046335 Design of Computer Networks Prof. Ariel Orda Room 914, ext 4646

04/20/23 A. Orda, R. Rom, A. Segall, 1

046335 Design of Computer Networks

Prof. Ariel OrdaRoom 914, ext 4646


Introduction

• Computer Network:

– A set of autonomous connected computers

• connected = can transmit information between computers

• autonomous = independent ( not Master-Slave)

– Related concepts:

• computerized communication = computers aid to communication of a different type ( e. g. telephony )

• distributed system = the network is transparent to the user and the operating system takes care of the communication ( the difference between this and a computer network is minimal )

• communication system = there is exchange of information, but there is no communication network ( e.g. Master -Slave )


Computer Network: reasoning and usage

• Information Sharing

• Resource Sharing: Files, Databases, Printers, Applications.

• Reliability: Resource backup

• Efficiency: work in parallel on different parts of the problem.

• Cost: changes in relative cost of computation / communication

• Network versus point-to-point communication

– Most of the time no need for session between any two given users

– While a session is in progress, actual communication is not continuous

– Every node can connect to any other node


• Network Components:

– End systems and computers ( hosts ): network users

– Communication sub-network:

• transmission of information between users

• does not generate information ( except to support communication )

– Communication sub-network links:

• Point-to-Point: twisted pair, coaxial cable, optical fiber, infra-red, wireless (Bluetooth, WiFi, etc).

• Broadcast: radio, microwave, bus, satellite

– source-destination data transmission: switching (to be explained later)

– other network examples:

• transportation network, phone network

– first part in network design is network topology


Network types, by distance between switches

Distance Geography Example0.1m Circuit board Parallel Processor1m System Multiprocessor10m Room100 m Building1 km Campus

|| Local Area Network (LAN)|

10 km City Metropolitan Area Network100 km Country Long Haul (WAN)1000 km Continent Long Haul Inter-network

Note: Distance between switches normally determines the data transmission speed


Network topology types

Point-to-Point Topologies Broadcast Topologies

B

A

S EF

HJ

D

CG

IK

Z

M

N

L

Wireless Ad-Hoc


Logical design of networks ( architecture )

• Layered architecture

– each layer is responsible for a collection of functions and provides service for upper layers

– Modular architecture facilitates design and maintenance

• Protocol: conversation between identical layers at different locations

• Interface: conversation between adjacent layers at the same site


OSI Reference Model - layer description• Physical Layer - bit transmission, electrical and mechanical problems

• Data Link (DLC) - Reliable data transmission on links, overcomes noise problems. Normally uses data frames and ack frames.

• Network Layer - Responsible for Operation of the Communication Sub-Network:

– Routing: data flow in the network

– Flow Control: stops network overflow

– Inter-network transmission

• Transport Layer

– Reliable end-to-end data transmission

– Differentiates between types of traffic, provides for each: reliability, order, delay

• Session Layer

– Different types of machines can maintain a conversation

– Call control ( unidirectional or bi-directional), token control, synchronization

• Presentation

– Encryption, compression, etc.

• Application: everything else

• In common channel networks, MAC layer, an additional sub-layer under DLC, to control channel access


Switching Methods• Circuit Switching

– Needs setup

– used in phone systems

– reserved fixed bandwidth

– no congestion problem

• Message Switching

– messages are forwarded in one piece ( store & forward )

– no fixed path between source and destination

– maximum message size not specified

– no need for preparation phase in the network ( setup)

– large memory requirements ( to accommodate large messages)

• Packet Switching

– packets are forwarded individually, possibly on different paths

– efficient bandwidth use

– low delay and low memory requirements

– may produce traffic jams

– packets may arrive out of order


Switching methods ( continued )

• Virtual Circuit Switching

– Circuit Switching + Packet Switching combination

– Packetized Data is being switched

– Path is established upon call setup and is fixed throughout the call

– No reserved Bandwidth

– Properties:

• Need for preparation phase

• Packets arrive in order

• There may be gaps because of losses if there is no DLC on links

• Fixed Path

• Congestion Problem can still arise

VC Switching is very popular in modern high-speed networks


A B C DA B C DA B C D

Transmission TimePropagation TimeProcessing Time

Setup Time

Data Exchange Phase

Dismantle Time

Msg

Msg

Msg

1

2

3

1

2

31

2

3

End-To-End Propagation

Circuit Switching Message Switching Packet Switching

Switching Methods (continued)


Design Problems

• Design Problems

– Switch design

– Communication means type

– Switching method

– Use of communication means

– Topological Design

– Routing method

– Flow and Congestion Control

• Design Criteria

– Performance:

• Delay– maximal or average– per user or for entire

network

• Throughput

– Cost

– Reliability and Survivability

– Adaptivity and Scaling

– Simplicity of Protocols


Queues

• Packets arrive randomly

• Wait in line to be transmitted

• Service time is the transmission time

• Random elements:

– packet arrival time

– service time, if packets are not of fixed length

• Need for statistical specification

Communication link as a queue


General queue specification

• In this course we shall treat only M/M/n queues.

serviceinput output

M / M /n

Poisson arrivals

Exponentialservice Number of servers


• Follows that:

– During a small time interval holds:

Prob( one arrival during (t, t+ t)) =

Exponential arrivals

• Definition 1: Numbers of arrivals in non-overlapping intervals are independent and probability of k arrivals during time interval t :

tk

k ek

ttP

!

)( is the average arrival rate

t ( )t o t

Prob ( no arrival during ( , )) 1 ( )t t t t o t

0)(

lim x

xoox namely o(x) goes down to 0 faster than x

probability of 2 or more arrivals during ( , ) is ( )t t t o t


• Probability that a user requires service time < t (service time cdf):

• Probability that a user in service at time t is still in service at time

• Probability that a user in service at time t completes it by time

Exponential service time (ST)

)( tt

)( tt

( ) 1 - service ratetF t e

)( tot

( )

Pr ( | ) 1 ( )t t

tt

eob ST t t ST t e t o t

e


System State

Pk(t + t) = Pk(t) [1 - t + o(t)] [1 - t + o(t)]+Pk+1(t)[1 - t + o(t)] [t +o(t)]

+Pk-1(t)[t + o(t)] [1 - t + o(t)] + o(t) k > 0

Pk(t ) = Probability that there are k users in the system

none has arrived none has left

Pk(t + t) - Pk(t) = [Pk-1(t) - ( + )Pk(t) +Pk+1(t)].t + o(t)

tPtPtPdt

tdPkkk

k11

P 0 ( t + t ) = P 0 ( t ) . [ 1 - t + o ( t ) ] + P 1 ( t ) . [ 1 - t + o ( t ) ] [ t + o ( t ) ]

+ o ( t )

d P t

d tP t P t0

0 1

For k=0:

In the limit:


Example

0 00 tPdt

tdP

00 0

0

( ); ( ) (0) = ;

( )t tdP t

dt P t P e eP t

Now we can calculate )(1 tP

)()()()(

1101 tPetPtPdt

tdP t

This is a differential equation for whose solution is : 1P

tettP )(1

We can continue this way for every k

0; system empty at 0t


Steady State ( )t

Notation: assuming the limit exists )(lim 00 tPP t

ndt

tdPn each for 0)(

10 PP

0 )( 11 kPPP kkk

k

k

k PPP

00

k

kk

k

kk PPPPP

)1( ; 1 ; 1

11 00

00

01

1

00 P

In steady state holds

Then

Solution

Calculation of P0 and Pk

The solution is valid if . For the system has no steady state. In general,

condition for existence of steady state is .

1


State Transition Diagram

• Based on transition rates

• State “ flow” conservation

• Example: dashed circles.

• Example : ellipse:

• Steady state equations can be written directly from the state diagram

• Can also write diagram for :

– as a function of the state

– as a function of the state

1 kk PP

0 )( 11 kPPP kkk


Little’s formula

• Explanation:

– average user arrives to system and finds users

– when he leaves, there are users, therefore while he was in the system users arrived

– the period he was in the system is and during this period arrived

• Little’s theorem holds also for more complicated systems

• Use for M/M/1

TN Average number

of users in the system

Average delay

Average arrival rate

N

TT

NN

0 0

(1 )1

kk

k k

N k P k

1

11N

T

046335 Design of Computer Networks Prof. Ariel Orda Room 914, ext 4646

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