traffic behavior and queuing in qos...

Traffic Behavior and Queuing

in QoS Environment

Instructor: Hamid R. Rabiee

Spring 2012

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

2

Outline

Basic concepts

Source models

Service models (demo)

Single-queue systems

Priority/shared service systems

Networks of queues

3

Outline

Basic concepts Performance measures

Solution methodologies

Queuing system concepts

Stability and steady-state

Causes of delay and bottlenecks

Source models

Service models(demo)



Networks of queues

4

Performance Measures

Delay

Delay variation (jitter)

Packet loss

Efficient sharing of bandwidth

Relative importance depends on traffic type (audio/video, file transfer,

interactive)

Challenge: Provide adequate performance for (possibly) heterogeneous

traffic

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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)

6

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

7

Little’ s Law

For a given arrival rate, the time in the system is proportional to packet occupancy

N = T

where

N: average number 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 may cause large delays

8

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 number 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

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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

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Burstiness Causes Interference

Note that the departures are less bursty

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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

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Packet Length Variation Causes Interference

Regular arrivals, irregular packet lengths

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High Utilization Exacerbates Interference

As the work arrival rate:

(packet arrival rate * packet length)

increases, the opportunity for interference increases

Time

Queuing 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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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

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Bottlenecks Cause Shaping

Bottleneck

90% utilization

Transmission time

sec

Exponential

interarrivals

sec

# of packets

# of packets

Incoming traffic

Interarrival timesOutgoing traffic

Interdeparture times

Fixed

packet

length

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Bottleneck

90% utilization

Outgoing traffic

Interdeparture times

Incoming traffic

Interarrival times

Large

Medium

Small

sec

# of packets

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Packet Trains

Histogram of inter-departure times for small packets

sec

# of packets

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Outline

Basic concepts

Source models

Poisson traffic

Batch arrivals

Example applications – voice, video, file transfer




Networks of queues

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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)

Time

Interarrival 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

22

Markov Modulated Rate Process (MMRP)

Extension: Models with more than two states and/or stochastic

transmission process

Stay in each state an exponentially

distributed time,

Transmit according to a deterministic process

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 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)

DataFTP

telnet

web

* Poisson type

* Sometimes batch-

arrivals, or bursty,

or sometimes on-off

Zero or near-zero 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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Outline

Basic concepts

Source models

Service models

Single vs. multiple-servers

FIFO, priority, and shared servers

Demo



Networks of queues

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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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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

Arrivals

Transmission Line

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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

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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 …)

32

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

33

Shared Servers

Again we have multiple classes/queues, but they are served with a “soft” priority

scheme

Round-robin

Weighted fair queuing

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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 (in terms of packet transmission rate)

Round-robin cannot be used to enforce bandwidth allocation among the

queues.

35

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” 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

36

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

Implementation: For each packet

Calculate its “finish time” (under the weighted bit-by-bit round robin scheme)

Transmit the packet with the minimum finish time

37

Weighted Fair Queuing Illustration

Weights:

Queue 1 = 3

Queue 2 = 1

Queue 3 = 1

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A Practical Combination (e.g. Cisco)

Example – voice in PQ, guaranteed b/w traffic in WFQs

(all at middle priority), and best effort traffic in low priority queue

39

Demo: Comparing FIFO, WFQ and PQ

Two traffic streams mixing on a common interface Video

FTP

Apply different service schemes FIFO

PQ

WFQ

Run simulation and compare queuing delays

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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: Summary 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



M/M/1……M/M/m/k

M/G/1……G/G/1

Demo: Analytics vs. simulation


Networks of queues

48

M/M/1 System

Nomenclature: M stands for “Memory-less” (a property of the exponential distribution)

M/M/1 stands for Poisson arrival process (which is “probabilistically memory-less”)

M/M/1 stands for exponentially distributed transmission times

Assumptions:

Arrival process is Poisson with rate l packets/sec

Packet transmission times are exponentially distributed with mean 1/m

One server

Independent inter-arrival times and packet transmission times

Transmission time is proportional to packet length

Note 1/m is secs/packet so m is packets/sec (packet transmission rate of the queue)

Utilization factor: r = 1/m

49

Delay Calculation

Let

Q = Average time spent waiting in queue

T = Average packet delay (transmission plus queuing)

Note that T = 1/m + 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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The analysis gives the steady-state probabilities of number of

packets in queue or transmission

P{n packets} = rn(1-r) where r= /m

From this we can get the averages:

N = r/(1 - r)

T = N/ = r/(1 - r) = 1/(m - )

51

M/M/1 Results

Example: How Delay Scales with Bandwidth

Occupancy and delay formulas

N = r/(1 - r) T = 1/(m - ) r= /m

Assume:

Traffic arrival rate is doubled

System transmission capacity m is doubled

Then:

Queue sizes stay at the same level (r stays the same)

Packet delay is cut in half (m and are doubled

A conclusion: In high speed networks

Propagation delay increases in importance relative to transmission and queuing delays

Buffer size and packet loss may still be a problem

52

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 r= /mmapproaches 1

There are analytical formulas for the occupancy

probabilities and average delay of these systems

53

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

There are 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)

55

M/G/1 System

Same as M/M/1 but the packet transmission time distribution is general, with given

mean 1/m and variance s2

Utilization factor r = /m

Pollaczek-Kinchine formula for

Average time in queue = (s2 + 1/m2)/2(1- r)

Average delay = 1/m + (s2 + 1/m2)/2(1- r)

The formulas for the steady-state occupancy probabilities are more complicated

Insight: As s2 increases, delay increases

56

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, independent interarrival times and

packet transmission times

Heavy traffic approximation:

Average time in queue ~ (s2 + 2)/2(1- r)

Becomes increasingly accurate as r

57

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 ?

Compare analytical formulas with simulation results

58

Demo: M/G/1 Analytical Results

Packet Size Distribution

Delay T (sec) Queue Size (packets)

Exponential

mean = 10000

variance = 1.0 *1080.02 1.0

Constant

mean = 10000

variance = 0.0

0.015 0.75

Lognormal

mean = 10000

variance = 9.0 *1080.06 3.0

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Demo: M/G/1 Simulation Results

Average Delay (sec) Average Queue Size (packets)

60

Demo: M/G/1 Limitations

Application traffic mix not memoryless

Video

constant packet inter-arrivals

Http

bursty traffic

Delay

P-K formula

Simulation

61

Outline

Basic concepts

Source models




Preemptive vs. non-preemptive

Cyclic, WFQ, PQ systems

Demo: Simulation results

Networks of queues

Hybrid simulation (demo)

62

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

63

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

This Type Systems Could Modeled by M/G/1 type assumptions

64

Weighted Fair Queuing

A combination of priority and cyclic service

No exact analytical formulas are available

65

Outline

Basic concepts

Source models




Networks of queues

Violation of M/M/. assumptions

Effects on delays and traffic shaping

Analytical approximations

66

Two Queues in Series

First queue shapes the traffic into second queue

Arrival times and packet lengths are correlated

M/G/1 formulas yield significant error for second queue

How about M/M/1 if packet lengths are exponential?

67

Two bottlenecks in series

Bottleneck

Exponential

inter-arrivals

Bottleneck

No queuing delayDelay

Spaced-apart

inter-arrivals

Spaced-apart

departures

68

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

69

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

70
http://www.juniper.net/techcenter/techpapers/200020.pdfhttp://www.juniper.net/techcenter/techpapers/200020.pdfhttp://www.juniper.net/techcenter/techpapers/200020.pdfhttp://www.athenasc.com/probbook.htmlhttp://secure.opnet.com/services/muc/mtdlogis_cse_stdies_81.htmlhttp://secure.opnet.com/services/muc/mtdlogis_cse_stdies_81.htmlhttp://secure.opnet.com/services/muc/mtdlogis_cse_stdies_81.html

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