Traffic Behavior and Queuing in a Qo S

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

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 2

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

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 4

Traffic Behavior and Queuing in a Qo. S Environment Performance Measures • • • 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 Copyright © 2002 OPNET Technologies, Inc. 5

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 6

Traffic Behavior and Queuing in a Qo. S Environment Examples of Applications Copyright ©

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 8

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 9

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 10

Traffic Behavior and Queuing in a Qo. S 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 person) • Over a long horizon: Rate of park earnings = Rate of people’s payment or N = T Copyright © 2002 OPNET Technologies, Inc. 11

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 12

Traffic Behavior and Queuing in a Qo. S Environment Burstiness Causes Interference • Note

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 14

Traffic Behavior and Queuing in a Qo. S Environment Packet Length Variation Causes Interference

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

Traffic Behavior and Queuing in a Qo. S Environment Bottlenecks • Types of bottlenecks – – At access points (flow control, prioritization, Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 17

Traffic Behavior and Queuing in a Qo. S 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 2 nd packet Copyright © 2002 OPNET Technologies, Inc. 18

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

Traffic Behavior and Queuing in a Qo. S Environment Incoming traffic Outgoing traffic Small

Traffic Behavior and Queuing in a Qo. S Environment Packet Trains Inter-departure times for

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

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 23

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 24

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 25

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

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

Traffic Behavior and Queuing in a Qo. S Environment Source Type Properties Characteristics Qo. S Requirements Model Voice * Alternating talkspurts 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 * Poisson type * Sometimes batcharrivals, or bursty, or sometimes on-off Zero or near-sero packet loss Delay may be important Poisson, Poisson with batch arrivals, Two-state MMRP FTP telnet web Copyright © 2002 OPNET Technologies, Inc. 28

Traffic Behavior and Queuing in a Qo. S Environment Typical Voice Source Behavior Copyright

Traffic Behavior and Queuing in a Qo. S Environment MPEG 1 Video Source Model • The MPEG 1 MMRP model can be extremely bursty, and has “long range dependency” behavior due to the deterministic frame sequence Diagram Source: Mark W. Garrett and Walter Willinger, “Analysis, Modeling, and Generation of Self-Similar VBR Video Traffic, BELLCORE, 1994 Copyright © 2002 OPNET Technologies, Inc. 30

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 31

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 32

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 33

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 34

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 35

Traffic Behavior and Queuing in a Qo. S 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 …) Copyright © 2002 OPNET Technologies, Inc. 36

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 37

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

Traffic Behavior and Queuing in a Qo. S 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. Copyright © 2002 OPNET Technologies, Inc. 39

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 40

Traffic Behavior and Queuing in a Qo. S 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 wk be the weight of the kth queue – Think of round-robin with queue k transmitting wk bits upon its turn – If all queues have always something to send, the kth queue receives bandwidth equal to a fraction wk / Si wi of the total bandwidth • Fair queuing corresponds to wk = 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 Copyright © 2002 OPNET Technologies, Inc. 41

Traffic Behavior and Queuing in a Qo. S Environment Weighted Fair Queuing Illustration Weights:

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

Traffic Behavior and Queuing in a Qo. S Environment Demo: FIFO Bottleneck 90% utilization

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 45

Traffic Behavior and Queuing in a Qo. S Environment Demo: Priority Queuing (PQ) PQ

Traffic Behavior and Queuing in a Qo. S Environment Demo: PQ Queuing Delays PQ

Traffic Behavior and Queuing in a Qo. S Environment Demo: Weighted Fair Queuing (WFQ)

Traffic Behavior and Queuing in a Qo. S Environment Demo: WFQ Queuing Delays PQ

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 50

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 51

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 52

Traffic Behavior and Queuing in a Qo. S 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 Nq = Q where Nq = Average number waiting in queue • These quantities can be calculated with formulas derived by Markov chain analysis (see references) Copyright © 2002 OPNET Technologies, Inc. 53

Traffic Behavior and Queuing in a Qo. S Environment M/M/1 Results • 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/( - ) Copyright © 2002 OPNET Technologies, Inc. 54

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 55

Traffic Behavior and Queuing in a Qo. S 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 analytical formulas for the occupancy probabilities and average delay of these systems Copyright © 2002 OPNET Technologies, Inc. 56

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 57

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 58

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

Traffic Behavior and Queuing in a Qo. S 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 ~ (s 2 + 2)/2(1 - ) • Becomes increasingly accurate as Copyright © 2002 OPNET Technologies, Inc. 60

Traffic Behavior and Queuing in a Qo. S Environment Demo: M/G/1 Packet inter-arrival times exponential (0. 02) sec Packet size 1250 bytes (10000 bits) Capacity 1 Mbps Packet size distribution: exponential constant lognormal What is the average delay and queue size ? Copyright © 2002 OPNET Technologies, Inc. 61

Traffic Behavior and Queuing in a Qo. S Environment Demo: M/G/1 Analytical Results Packet Size Distribution Delay T (sec) Queue Size (packets) Exponential mean = 10000 variance = 1. 0 *108 0. 02 1. 0 Constant mean = 10000 variance = N/A 0. 015 0. 75 Lognormal mean = 10000 variance = 9. 0 *108 0. 06 3. 0 Copyright © 2002 OPNET Technologies, Inc. 62

Traffic Behavior and Queuing in a Qo. S Environment Demo: M/G/1 Simulation Results Average

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

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 65

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 66

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 67

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

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 69

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 70

Traffic Behavior and Queuing in a Qo. S Environment Two bottlenecks in series Exponential

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 72

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 73

Traffic Behavior and Queuing in a Qo. S 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) Copyright © 2002 OPNET Technologies, Inc. 74

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 75

Traffic Behavior and Queuing in a Qo. S 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 Copyright © 2002 OPNET Technologies, Inc. 76

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

Traffic Behavior and Queuing in a Qo. S 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 wk 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) Copyright © 2002 OPNET Technologies, Inc. 78

Traffic Behavior and Queuing in a Qo. S Environment Hybrid Simulation (FIFO Case) • Critical Question: Given arrival times ak and ak+1, workload wk, and background traffic descriptor, how do we find wk+1? Arrival times/Workload found a 1 w 1 a 2 w 2 a 3 . . . w 3 . . . Time 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 • Note: wk+1 consists of wk and two more terms: – Background arrivals in interval ak+1 - ak – (Minus) transmitted workload in interval ak+1 - ak • 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 ak+1 - ak Copyright © 2002 OPNET Technologies, Inc. 79

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

Traffic Behavior and Queuing in a Qo. S Environment Long Interval Case • Long interval ak+1 - ak (i. e. , ak+1 > dk) • Queue may be idle during portions of the interval ak+1 - ak • Need to generate/simulate – The new arrivals in ak+1 - ak – 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 Copyright © 2002 OPNET Technologies, Inc. 81

Traffic Behavior and Queuing in a Qo. S 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 wk+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 Copyright © 2002 OPNET Technologies, Inc. 82

Traffic Behavior and Queuing in a Qo. S 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 wk+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) Copyright © 2002 OPNET Technologies, Inc. 83

Traffic Behavior and Queuing in a Qo. S Environment Demo End-to-end Delay: Baseline Network

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

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

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

Traffic Behavior and Queuing in a Qo. S Environment Comparison: Hybrid vs Explicit Simulation

Traffic Behavior and Queuing in a Qo. S 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. pdf • Probability and Queuing Models – Bertsekas and Tsitsiklis, Introduction to Probability, Athena Scientific, 2002, 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 Copyright © 2002 OPNET Technologies, Inc. 90