This document discusses unit 2 of a course on high speed networks. It covers queuing analysis and models, including single server queues, effects of congestion and congestion control, traffic management, and congestion control in packet switching networks and frame relay. It provides an overview of key concepts like performance measures, solution methodologies, queuing system concepts, stability and steady-state, and causes of delay and bottlenecks. It also discusses analytical and simulation approaches to modeling queues and provides examples.

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

14. Packet Length Variation Causes
Interference
Regular arrivals, irregular packet lengths

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
22

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
23

24. Number of Servers

Number of servers available
Single Server Queue
Multiple Server Queue
24

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)‫‏‬
25

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
26

27. Default




Infinite buffer capacity
Infinite population size
FCFS service discipline
Example

G/G/1  G/G/1/
27

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
29

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
33

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*
34

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
35

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

41. 41

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
42

43. Figure 10.2
43

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

45. Figure 10.3
45

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
46

47. Figure 10.4
47

48. Congestion Control

Backpressure



Request from destination to source to reduce rate
Choke packet: ICMP Source Quench
Implicit congestion signaling

Source detects congestion from transmission
delays and discarded packets and reduces flow
48

49. Explicit congestion signaling


Direction
 Backward
 Forward
Categories
 Binary
 Credit-based
 rate-based
49

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

51. Figure 10.5
51

52. Frame Relay Congestion Control










Minimize frame size
Maintain QoS
Minimize monopolization of network
Simple to implement, little overhead
Minimal additional network traffic
Resources distributed fairly
Limit spread of congestion
Operate effectively regardless of flow
Have minimum impact other systems in network
Minimize variance in QoS
52

53. 53

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
54

55. 55

56. Figure 10.7
56

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
57

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
58

59. Questions
?
59