to simulate the new workload arrivals in a k+1 - a k –Do the accounting (add to w k and subtract the transmitted workload in a k+1 - a k ) k d a k Time... Short Interval w k w k+1 = w k + (New bkg arrivals) - (Old bkg transmissions) d a k+1 w

81 Copyright © 2002 OPNET Technologies, Inc. 81 Traffic Behavior and Queuing in a QoS Environment Long Interval Case Long interval a k+1 - a k (i.e., a k+1 > d k ) Queue may be idle during portions of the interval a k+1 - a k Need to generate/simulate –The new arrivals in a k+1 - a k –The lengths of the busy periods and the idle periods Can be done by sampling the background arrival distribution in each busy period Other alternatives are possible

82 Copyright © 2002 OPNET Technologies, Inc. 82 Traffic Behavior and Queuing in a QoS Environment Steady-State Queue Length Distribution If the interval between two successive explicit packets is very long, we can assume that the queue found by the second packet is in steady state So, we can obtain w k+1 by sampling the steady-state distribution Applies to cases where the steady-state distribution can be found or can be reasonably approximated –M/M/1 and other M/M/. Queues –Some M/G/. systems

83 Copyright © 2002 OPNET Technologies, Inc. 83 Traffic Behavior and Queuing in a QoS Environment Micro Simulation: Conceptual Framework Handles complex queuing systems –Micro-packets are generated to represent traffic load within the context of the queue only (i.e., they are not transmitted to any external links) –For long intervals, where convergence to a steady-state is likely »Try to detect convergence during the microsim »Estimate steady-state queue length distribution »Sample the steady state distribution to estimate w k+1 Microsim speeds up the simulation without sacrificing accuracy Microsim provides a general framework –Applies to non-stationary background traffic –Applies to non-FIFO service models (with proper modification)

84 Copyright © 2002 OPNET Technologies, Inc. 84 Traffic Behavior and Queuing in a QoS Environment Examples of Applications

85 Copyright © 2002 OPNET Technologies, Inc. 85 Traffic Behavior and Queuing in a QoS Environment Demo End-to-end Delay: Baseline Network Traffic modeled as 1) Explicit traffic 2) Background traffic

86 Copyright © 2002 OPNET Technologies, Inc. 86 Traffic Behavior and Queuing in a QoS Environment Target Flow: ETE delay as a function of ToS Target flow: Seattle  Houston - modeled using explicit traffic –Varying its Type of Service (ToS) »Best Effort (0) »Streaming Multimedia (4)

87 Copyright © 2002 OPNET Technologies, Inc. 87 Traffic Behavior and Queuing in a QoS Environment Explicit Simulation Results for Target Flow –Total traffic volume »500 Mbps –Time modeled » 35 minutes –Simulation duration »31 hours

88 Copyright © 2002 OPNET Technologies, Inc. 88 Traffic Behavior and Queuing in a QoS Environment Hybrid Simulation Results for Target Flow –Total traffic volume »500 Mbps –Time modeled » 35 minutes –Simulation duration »14 minutes

89 Copyright © 2002 OPNET Technologies, Inc. 89 Traffic Behavior and Queuing in a QoS Environment Comparison: Hybrid vs Explicit Simulation

90 Copyright © 2002 OPNET Technologies, Inc. 90 Traffic Behavior and Queuing in a QoS Environment References Networking –Bertsekas and Gallager, Data Networks, Prentice-Hall, 1992 Device Queuing Implementations –Vegesna, IP Quality of Service, Ciscopress.com, 2001 –http://www.juniper.net/techcenter/techpapers/200020.pdfhttp://www.juniper.net/techcenter/techpapers/200020.pdf Probability and Queuing Models –Bertsekas and Tsitsiklis, Introduction to Probability, Athena Scientific, 2002, http://www.athenasc.com/probbook.html http://www.athenasc.com/probbook.html –Cohen, The Single Server Queue, North-Holland, 1992 –Takagi, Queuing Analysis: A Foundation of Performance Evaluation. (3 Volumes), North-Holland, 1991 –Gross and Harris, Fundamentals of Queuing Theory, Wiley, 1985 –Cooper, Introduction to Queuing Theory, CEEPress, 1981 OPNET Hybrid Simulation and Micro Simulation –See Case Studies papers in http://secure.opnet.com/services/muc/mtdlogis_cse_stdies_81.html http://secure.opnet.com/services/muc/mtdlogis_cse_stdies_81.html