CEN 4500C Computer Networks FundamentalsAhmed Helmy (www.cise.ufl.edu/~helmy)Computer & Information Science & Engineering (CISE) DeptUniversity of FloridaFall 2007

Course Outline~6 homeworks (+ extra mini-projects) + 2 exams1 mid-term covering the first half of semesterThe Internet (Overview), Layering, Multiplexing, Applications, Transport, Congestion Control, MAC protocols (partial !) [depending on lecture progress]2nd exam (final or 2nd mid-term) covering 2nd halfMAC protocols (partial), Wireless Networking and Mobility, Routing (unicast, multicast), Security (partial!) [depending on progress]1 required text book (Kurose, Ross)Lecture slides: altered version of book slides

(Open) Questions to think about:Throughout the semester we can ask the following questions about the services and the design of the Internet:What do you like about the Internet?What do you not like about the Internet and would want to change?How would you change it and how would you achieve such change?

Intro & MotivationWhats the Internet to you?Web browsers, wireless Internet Cafs, cellular phones!, home networks, networked cars, networked embedded devices, inter-planetary networks? Very complex, time varying, hard to draw !Why study the Internet?To learn engineering lessons from historyAnalyze todays problems and improve performanceProvide future designs for better Internet and new applicationsIs the Internet the only form of computer networking? (open question)

Topics (Chapters) to CoverFrom main text book (Kurose, Ross)Ch1: Overview, IntroCh2: ApplicationsCh3: Transport LayerCh4: Network LayerCh5: Link Layer, MAC, LANsCh6: Wireless, Mobile NetworksCh7: Multimedia [partial: Diffserv, Intserv]Ch8: Security [partial]Notes: Ordering maybe slightly modified as semester progresses.Personal notes, additions will be provided by Prof. as needed.

Chapter 1IntroductionComputer Networking: A Top Down Approach ,4th edition. Jim Kurose, Keith RossAddison-Wesley, July 2007.

Chapter 1: IntroductionOverview:whats the Internet?whats a protocol?network edge; hosts, access net, physical medianetwork core: Internet structureprotocol layers, service modelsnetwork core: packet/circuit switching,performance: loss, delay, throughputsecurityhistory

Chapter 1: roadmap1.1 What is the Internet?1.2 Network edge end systems, access networks, links1.3 Network core circuit switching, packet switching, network structure1.4 Delay, loss and throughput in packet-switched networks1.5 Protocol layers, service models1.6 Networks under attack: security1.7 History

Whats the Internet: nuts and bolts viewmillions of connected computing devices: hosts = end systems run network appscommunication linksfiber, copper, radio, satellitetransmission rate (bandwidth)routers: forward packets (chunks of data)

Whats the Internet: nuts and bolts viewprotocols control sending, receiving of msgsTCP, IP, HTTP, EthernetInternet: network of networksloosely hierarchicalpublic Internet versus private intranetInternet standardsRFC: Request for commentsIETF: Internet Engineering Task Force

Whats the Internet: a service viewcommunication infrastructure enables distributed applications:Web, VoIP, email, games, e-commerce, file sharingcommunication services provided to apps:reliable data delivery from source to destinationbest effort (unreliable) data delivery

Whats a protocol?Network protocols:All communication in Internet governed by protocolsGeneric protocol: specific messages sentspecific actions taken when messages are received, or other events (e.g., timer expiration, exception detection)

Protocol Representation:Finite State MachinesProtocol Specification, via Standards

Whats a protocol?Example sequence of a computer network protocol:

TCP connection requesthostserverProtocol Design and Analysis are extremely important in Internet study, development and research

Chapter 1: roadmap1.1 What is the Internet?1.2 Network edge end systems, access networks, links1.3 Network core circuit switching, packet switching, network structure1.4 Delay, loss and throughput in packet-switched networks1.5 Protocol layers, service models1.6 Networks under attack: security1.7 History

A closer look at network structure:Network edge: applications and hostsAccess networks, physical media: wired, wireless communication links Network core: interconnected routersnetwork of networks

The network edge:End systems (hosts):run application programse.g. Web, emailat edge of networkClient-server modelclient host requests, receives service from always-on servere.g. Web browser/server; email client/serverPeer-to-peer model: minimal (or no) use of dedicated serverse.g. Kazaa, BitTorrenth

Network edge: reliable data transfer serviceGoal: data transfer between end systemshandshaking: setup (prepare for) data transfer ahead of timeHello, initial establishmentset up state in two communicating hostsTCP - Transmission Control Protocol Internets reliable data transfer service

TCP service [RFC 793]reliable, in-order byte-stream data transferloss: acknowledgements and retransmissionsflow control: sender wont overwhelm receivercongestion control: senders slow down sending rate when network congested

Network edge: best effort (unreliable) data transfer serviceGoal: data transfer between end systemssame as before!UDP - User Datagram Protocol [RFC 768]: connectionless unreliable data transferno flow controlno congestion controlApps using TCP: HTTP (Web), FTP (file transfer), Telnet (remote login), SMTP (email)

Apps using UDP:streaming media, teleconferencing, DNS, Internet telephony

Access networks and physical mediaQ: How to connect end systems to edge router?residential access netsinstitutional access networks (school, company)mobile access networksKeep in mind: bandwidth (bits per second) of access network?shared or dedicated?

Residential access: point to point accessDialup via modemup to 56Kbps direct access to router (often less)Cant surf and phone at same time: cant be always onDSL: digital subscriber linedeployment: telephone company (typically)up to 1 Mbps upstream (today typically < 256 kbps)up to 8 Mbps downstream (today typically < 1 Mbps)dedicated physical line to telephone central office

Residential access: cable modemsHFC: hybrid fiber coaxasymmetric: up to 30Mbps downstream, 2 Mbps upstreamnetwork of cable and fiber attaches homes to ISP routerhomes share access to router deployment: available via cable TV companies

Residential access: cable modems

Cable Network Architecture: Overviewhomecable headendcable distributionnetwork (simplified)Typically 500 to 5,000 homes

Cable Network Architecture: Overviewhomecable headendcable distributionnetwork

Cable Network Architecture: Overviewhomecable headendcable distributionnetwork (simplified)

Cable Network Architecture: Overviewhomecable headendcable distributionnetworkFDM (frequency division multiplexing)

Company access: local area networkscompany/univ local area network (LAN) connects end system to edge routerEthernet: 10 Mbs, 100Mbps, 1Gbps, 10Gbps Ethernetmodern configuration: end systems connect into Ethernet switchLANs: chapter 5

Wireless access networksshared wireless access network connects end system to routervia base station aka access pointwireless LANs:802.11b/g/n (WiFi): 11, 54, 111 Mbpswider-area wireless accessprovided by telco operator~1Mbps over cellular (EVDO, HSDPA)WiMAX (10s Mbps) over wide area?Wireless Networks: Chapter 6Future: Mobile Ad Hoc and Sensor Networks!

Home networksTypical home network components: DSL or cable modemrouter/firewall/NATEthernetwireless access pointwirelessaccess pointwirelesslaptopsrouter/firewallcablemodemto/fromcableheadendEthernet

Physical MediaBit: propagates between transmitter/rcvr pairsphysical link: what lies between transmitter & receiverguided media: signals propagate in solid media: copper, fiber, coaxunguided media: signals propagate freely, e.g., radioTwisted Pair (TP)two insulated copper wiresCategory 3: traditional phone wires, 10 Mbps EthernetCategory 5: 100Mbps Ethernet

Physical Media: coax, fiberCoaxial cable:two concentric copper conductorsbidirectionalbaseband:single channel on cablelegacy Ethernetbroadband: multiple channels on cable HFC (hybrid fiber-coax)Fiber optic cable:glass fiber carrying light pulses, each pulse a bithigh-speed operation:high-speed point-to-point transmission (100s Gps)WDM Networks: Wavelength division multiplexinglow error rate: repeaters spaced far apart ; immune to electromagnetic noise

Physical media: radiosignal carried in electromagnetic spectrumno physical wirebidirectionalpropagation environment effects:reflection obstruction by objectsInterferencedynamic link characteristics Radio link types:terrestrial microwavee.g. up to 45 Mbps channelsLAN (e.g., Wifi)11Mbps, 54 Mbpswide-area (e.g., cellular)3G cellular: ~ 1 MbpssatelliteKbps to 45Mbps channel (or multiple smaller channels)270 msec end-end delaygeosynchronous versus low altitude

Chapter 1: roadmap1.1 What is the Internet?1.2 Network edge end systems, access networks, links1.3 Network core network structure, circuit switching, packet switching 1.4 Delay, loss and throughput in packet-switched networks1.5 Protocol layers, service models1.6 Networks under attack: security1.7 History

Internet Structure: loose hierarchyhierarchy based on administrative regions/providers

POP

POP

POP

NAP

Routing Arbiter

ISP

Backbone

ISP

ISP

e.g. vBNS

e.g. AOL, Earthlink

POP: Point of Presence

ISP: Internet Service Provider

NAP: Network Access Point

vBNS: very high speed network service Sprint

Internet Hierarchyhierarchy based on routing (more later)

AS1

AS2

AS3

Border Router (BR)

AS4

AS: Autonomous System

IGP: Interior Gateway Protocol

BGP: Border Gateway Protocol

BGP

IGP

(RIP [D.V.], OSPF [L.S.])

Internet structure: network of networksroughly hierarchicalat center: tier-1 ISPs (e.g., Verizon, Sprint, AT&T, Cable and Wireless), national/international coveragetreat each other as equalsTier 1 ISPTier 1 ISPTier 1 ISP

Tier-1 ISP: e.g., Sprint

Internet structure: network of networksTier-2 ISPs: smaller (often regional) ISPsConnect to one or more tier-1 ISPs, possibly other tier-2 ISPs

Tier 1 ISPTier 1 ISPTier 1 ISP

Internet structure: network of networksTier-3 ISPs and local ISPs last hop (access) network (closest to end systems)

Tier 1 ISPTier 1 ISPTier 1 ISP

Internet structure: network of networksa packet passes through many networks!

Tier 1 ISPTier 1 ISPTier 1 ISP

100 node transit-stub topologySo, what does the Internet look like? Have you seen it lately?!

Map of the multicast backbone [Mbone] (~3000 nodes) [2002]

Map of the Internet (~50,000 nodes)

It is not simple It is really complexin scalein interactions and dynamicsin failure modes (loss, crashes, loops, etc)We need a very systematic approach to design protocols for such a complex network

Chapter 1: roadmap1.1 What is the Internet?1.2 Network edge end systems, access networks, links1.3 Network core circuit switching, packet switching, network structure1.4 Delay, loss and throughput in packet-switched networks1.5 Protocol layers, service models1.6 Networks under attack: security1.7 History

Protocol LayersNetworks are complex! many pieces:hostsrouterslinks of various mediaapplicationsprotocolshardware, softwareQuestion: Is there any hope of organizing structure of network?

Or at least our discussion of networks?

Why layering?Dealing with complex systems:explicit structure allows identification, relationship of complex systems pieceslayered reference model for discussionmodularization eases maintenance, updating of systemchange of implementation of layers service transparent to rest of systemchange in one layer doesnt affect rest of system(is this true?!)Can layering be considered harmful?

Internet protocol stackapplication: supporting network applicationsFTP, SMTP, HTTPtransport: process-process data transferTCP, UDPnetwork: routing of datagrams from source to destinationIP, routing protocolslink: data transfer between neighboring network elementsPPP, Ethernetphysical: bits on the wire

ISO/OSI reference modelpresentation: allow applications to interpret meaning of data, e.g., encryption, compression, machine-specific conventionssession: synchronization, checkpointing, recovery of data exchangeInternet stack missing these layers!these services, if needed, must be implemented in applicationneeded?

Encapsulationsourceapplicationtransportnetworklinkphysicalsegmentdatagramdestinationapplicationtransportnetworklinkphysicalrouterswitchmessageframe

Layering & protocol stacks: (the protocol hour glass)

Application

Transport

Network

Data Link

Physical

TCP/UDP

IP

Ethernet

FDDI

Toekn ring

RTP/RTCP

RSVP

TCP/UDP

Reliable Mcast

IPv6/

Unicast routing

Mcast routing

DVMRP,PIM

Gig. Ethernet

ATM

WDM

Wireless

Chapter 1: roadmap1.1 What is the Internet?1.2 Network edge end systems, access networks, links1.3 Network core circuit switching, packet switching, network structure1.4 Delay, loss and throughput in packet-switched networks1.5 Protocol layers, service models1.6 Networks under attack: security1.7 History

The Network Coremesh of interconnected routersthe fundamental question: how is data transferred through net?circuit switching: dedicated circuit per call: telephone netpacket-switching: data sent thru net in discrete chunks

Network Core: Circuit SwitchingEnd-end resources reserved for calllink bandwidth, switch capacitydedicated resources: no sharingcircuit-like (guaranteed) performancecall setup requiredre-establish call upon failure

Network Core: Circuit Switchingnetwork resources (e.g., bandwidth) divided into piecespieces allocated to callsresource piece idle if not used by owning call (no sharing)dividing link bandwidth into piecesfrequency divisiontime division

Circuit Switching: FDM and TDM

Numerical exampleHow long does it take to send a file of 640,000 bits from host A to host B over a circuit-switched network?All links are 1.536 MbpsEach link uses TDM with 24 slots/sec500 msec to establish end-to-end circuit

Lets work it out!Each link gets 1.526Mbps/24=64kbpsTime needed for 640kbps=640/64+0.5=10.5 secondsPlus propagation!

Network Core: Packet Switchingeach end-end data stream divided into packetsuser A, B packets share network resources each packet uses full link bandwidth resources used as needed

resource contention: aggregate resource demand can exceed amount availablecongestion: packets queue, wait for link usestore and forward: packets move one hop at a timeNode receives complete packet before forwarding

Packet Switching: Statistical MultiplexingSequence of A & B packets does not have fixed pattern, bandwidth shared on demand statistical multiplexing.TDM: each host gets same slot in revolving TDM frame.

ABC100 Mb/sEthernet1.5 Mb/sstatistical multiplexingqueue of packetswaiting for outputlink

Packet-switching: store-and-forwardtakes L/R seconds to transmit (push out) packet of L bits on to link at R bpsstore and forward: entire packet must arrive at router before it can be transmitted on next linkdelay = 3L/R (assuming zero propagation delay)Example:L = 7.5 MbitsR = 1.5 Mbpstransmission delay = 15 secRRRLmore on delay shortly

Packet switching versus circuit switching1 Mb/s linkeach user: 100 kb/s when activeactive 10% of time

circuit-switching: 10 userspacket switching: with 35 users, probability > 10 active at same time is less than .0004

Packet switching allows more users to use network!N users1 Mbps linkQ: how did we get value 0.0004?

Packet switching versus circuit switchinggreat for bursty dataresource sharing (scalable!)simpler, no call setup, more robust (re-routing)excessive congestion: packet delay and lossWithout admission control: protocols needed for reliable data transfer, congestion controlQ: How to provide circuit-like behavior?bandwidth guarantees needed for audio/video appsstill an unsolved problem (chapter 7), virtual circuitIs packet switching a slam dunk winner?Q: human analogies of reserved resources (circuit switching) versus on-demand allocation (packet-switching)?

Chapter 1: roadmap1.1 What is the Internet?1.2 Network edge end systems, access networks, links1.3 Network core circuit switching, packet switching, network structure1.4 Delay, loss and throughput in packet-switched networks1.5 Protocol layers, service models1.6 Networks under attack: security1.7 History

How do loss and delay occur?packets queue in router buffers packet arrival rate to link exceeds output link capacitypackets queue, wait for turnAB

Four sources of packet delay1. nodal processing: check bit errorsdetermine output link2. queueingtime waiting at output link for transmission depends on congestion level of router

Delay in packet-switched networks3. Transmission delay:R=link bandwidth (bps)L=packet length (bits)time to send bits into link = L/R4. Propagation delay:d = length of physical links = propagation speed in medium (~2x108 m/sec)propagation delay = d/sNote: s and R are very different quantities!

Caravan analogycars propagate at 100 km/hrtoll booth takes 12 sec to service car (transmission time)car~bit; caravan ~ packetQ: How long until caravan is lined up before 2nd toll booth?

Time to push entire caravan through toll booth onto highway = 12*10 = 120 secTime for last car to propagate from 1st to 2nd toll both: 100km/(100km/hr)= 1 hrA: 62 minutes

Caravan analogy (more)Cars now propagate at 1000 km/hrToll booth now takes 1 min to service a carQ: Will cars arrive to 2nd booth before all cars serviced at 1st booth?

Yes! After 7 min, 1st car at 2nd booth and 3 cars still at 1st booth.1st bit of packet can arrive at 2nd router before packet is fully transmitted at 1st router!See Ethernet applet at AWL Web site

Nodal delaydproc = processing delaytypically a few microsecs or lessdqueue = queuing delaydepends on congestiondtrans = transmission delay= L/R, significant for low-speed linksdprop = propagation delaya few microsecs to hundreds of msecs

Queueing delay (revisited)R=link bandwidth (bps)L=packet length (bits)a=average packet arrival ratetraffic intensity = La/RLa/R ~ 0: average queueing delay smallLa/R -> 1: delays become largeLa/R > 1: more work arriving than can be serviced, average delay infinite!

Real Internet delays and routesWhat do real Internet delay & loss look like? Traceroute program: provides delay measurement from source to router along end-end Internet path towards destination. For all i:sends three packets that will reach router i on path towards destinationrouter i will return packets to sendersender times interval between transmission and reply.

3 probes3 probes3 probes

Real Internet delays and routes1 cs-gw (128.119.240.254) 1 ms 1 ms 2 ms2 border1-rt-fa5-1-0.gw.umass.edu (128.119.3.145) 1 ms 1 ms 2 ms3 cht-vbns.gw.umass.edu (128.119.3.130) 6 ms 5 ms 5 ms4 jn1-at1-0-0-19.wor.vbns.net (204.147.132.129) 16 ms 11 ms 13 ms 5 jn1-so7-0-0-0.wae.vbns.net (204.147.136.136) 21 ms 18 ms 18 ms 6 abilene-vbns.abilene.ucaid.edu (198.32.11.9) 22 ms 18 ms 22 ms7 nycm-wash.abilene.ucaid.edu (198.32.8.46) 22 ms 22 ms 22 ms8 62.40.103.253 (62.40.103.253) 104 ms 109 ms 106 ms9 de2-1.de1.de.geant.net (62.40.96.129) 109 ms 102 ms 104 ms10 de.fr1.fr.geant.net (62.40.96.50) 113 ms 121 ms 114 ms11 renater-gw.fr1.fr.geant.net (62.40.103.54) 112 ms 114 ms 112 ms12 nio-n2.cssi.renater.fr (193.51.206.13) 111 ms 114 ms 116 ms13 nice.cssi.renater.fr (195.220.98.102) 123 ms 125 ms 124 ms14 r3t2-nice.cssi.renater.fr (195.220.98.110) 126 ms 126 ms 124 ms15 eurecom-valbonne.r3t2.ft.net (193.48.50.54) 135 ms 128 ms 133 ms16 194.214.211.25 (194.214.211.25) 126 ms 128 ms 126 ms17 * * *18 * * *19 fantasia.eurecom.fr (193.55.113.142) 132 ms 128 ms 136 mstraceroute: gaia.cs.umass.edu to www.eurecom.frThree delay measurements from gaia.cs.umass.edu to cs-gw.cs.umass.edu * means no response (probe lost, router not replying)trans-oceaniclink

Packet lossqueue (aka buffer) preceding link in buffer has finite capacitypacket arriving to full queue dropped (aka lost)lost packet may be retransmitted by previous node, by source end system, or not at allABpacket being transmittedpacket arriving tofull buffer is lostbuffer (waiting area)

Throughputthroughput: rate (bits/time unit) at which bits transferred between sender/receiverinstantaneous: rate at given point in timeaverage: rate over long(er) period of timeserver, withfile of F bits to send to clientlink capacity Rs bits/seclink capacity Rc bits/secserver sends bits (fluid) into pipe

Throughput (more)Rs < Rc What is average end-end throughput? Rs bits/sec

Throughput: Internet scenarioper-connection end-end throughput: min(Rc,Rs,R/10)in practice: Rc or Rs is often bottleneck10 connections (fairly) share backbone bottleneck link R bits/secRsRsRsRcRcRcR

Chapter 1: roadmap1.1 What is the Internet?1.2 Network edge end systems, access networks, links1.3 Network core circuit switching, packet switching, network structure1.4 Delay, loss and throughput in packet-switched networks1.5 Protocol layers, service models1.6 Networks under attack: security1.7 History

Network Securityattacks on Internet infrastructure:infecting/attacking hosts: malware, spyware, worms, unauthorized access (data stealing, user accounts)denial of service: deny access to resources (servers, link bandwidth) Internet not originally designed with (much) security in mindoriginal vision: a group of mutually trusting users attached to a transparent network Internet protocol designers playing catch-upSecurity considerations in all layers!

What can bad guys do: malware?Spyware:infection by downloading web page with spywarerecords keystrokes, web sites visited, upload info to collection siteVirusinfection by receiving object (e.g., e-mail attachment), actively executingself-replicating: propagate itself to other hosts, usersWorm:infection by passively receiving object that gets itself executedself- replicating: propagates to other hosts, usersSapphire Worm: aggregate scans/sec in first 5 minutes of outbreak (CAIDA, UWisc data)

Denial of service attacksattackers make resources (server, bandwidth) unavailable to legitimate traffic by overwhelming resource with bogus trafficselect targetbreak into hosts around the network (malware)

send packets toward target from compromised hoststarget

Sniff, modify, delete your packetsPacket sniffing: broadcast media (shared Ethernet, wireless)promiscuous network interface reads/records all packets (e.g., including passwords!) passing byABCEthereal software is a (free) packet-sniffer (maybe used for lab experiments)

Masquerade as youIP spoofing: send packet with false source addressABC

Masquerade as youIP spoofing: send packet with false source addressrecord-and-playback: sniff sensitive info (e.g., password), and use laterpassword holder is that user from system point of viewABCsrc:B dest:A user: B; password: foo

Network Securitychapter 8: focus on securitycrypographic techniques: obvious uses and not so obvious usesprovides challenging issues, esp. for emerging mobile networks

Chapter 1: roadmap1.1 What is the Internet?1.2 Network edge end systems, access networks, links1.3 Network core circuit switching, packet switching, network structure1.4 Delay, loss and throughput in packet-switched networks1.5 Protocol layers, service models1.6 Networks under attack: security1.7 History

Internet History1961: Kleinrock - queueing theory shows effectiveness of packet-switching1964: Baran - packet-switching in military nets1967: ARPAnet conceived by Advanced Research Projects Agency1969: first ARPAnet node operational

1972: ARPAnet public demonstrationNCP (Network Control Protocol) first host-host protocol first e-mail programARPAnet has 15 nodes1961-1972: Early packet-switching principles

Internet History1970: ALOHAnet satellite network in Hawaii1974: Cerf and Kahn - architecture for interconnecting networks1976: Ethernet at Xerox PARCate70s: proprietary architectures: DECnet, SNA, XNAlate 70s: switching fixed length packets (ATM precursor)1979: ARPAnet has 200 nodesCerf and Kahns internetworking principles:minimalism, autonomy - no internal changes required to interconnect networksbest effort service modelstateless routersdecentralized controldefine todays Internet architecture1972-1980: Internetworking, new and proprietary nets

Internet History1983: deployment of TCP/IP1982: smtp e-mail protocol defined 1983: DNS defined for name-to-IP-address translation1985: ftp protocol defined1988: TCP congestion controlnew national networks: Csnet, BITnet, NSFnet, Minitel100,000 hosts connected to confederation of networks

1980-1990: new protocols, a proliferation of networks

Internet HistoryEarly 1990s: ARPAnet decommissioned1991: NSF lifts restrictions on commercial use of NSFnet (decommissioned, 1995)early 1990s: Webhypertext [Bush 1945, Nelson 1960s]HTML, HTTP: Berners-Lee1994: Mosaic, later Netscapelate 1990s: commercialization of the Web

Late 1990s 2000s:more killer apps: instant messaging, P2P file sharingnetwork security to forefrontest. 50 million host, 100 million+ usersbackbone links running at Gbps

1990, 2000s: commercialization, the Web, new apps

Internet History2007:~500 million hostsVoice, Video over IPP2P applications: Napster, BitTorrent (file sharing) Skype (VoIP), PPLive (video)more applications: YouTube, gaming, social networkingwireless, mobility, networked embedded sensors,

Introduction: SummaryCovered a ton of material!Internet overviewwhats a protocol?network edge, core, access networkpacket-switching versus circuit-switchingInternet structureperformance: loss, delay, throughputlayering, service modelssecurityhistoryYou now have: context, overview, feel of networkingmore depth, detail to follow!

Probability BackgroundDiscrete random variables:

where E[X] is the expected (or mean) value2nd moment:

Continuous random variables:

where F[x] is the cumulative distribution, f(y) is the probability density function, F[-]=0, F[]=1Variance: Var[X]=E[(X-E[X])2]=E[X2]-(E[X])2Standard deviation

Bernoulli experiment:probability of success p, failure q=1-pGeometric distribution:X is the number of (independent identically distributed i.i.d.) Bernoulli experiments to get successPr[X=k]=qk-1p (1st k-1 failures then success)E(X)=kPr[X=k]=1/pp=0.1, E(X)=1/p=10

Binomial distribution:x is the number of successes in n Bernoulli experiments/trials

E[X]=np

Exponential distribution:F[x]=1-e-x, f(x)=e-x, Pr[X>x]=1-F[x]=e-x, E[X]=1/

Poisson Distribution:Pr[X=k]= (k/k!) e-,E[X]=Var[X]= Used in queuing theory:Pr[k items arriving in T interval]= ((T)k/k!) e-T,Expected number of items to arrive in T=T, where is the rate of arrival

Poisson processes are used in M/M/1 and M/D/1 queuing modelsInter-arrival times TaPr[Ta

Autocorrelation function R(t1,t2) is a measure of the relationship between the instances of the stochastic process at time t1 & t2 [x(t1) & x(t2)]R(t1,t2)=E[x(t1).x(t2)]A related measure is the autocovariance C(t1,t2)=R(t1,t2)-(t1).(t2), where (t) is the mean of the stochastic processAutocorrelation measures the degree of dependence between instances of the stochastic process If R0 as t2-t1 is large no correlation between the different instants short memory processIf R is substantial for large t, then there is high correlation between values and this is considered a long memory process

Two simple multiple access control techniques.

Each mobiles share of the bandwidth is divided into portions for the uplink and the downlink. Also, possibly, out of band signaling.

As we will see, used in AMPS, GSM, IS-54/136