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