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Copyright © 2002 OPNET Technologies, Inc. 1
Traffic Behavior and Queuing in a QoS Environment
Session 1813Traffic Behavior and Queuing in a QoS EnvironmentNetworking Tutorials
Prof. Dimitri P. BertsekasDepartment of Electrical EngineeringM.I.T.
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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
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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)
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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)
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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
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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
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Traffic Behavior and Queuing in a QoS Environment
Examples of Applications Analytical Modeling Discrete-Event Simulation
M/G/./. & G/G/./. FIFO
Analysis
M/G/./. & G/G/./. Priority
Analysis
Decomposition with Kleinrock Independence Assumption
DES only with Explicit Traffic
Hybrid DES with Explicit
and Background
Traffic Single Link with FIFO Service
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
Single Link with QoS-Based QueueingUsing QoS to differentiate service levels for the same type of traffic
N/AYes (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/AHighly
approximateN/A Yes Yes
Network of Queues
General network model extending the previous QoS queueing model
N/AHop-by-hop
Analysis (loss of accuacy)
Yes (some loss of accuracy - e.g., traffic
shaping)
Yes (Run time a function of network
complexity)
Yes [Fast with minimal loss of
accuracy]
Reduction of the general model to a representative end-to-end path
N/AHop-by-hop
Analysis (loss of accuacy)
N/AYes (Run time a
function of network complexity)
Yes [Fast with minimal loss of
accuracy]
Analysis Scenarios
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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)
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Stability and Steady-State• A single queue system is stable if
packet arrival rate < system transmission capacity
• For a single queue, the ratiopacket 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
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Little’s Law• For a given arrival rate, the time in the system is proportional
to packet occupancyN = Twhere 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
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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 paymentor N = T
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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
TimeArrival TimesDeparture Times13421342
TimeArrival TimesDeparture Times13421342
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Burstiness Causes Interference• Note that the departures are less bursty
TimeQueuing DelaysBursty Traffic12341234
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Burstiness ExampleDifferent 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
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Packet Length Variation Causes Interference
Regular arrivals, irregular packet lengths
TimeQueuing Delays
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High Utilization Exacerbates Interference
As the work arrival rate: (packet arrival rate * packet length)
increases, the opportunity for interference increases
TimeQueuing Delays
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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
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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
Time
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Bottlenecks Cause Shaping
Bottleneck 90% utilization
Outgoing trafficIncoming traffic
Exponentialinter-arrivals
gap
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Bottleneck 90% utilization
Outgoing trafficIncoming traffic
Large
Medium
Small
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Packet Trains
Inter-departure times for small packets
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Variable packet sizesHistogram of inter-departure times for small packets
sec
# of packets
Peaks smeared
Variable packet sizes
Constant packet sizes
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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)
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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)
TimeInterarrival Times
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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
TimeInterarrival Times
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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 0 State 1
OFF ON
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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.
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Source Type Properties
Characteristics QoS Requirements
Model
Voice * Alternating talk- spurts and silence intervals. * Talk-spurts produce constant packet-rate traffic
Delay < ~150 msJitter < ~30 msPacket 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 msJitter < ~ 30 msPacket loss < ~1%
K-state (on-off) Markov Modulated Rate Process (MMRP)
InteractiveFTPtelnetweb
* 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
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Typical Voice Source Behavior
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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
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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)
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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)
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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
ArrivalsTransmissionLine
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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
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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
ArrivalsTransmissionLines
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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 …)Class 1 Arrivals
High PriorityTransmission
LineClass 3 Arrivals
Low PriorityClass 2 ArrivalsInterm. Priority
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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
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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
Class 1 ArrivalsWeight 10
TransmissionLine
Class 3 ArrivalsWeight 1
Class 2 ArrivalsWeight 3
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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.
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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
Finish Time of Packet ii-1Arrival timesDeparture timesiii-1Finish Time of Packet ii-1Arrival timesDeparture timesiii-1
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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 / i 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
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Weighted Fair Queuing IllustrationWeights:Queue 1 = 3Queue 2 = 1Queue 3 = 1
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Combination of Several Queuing Schemes• Example – voice (PQ), guaranteed b/w (WFQ), Best Effort (Cisco’s LLQ implementation)
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Demo: FIFO
FIFOBottleneck 90% utilization
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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)
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Demo: Priority Queuing (PQ)
PQBottleneck 90% utilization
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Demo: PQ Queuing Delays
FIFO
PQ Video
PQ FTP
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Demo: Weighted Fair Queuing (WFQ)
WFQBottleneck 90% utilization
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Demo: WFQ Queuing Delays
FIFO
WFQ/PQ Video
PQ FTP
WFQ FTP
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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
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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)
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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)
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Delay Calculation• Let
Q = Average time spent waiting in queueT = 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)
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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/( - )
N10λTμ01/μ
M/M/1 Results
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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
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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= /mapproaches 1 • There are analytical formulas for the occupancy
probabilities and average delay of these systems
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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
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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)
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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
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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
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Demo: M/G/1
Packet inter-arrival timesexponential (0.02) sec
Capacity1 Mbps
Packet size 1250 bytes(10000 bits)
Packet size distribution:exponential
constantlognormal
What is the average delay and queue size ?
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Demo: M/G/1 Analytical Results
Packet Size Distribution Delay T (sec) Queue Size (packets)
Exponentialmean = 10000
variance = 1.0 *108 0.02 1.0
Constantmean = 10000
variance = N/A 0.015 0.75
Lognormalmean = 10000
variance = 9.0 *108
0.06 3.0
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Demo: M/G/1 Simulation Results
Average Delay (sec) Average Queue Size (packets)
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Demo: M/G/1 LimitationsApplication traffic mix not memoryless
• Video » constant packet inter-arrivals
• Http» bursty traffic
Delay
P-K formula
Simulation
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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)
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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
Class 1 ArrivalsHigh Priority
TransmissionLine
Class 3 ArrivalsLow Priority
Class 2 ArrivalsInterm. Priority
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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
Class 1ArrivalsTransmission
LineClass 3ArrivalsClass 2Arrivals
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Weighted Fair Queuing• A combination of priority and cyclic service• No exact analytical formulas are available
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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)
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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
queueTimeFirst QueueTimeSecond Queue
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Two bottlenecks in series
Bottleneck
Exponentialinter-arrivals
Bottleneck
No queuing delayDelay
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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
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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
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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)
ExplicitBackgroundBackgroundBackgroundBackground
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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
Timea1a2a3a4d1d4d2d3. . .. . .DelayDelayDelayDelayArrival times at a linkDeparture times at the link
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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
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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
Time
aK aK+1wK wK+1
dK = aK + wK + sK
Explicit Explicit
Explicit ExplicitBackground Background
ARRIVAL TIMES
DEPARTURE TIMES
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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)
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Traffic Behavior and Queuing in a QoS 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?
• 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
Time
a1 a2 a3. . .
. . .
Arrival times/Workload found
w1 w2 w3
d1 = a1 + w1 + s1 d2 = a2 + w2 + s2 d3 = a3 + w3 + s3
Departure times
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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 )
k d
ak
Time. . .
Short Interval
wk
wk+1 = wk + (New bkg arrivals) - (Old bkg transmissions)
d
ak+1 wk+1
k+1
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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 possibleTime. . .Long Intervalakwkak+1wk+1dkIdle PeriodsBusy Periodsdk+1
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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
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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 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)
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Examples of Applications Analytical Modeling Discrete-Event Simulation
M/G/./. & G/G/./. FIFO
Analysis
M/G/./. & G/G/./. Priority
Analysis
Decomposition with Kleinrock Independence Assumption
DES only with Explicit Traffic
Hybrid DES with Explicit
and Background
Traffic Single Link with FIFO Service
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
Single Link with QoS-Based QueueingUsing QoS to differentiate service levels for the same type of traffic
N/AYes (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/AHighly
approximateN/A Yes Yes
Network of Queues
General network model extending the previous QoS queueing model
N/AHop-by-hop
Analysis (loss of accuacy)
Yes (some loss of accuracy - e.g., traffic
shaping)
Yes (Run time a function of network
complexity)
Yes [Fast with minimal loss of
accuracy]
Reduction of the general model to a representative end-to-end path
N/AHop-by-hop
Analysis (loss of accuacy)
N/AYes (Run time a
function of network complexity)
Yes [Fast with minimal loss of
accuracy]
Analysis Scenarios
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Demo End-to-end Delay: Baseline Network
Traffic modeled as1) Explicit traffic2) Background traffic
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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)
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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
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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
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Traffic Behavior and Queuing in a QoS Environment
Comparison: Hybrid vs Explicit Simulation
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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.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