cse 422 notes, set 4dennisp/cse422/slides/set4-1_student.pdfthese slides contain materials provided...

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CSE 422 Notes, Set 4 These slides contain materials provided with the text:

Computer Networking: A Top Down Approach,5th edition, by Jim Kurose and Keith Ross, Addison-Wesley, April 2009.

Additional figures are repeated, with permission, from Computer Networks, 2nd through 4th Editions, by A. S. Tanenbaum, Prentice Hall.

Some figures are repeated from an OPNET Technologies presentation by Dmitri Bertsekas and course notes from Rutgers University.

The remainder of the materials were developed by Philip McKinley and Dennis Phillips at Michigan State University

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Assignment:

Read Chapter 4 of Kurose-Ross

Transport Layer

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Chapter 4: Network Layer

Introduction (forwarding and routing)

Review of queueing theory

Routing algorithms Link state, Distance Vector

Router design and operation

IP: Internet Protocol IPv4 (datagram format, addressing, ICMP, NAT)

Ipv6

Routing in the Internet Autonomous Systems

Routing protocols (RIP, OSPF, BGP)


Network layer

deliver segment from sending to receiving host

on sending side encapsulates segments into datagrams

on receiving side, delivers segments to transport layer

network layer protocols in every host, router

router examines header fields in all IP datagrams passing through it

applicationtransportnetworkdata linkphysical


networkdata linkphysical network

data linkphysical

networkdata linkphysical







networkdata linkphysicalnetwork

data linkphysical

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Two Key Network-Layer Functions

routing: determine route taken by packets from source to destination

Distributed routing in the Internet

Could also be centralized (drawbacks?)

forwarding: move packets from router’s input to appropriate router output


1

23

0111

value in arriving

packet’s header

routing algorithm

local forwarding table

header value output link

0100

0101

0111

1001

3

2

2

1

Interplay between routing and forwarding

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Network layer connection and connection-less service

Flavors of service datagram network provides network-layer

connectionless service (e.g., IP)

“virtual circuit” network (such as ATM) provided network-layer connection service

analogous to the transport-layer services UDP and TCP, but: service: host-to-host

no choice: network provides one or the other

implementation: in network core, not on hosts

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A quick word about ATM…

Asynchronous Transfer Mode started in late 1980s

attempt to merge telecom and computer networks

Based on virtual circuit packet switching reserve the route between source and destination

do not reserve capacity

All data broken into tiny, fixed size packets these ATM cells were only 53 bytes long (!)

virtual circuit identifiers (not full destination addresses) in cell headers used to switch data streams through the network

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ATM Discussion

Why small, fixed-size packets?

Advantages of ATM?

Disadvantages?

So, what happened to ATM?

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Currently dominating: Datagrams

no call setup at network layer

routers: no state about end-to-end connections no network-level concept of “connection”

packets forwarded using destination host address packets between same source-dest pair may take

different paths



1. Send data 2. Receive data

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Datagram Issues

Since capacity is not reserved, datagrams compete for network resources: Communication links

Router buffers

Bursty traffic creates periods of high and low demand, resulting in queueing of datagrams at network routers.

Performance depends on complex interactions.

Advent of packet switching produced need to: analyze performance of existing networks

predict performance of new designs

Network Layer


Chapter 4: Network Layer

Introduction (forwarding and routing)

Review of queueing theory

Routing algorithms Link state, Distance Vector

Router design and operation

IP: Internet Protocol IPv4 (datagram format, addressing, ICMP, NAT)

Ipv6

Routing in the Internet Autonomous Systems

Routing protocols (RIP, OSPF, BGP)

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Brief Review of Queueing Theory

Definition: Any system in which arrivals place demands upon a finite-capacity resource may be termed a queueing system.

Applications of Queueing Theory analysis of computer networks

telephone switching systems

customer service centers

automobile traffic control

almost any application involving entities waiting for and receiving service

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For studying computer networks…

View network as collections of queues First-in, first-out (FIFO) data structures

Queueing theory provides probabilistic analysis of these queues

Examples: Average queue length Average waiting (and service) time Probability that queue is at a certain length Probability of queue overflow (packets will be

dropped)

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References:

Definitive text on queueing theory:

Kleinrock, Queueing Systems, Volume I: Theory, John Wiley, New York, 1975.

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Little’s Law

Parameters and metrics

N -average number of customers in the system (basically, queue size plus customer currently being serviced)

T -average delay per customer (time that the customer waits plus time that customer is serviced)

- average customer arrival rate

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Little’s Law

Relationship:

“Proof” A customer arrives at the queue

After a period of time T (average), the customer is at the front of the queue

How many new customers have queued behind this one?

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Examples

Example 1 Meijer at 5:30 p.m. N =6, =0.33

Example 2 Meijer at 1:00 a.m. N =0.25, =0.1

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Networking Example

Arrival of packet at a router is 2000 pps

Average time in the router 6 ms.

Average number of packets in router?

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Summary

Little’s Law: Mean number tasks in system = mean arrival rate x mean response time Observed for centuries, Little was first to prove

Applies to any queueing system in equilibrium, as long as nothing in black box is creating or destroying tasks

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Arrivals Departures

System

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Packet Queueing

If arrivals are regular or sufficiently spaced apart, no queueing delay occurs

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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

Same packet rate, different burstiness

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Length variation

Length variation also causes interference and, hence, delays

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Queueing Delays

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Traffic volume

High utilization exacerbates interference and leads to more queueing

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Queueing Delays

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Bottlenecks

Types of bottlenecks At network entry points

At routers within the network core

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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Analysis

How to capture the randomness associated with: Packet volume?

Packet arrival patterns?

Packet lengths?

Little’s Law is useful for analyzing an existing system, but designing a new system (e.g., a router) requires deeper analysis.

Example: how many buffers are needed, given expected traffic patterns and loads?

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Stochastic Processes Definition: A random variable is a variable

value depends on the outcome of a random experiment

For each outcome ω of an experiment, we associate a real number X(ω),

X(ω) is the value the random variable takes on when the experimental outcome is ω.

Example: payoffs for various rolls of dice

Definition: A stochastic process is a function of time X(t, ω), usually written as simply X(t)

values are random variables

can be discrete or continuous

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Examples

Dow Jones closing averages.

Number of cars that have pulled into Meijer’s parking lot by time t.

Number of packets generated by a host by time t.

Number of packets arriving at a router by time t.

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Poisson Processes

Definition: A stochastic process {A(t)|t > 0} taking on nonnegative integer values is said to be a Poisson process with rate if

A(t) is a counting process that represents the total number of arrivals that have occurred from 0 to time t.

The numbers of arrivals that occur in disjoint time intervals are independent.

The number of arrivals in any interval of length is Poisson distributed with parameter

P {A(t + ) − A(t) = n} =

for n =0, 1, 2, ...

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Example Customers join Meijer’s checkout lane with an average arrival

rate of one customer every 2 minutes. What is the probability that exactly 2 customers join the queue in a period of 5 minutes?

What is the probability that no customers join the queue in this time?

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Poisson Process Properties

Interarrival times are independent and exponentially distributed with parameter

P{n≤ t} = 1 − e−t, t ≥ 0

Why?

Graph?

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Different values of Probability that interarrival time is less than t (x axis)

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1 − e−t

time (t)

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Example

Assume that phone call times are exponentially distributed about some mean 1/λ, that is,

P{call duration ≤ t} = 1 − e−t

1/λ = mean length of a call. Why?

Suppose 1/λ = 2 minutes, so λ = 0.5/min

P{call duration ≤ 2 minutes} = 1 − e-0.5*2 = 0.632• Hmm. Not 0.5?

P{call duration ≤ 10 minutes} = 1 − e-0.5*10 = 0.993

P{call duration ≤ 20 minutes} = 1 − e-0.5*20 = 0.99995

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Consider this situation:

You are attending a retreat in a remote location No cell phone service !?!

Two public phones are available in the lobby of the lodge

You need to make a call, but both phones are currently busy A person nearby tells you that one person just

started his/her call, while the other has been on the phone for 30 minutes.

Which phone should you wait for?

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The Markov Property

The exponential distribution is said to be:

Specifically,

Why does this property hold?

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Queueing System Characterization

Five components

Interarrival-time pdf

Service-time pdf

Number of servers

Queuing discipline, that is, how customers are taken from the queue

Number of buffers (for customers)

We will consider infinite-buffer, single-server systems, using a FIFO queueing discipline

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Notation

Notation for first 3 components: A/B/m, with A and B chosen from M -Markov (exponential pdf)

D -Deterministic (all customers have same value)

G -General (arbitrary pdf)

Example of M/M/1?

Example of M/D/1?

Example of D/D/1?

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The M/M/1 Queueing System

Both arrival-time pdf and service-time pdf are exponential, with a single server

= arrival rate, µ = server capacity

Let the state i of the queueing system be the number of customers in the system

When a customer arrives or a customer departs the system, the system moves to an adjacent state (i +1 or i − 1)

Pi = P {system is in state i}

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M/M/1 Queue

Network Layer

m

m

1

Tq

T

N

Nq

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M/M/1 (cont.)

In equilibrium, Pi does not change over time!

Such queueing systems are known as birth-death systems. State diagram:

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n+1nn-1

m mm m

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State probabilitiesDiagram:

P0 = mP1

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Solve for P0

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M/M/1 at a glance…

What is ρ?

Since and m are constants, Pi alone describes the current state of the system.

Why can we describe the ENTIRE state of the system by a single parameter?

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Computing N

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Computing T

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Example

Checkout lane. = 0.25 and m = 1.0

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M/M/1 Results 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 - )

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Networking Example

On a network router, measurements show that packets arrive at a mean rate of 125 packets

per second (pps) and

the router takes about 2 milliseconds to forward them.

Assuming an M/M/1 model, What is the probability of buffer overflow if

the router had only 13 buffers?

How many buffers are needed to keep packet loss below one packet per million?

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Example (cont.)

Arrival rate λ =

Service rate μ =

Gateway utilization ρ = λ/μ =

Prob. of n packets in gateway =

Mean number of packets in router =

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Example (cont.)

Probability of buffer overflow:= P(more than 13 packets in gateway)

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Example (cont.)

To limit the probability of loss to less than 10-

6:

Network Layer

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