multiple access (lecture notes)

ECE 533 – Advanced Computer Communication Networks

Multiple Access

1

Multiple Access• Shared transmission medium

• A receiver can hear multiple transmitters• A transmitter can be heard by multiple receivers

• The major problem with multiple access is allocating the channel between the users; nodes do not know when the other nodes have data to send• Need to coordinate transmissions

2

Examples of Multiple Access Channels

• Local area networks (LANs)• Traditional Ethernet• Recent trend to non-‐multi-‐access LANs

• Satellite channels

• Wireless radio

Eytan Modiano

Slide 3

Examples of Multiple Access Channels

• Local area networks (LANs)

– Traditional Ethernet

– Recent trend to non-multi-access LANs

• Satellite channels

• Multi-drop telephone

• Wireless radio

NET

DLC

PHY

MAC

LLC

• Medium Access Control (MAC)

– Regulates access to channel

• Logical Link Control (LLC)

– All other DLC functions

• Medium Access Control (MAC)• Regulates access to channel

• Logical Link Control (LLC)• All other functionalities

3

Approaches to Multiple Access• Fixed Assignment (TDMA, FDMA, CDMA)

• Each node is allocated a fixed fraction of bandwidth• Equivalent to circuit switching• Very inefficient for low duty factor traffic

• Contention systems • Polling

• Reservations and Scheduling

• Random Access

4

Random Access: Aloha

Single receiver, many transmitters

Eytan Modiano

Slide 5

Aloha

Single receiver, many transmitters

Receiver

Transmitters

....

E.g., Satellite system, wirelessE.g., satellite systems, wireless

5

Random Access: Slotted Aloha• Time is divided into slots of one packet duration

• E.g., fixed size packets • When a node has a packet to send, it waits until the start of the

next slot to send it• Requires synchronization

• If no other nodes attempt transmission during that slot, the transmission is successful• Otherwise “collision”• Collided packet are retransmitted after a random delay

Eytan Modiano

Slide 6

Slotted Aloha

• Time is divided into “slots” of one packet duration

– E.g., fixed size packets

• When a node has a packet to send, it waits until the start of the next slot tosend it

– Requires synchronization

• If no other nodes attempt transmission during that slot, the transmissionis successful

– Otherwise “collision”

– Collided packet are retransmitted after a random delay

6

Slotted AlohaAssumptions

• Poisson external arrivals • No capture

• Packets involved in a collision are lost• Capture models are also be possible

• Immediate feedback• Idle (0), Success (1), Collision (e)

• If a new packet arrives during a slot, transmit in next slot• If a transmission has a collision, node becomes backlogged

• While backlogged, transmit in each slot with probability qruntil successful

• Infinite nodes where each arriving packet arrives at a new node• Equivalent to no buffering at a node (queue size = 1)• Pessimistic assumption gives a lower bound on Aloha

performance7

Slotted AlohaMarkov Chain

• State (n) of system is number of backlogged nodes • pi,i-‐1 = probability of one backlogged attempt and no new arrival• Pi,i = probability of one new arrival and no backlogged attempts

or no new arrival and no success• pi,i+1 = probability of new arrival and one or more backlogged

attempts • pi,i+j = probability of j new arrivals and one or more backlogged

attempts or j+1 new arrivals and no backlogged attempts• Steady state probabilities do not exists

• Backlog tends to infinity à system unstable

Eytan Modiano

Slide 8

0 1 2 3

P

P

PP34

10

03

13

Markov Chain for Slotted Aloha

• State (n) of system is number of backlogged nodes.

Pi,i-1 = prob. of one backlogged attempt and no new arrival

pi,i = prob. of one new arrival and no backlogged attempts or no newarrival and no success

pi,i+1 = prob of one new arrival and one or more backlogged attempts

pi,i+j = Prob. Of j new arrivals and one or more backlogged attempts or j+1new arrivals and no backlogged attempts

• Steady state probabilities do not exists

– Backlog tends to infinity => system unstable

– More later 8

Slotted Aloha• Let g(n) be the attempt rate (the expected number of packets

transmitted in a slot) in state n

g(n) = λ + nqr

• The number of attempted packets per slot in state n is approximately a Poisson random variable of mean g(n)

• P(m attempts) = g(n)me-‐g(n)/m!• P(idle) = probability of no attempts in a slot = e-‐g(n)• P(success) = probability of one attempt in a slot = g(n) e-‐g(n)• P(collision) = P(two or more attempts) = 1 – P(idle) –

P(success)

9

Slotted AlohaThroughput

• The throughput is the fraction of slots that contain a successful transmission = P(success) = g(n) e-‐g(n)• When system is stable, throughput must also equal the external

arrival rate (λ)

Eytan Modiano

Slide 10

Throughput of Slotted Aloha

• The throughput is the fraction of slots that contain a successful transmission =P(success) = g(n)e-g(n)

– When system is stable throughput must also equal the external arrival rate (λ)

– What value of g(n)maximizes throughput?

– g(n) < 1 => too many idle slots

– g(n) > 1 => too many collisions

– If g(n) can be kept close to 1, an external arrival rate of 1/e packets per slot can besustained

d

dg(n)g(n)e!g( n)

= e!g( n) ! g(n)e!g( n)= 0

" g(n) = 1

" P(success) =g(n)e!g( n) = 1/ e# 0.36

• What value of g(n) maximizes throughput?

• If g(n) < 1 à too many idle slots• If g(n) > 1 à too many collisions

ddg(n)

g(n)e−g(n) = e−g(n) − g(n)e−g(n) = 0

⇒ g(n) =1⇒ P(success) = g(n)e−g(n) =1/ e ≈ 0.36

• If g(n) can be kept close to 1, an external arrival rate of 1/e packets per slots can be sustained 10

Slotted AlohaInstability of Slotted Aloha

• If backlog increases beyond unstable point (bad luck), then it tends to increase without limit and departure rate drops to 0

• Drift in state n, D(n) is the expected change in backlog over one time slots• D(n) = λ -‐ g(n) e-‐g(n)

Eytan Modiano

Slide 11

Instability of Slotted Aloha

• If backlog increases beyond unstable point (bad luck) then it tends toincrease without limit and the departure rate drops to 0

• Drift in state n, D(n) is the expected change in backlog over one time slot

– D(n) = λ - P(success) = λ - g(n)e-g(n)

11

Slotted AlohaStabilizing Slotted Aloha

• Choosing qr small increases the backlog at which instability occurs (since g(n) = λ + nqr), and also increases delay (since mean retry time is 1/qr)

• Solution: estimate the backlog (n) from past feedback• Given the backlog estimate, choose qr to keep g(n) = 1

Assume all arrivals are immediately backlogged g(n) = nqr, P(success) = nqr(1-‐qr)n-‐1To maximize P(success) choose qr=min{1,1/n}

• When the estimate of n is perfect: Idles occur with probability 1/e, Successes with 1/e, and Collisions with 1-‐2/e

• When the estimate is too large, too many idle slots occur• When the estimate is too small, too many collisions occur

• Nodes can use feedback information to make estimates• A good rule is increase the estimate of n on each collision, and to

decrease it on each idle slot or successful slot

12

Slotted AlohaStabilized Slotted Aloha

• Assume all arrivals are immediately backlogged • g(n) = nqr = attempt rate • P(success) = nqr(1-‐qr)n-‐1

• for max throughput set g(n) = 1 à qr=min{1,1/n’}, where n’ is the estimate of n

• Let nk = estimate of backlog after kth slot

nk+1 =max{λ,nk +λ −1}nk +λ +1/ (e− 2)"#$

upon idle or success

upon a collision

• Can be shown to be able to stable for λ < 1/e

13

Slotted AlohaTDM vs Slotted Aloha

• Aloha achieves lower delays when arrival rates are low• TDM results in very large delays with large number of of

users, while Aloha is independent of the number of users

Eytan Modiano

Slide 14

TDM vs. Slotted Aloha

• Aloha achieves lower delays when arrival rates are low

• TDM results in very large delays with large number of users, while Aloha isindependent of the number of users

0 0.2 0.4 0.6 0.8

ARRIVAL RATE

4

8

DELAY

ALOHA

TDM, m=8

TDM, m=16

14

Random Access: Pure (unslotted) Aloha• New arrivals are transmitted immediately (no slots)

• No need for synchronization• No need for fixed length packets

• A backlogged packet is retried after an exponentially distributed random delay with some mean 1/x

• The total arrival process is a time varying Poisson process of rate g(n) = λ + nx (n = backlog, 1/x = average time between retransmissions)

• Note that an attempt suffers a collision if the previous attempt is not yet finished (ti-‐ti-‐1 < 1) or the next attempt starts too soon (ti+1-‐ti < 1)

Eytan Modiano

Slide 15

Pure (unslotted) Aloha

• New arrivals are transmitted immediately (no slots)

– No need for synchronization

– No need for fixed length packets

• A backlogged packet is retried after an exponentially distributed randomdelay with some mean 1/x

• The total arrival process is a time varying Poisson process of rate g(n) = λ +nx (n = backlog, 1/x = ave. time between retransmissions)

• Note that an attempt suffers a collision if the previous attempt is not yetfinished (ti-ti-1<1) or the next attempt starts too soon (ti+1-ti<1)

t t t1 2 3

t4

t5

Retransmission

New Arrivals

43! !

Collision

15

Pure (unslotted) AlohaThroughput

• An attempt is successful if the inter-‐attempt intervals on both sides exceed 1 (for unit duration packets) • P(success) = e-‐g(n) e-‐g(n) = e-‐2g(n)• Throughput (success rate) = g(n) e-‐2g(n)

• For max throughput at g(n) = 1/2, Throughput = 1/2e ≈ 0.18

• Stabilization issues are similar to slotted aloha• Advantages of unslottedaloha are simplicity and possibility

of unequal length packets

16

Random Access: CSMACSMA: Carrier Sense Multiple Access

• In certain situations nodes can hear each other by listening to the channel “carrier sensing”

• CSMA: Polite version of Aloha • Nodes listen to the channel before they start transmission

• Channel idle à Transmit• Channel busy àWait (join backlog)

• When do backlogged nodes transmit? • When channel becomes idle backlogged nodes attempt

transmission with probability qr• Persistent protocol, qr = 1• Non-‐persistent protocol, qr < 1

17

CSMA• Let τ = the maximum propagation delay on the channel

• When a node starts/stops transmitting, it will take this long for all nodes to detect busy/idle

• For initial understanding, view the system as slotted “mini-‐slots” of duration equal to the maximum propagation delay • Normalize the mini-‐slot duration β=τ/Dtp and packet

duration = 1

Eytan Modiano

Slide 3

CSMA

• Let τ = the maximum propagation delay on the channel

– When a node starts/stops transmitting, it will take this long for all nodes todetect channel busy/idle

• For initial understanding, view the system as slotted with "mini-slots" ofduration equal to the maximum propagation delay

– Normalize the mini-slot duration to β = τ/Dtp and packet duration = 1

• Actual systems are not slotted, but this hypothetical system simplifies theanalysis and understanding of CSMA

! <"">

minislotspacket

<----------- 1 ---------------->

• Actual systems are not slotted, but this hypothetical system simplifies the analysis and understanding of CSMA

18

Slotted CSMARules

• When a new packet arrives • If current mini-‐slot is idle, start transmitting in the next mini-‐slot• If current mini-‐slot is busy, node joins backlog• If a collision occurs, nodes involved in collision become

backlogged

• Backlogged nodes attempt transmission after an idle mini-‐slot with probability qr < 1 (non-‐persistent)• Transmission attempts only follow an idle mini-‐slot• Each “busy-‐period” (success or collision) is followed by an idle slot

before a new transmission can begin

• Time can be divided into epochs: • A successful packet followed by and idle mini-‐slot (duration = β+1)• A collision followed by an idle mini-‐slot (duration = β+1) • An idle mini slot (duration = β) 19

Slotted CSMAAnalysis

• Let the state of the system be the number of backlogged nodes

• Let the state transition times be the end of idle slots • Let T(n) = average amount of time between state transitions when

the system is state n T(n) = β + (1 – e-‐λβ(1-‐qr)n)

when qr is small (1-‐qr)n ≈ e-‐qrnà T(n) = β + (1 – e-‐λβ-‐nqr)• At the beginning of each epoch, each backlogged node

transmits with probability qr• New arrivals during the previous idle slot are also

transmitted• With backlog n, the number of packets that attempt

transmission at the beginning of an epoch is approximately Poisson with rate

g(n) = λβ + nqr 20

Slotted CSMAAnalysis

• The probability of success (per epoch) is

Ps = g(n)e-‐g(n)

• The expected duration of an epoch is approximately

T(n) ≈ β + (1 – e-‐g(n))

• Thus, the success rate per unit time is

λ < departure rate = g(n)e−g(n)

β +1− e−g(n)

21

Slotted CSMAMaximum Throughput

• The optimal value of g(n) can again be obtained

• Tradeoff between idle slots and time wasted on collisions • High throughput when β is small • Stability issues similar to Aloha (less critical)

g(n) ≈ 2β λ <1

1+ 2β

Eytan Modiano

Slide 7

Maximum Throughput for CSMA

• The optimal value of g(n) can again be obtained:

• Tradeoff between idle slots and time wasted on collisions

• High throughput when β is small

• Stability issues similar to Aloha (less critical)

Arrival rate

Departure rate1-!2!

!!2

g(n) = + nq"!r

g(n) ! 2" ! <1

1+ 2"

22

Unslotted CSMA• Slotted CSMA is not practical

• Difficult to maintain synchronization • Mini-‐slots are useful for understanding but not critical

to the performance of CSMA

• Unslotted CSMA will have slightly lower throughput due to increased probability of collision

• Unslotted CSMA has a smaller effective value of β than slotted CSMA • Essentially β becomes average instead of maximum

propagation delay

23

Random Access: CSMA/CD and Ethernet

• CSMA with Collision Detection (CD) capability• Nodes able to detect collisions • Upon detection of a collision nodes stop transmission

• Reduce the amount of time wasted on collisions• Protocol:

• All nodes listen to transmissions on the channel• When a node has a packet to send:

• Channel idle à Transmit• Channel busy à Wait a random delay (binary exponential

back-‐off)• If a transmitting node detects a collision it stops

transmission • Waits a random delay and tries againEytan Modiano

Slide 9

CSMA/CD and Ethernet

• CSMA with Collision Detection (CD) capability

– Nodes able to detect collisions

– Upon detection of a collision nodes stop transmission

Reduce the amount of time wasted on collisions

• Protocol:

– All nodes listen to transmissions on the channel

– When a node has a packet to send:

Channel idle ⇒ Transmit

Channel busy ⇒ wait a random delay (binary exponential back-off)

– If a transmitting node detects a collision it stops transmission

Waits a random delay and tries again

Two way cable

WS WS WS WS WS WS

24

CSMA/CD and EthernetTime to detect collision

• A collision can occur while the signal propagates between the two nodes

• It would take an additional propagation delay for both users to detect the collision and stop transmitting

• It τ is the maximum propagation delay on the cable, then if a collision occurs, it can take up to 2τ seconds for all nodes involved in the collision to detect and stop transmission

Eytan Modiano

Slide 10

Time to detect collisions

• A collision can occur while the signal propagates between the two nodes

• It would take an additional propagation delay for both users to detect the collisionand stop transmitting

• If τ is the maximum propagation delay on the cable then if a collision occurs, it cantake up to 2τ seconds for all nodes involved in the collision to detect and stoptransmission

WS WSττ = prop

delay

25

CSMA/CD and EthernetApproximate model for CSMA/CD

• Simplified approximation for added insight

• Consider a slotted system with “mini-‐slots” of duration 2τ

• If a node starts transmission at the beginning of a mini-‐slot, by the end of the mini-‐slot either • No collision occurred and the rest of the transmission

will be uninterrupted• A collision occurred, but by the end of the mini-‐slot the

channel would be idle again

• Hence a collision at most affects one mini-‐slot

Eytan Modiano

Slide 11

Approximate model for CSMA/CD

• Simplified approximation for added insight

• Consider a slotted system with “mini-slots” of duration 2τ

• If a node starts transmission at the beginning of a mini-slot, by the end of the mini-slot either

– No collision occurred and the rest of the transmission will be uninterrupted

– A collision occurred, but by the end of the mini-slot the channel would be idle again

• Hence a collision at most affects one mini-slot

2τ <−−>

Mini-slotspacket

<----------- 1 ---------------->

26

CSMA/CD and EthernetAnalysis of CSMA/CD

• Assume N users and that each attempts transmission during a free “mini-‐slot” with probability p • P includes new arrivals and retransmissions

• To maximize P[success];

P[i users attempt]=Ni!

"#

$

%&Pi (1−P)N−i

P[exactly 1 attempt]= P[succes]= NP(1−P)N−1

ddP[NP(1−P)N−1]= N(1−P)N−1 − N(N −1)P(1−P)N−2 = 0

⇒ Popt =1N

à Average attempt rate of one per slotà Notice the similarity to slotted Aloha

27


• Let X be the average number of slots per successful transmission

P[success]= NP(1−P)N−1 = 1− 1N

"

#$

%

&'N−1

Ps = limN→∞ P[success]=1e

P[X = i]= (1−Ps )i−1Ps

⇒ E[X]= 1Ps= e

• Once a mini-‐slot has been successfully captured, transmission continues without interruption

• New transmission attempts will begin at the next mini-‐slot after the end of the current packet transmission

28


• Let S be the average amount of time between successful packet transmissions

• Efficiency = DTp/S = DTp/(DTp+ τ + 2τ(e-‐1))

• Let β=τ/DTp à Efficiency ≈ 1/(1 + 4.4β) = λ < 1/(1 + 4.4β)

• Compare to CSMA without CD where

S = (e−1)2τ +DTp +τ

Idle/collisionmini-‐slots Packet transmission

time

Average time until start of next mini-‐slot

λ <1

1+ 2β

29

CSMA/CD and EthernetNotes on CSMA/CD

• Can be viewed as a reservation system where the mini-‐slot are used for making reservations for data slots

• In this case, Aloha is used for making reservations during the mini-‐slots

• Once a user captures a mini-‐slot it continues to transmit without interruptions

• In practice, of course, there are no mini-‐slots • Minimal impact on performance but analysis is more

complex

30

CSMA/CD and EthernetExamples

• Example: Ethernet• Transmission rate = 10 Mbps• Packet length = 1000 bits, DTp = 10-‐4 sec• Cable distance = 1 mile, τ = 5×10-‐4

à β = 5×10-‐2 and E = 80%

• Example: GEO Satellite – propagation delay 1/4 secondà β = 2500, and E ≈ 0%

• CSMA/CD only suitable for short propagation scenarios

• How is Ethernet extended to 100 Mbps?

• How is Ethernet extended to 1 Gbps? 31

Migration to Switched LANs• Traditional Ethernet

• Nodes connected with coax Long “runs” of wire everywhere• CSMA/CD protocol

• “Hub” Ethernet• Nodes connected to hubHub acts as a broadcast repeaterShorted cable “runs”, Useful for 100Mbps• CSMA/CD protocol• Easy to add/remove users• Easy to localize faults • Cheap cabling (twisted pair, 10baseT)

• Switched Ethernet• No CSMA/CDEasy to increase data rate (e.g., Gbit Ethernet)• Nodes transmit when they want• Switch queues the packets and transmits to destination • Typical switch capacity of 20-‐40 ports• Each node can now transmit at the full rate of 10/100

Gbps• Modularity: Switches can be connected to each other

using high rate portsEytan Modiano

Slide 17

Migration to switched LANs

WS WS WS WS WS WS

WS

WS

WS

WS

WS

WS

• Traditional Ethernet– Nodes connected with coax

Long “runs” of wire everywhere

– CSMA/CD protocol

• “Hub” Ethernet

– Nodes connected to hub Hub acts as a broadcast repeater

Shorted cable “runs”, Useful for 100 Mbps


– Easy to add/remove users

– Easy to localize faults

– Cheap cabling (twisted pair, 10baseT)

• Switched Ethernet

– No CSMA/CD Easy to increase data rate (e.g., Gbit Ethernet)

– Nodes transmit when they want

– Switch queues the packets and transmits todestination

– Typical switch capacity of 20-40 ports

– Each node can now transmit at the full rate of10/100/Gbps

– Modularity: Switches can be connected to eachother using high rate ports

WS

WS

WS

WS

WS

WS

Packet

Switch

Connect

To other

Switchs

Eytan Modiano

Slide 17


WS WS WS WS WS WS

WS

WS

WS

WS

WS

WS


















WS

WS

WS

WS

WS

WS

Packet

Switch

Connect

To other

Switchs

Eytan Modiano

Slide 17


WS WS WS WS WS WS

WS

WS

WS

WS

WS

WS


















WS

WS

WS

WS

WS

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Packet

Switch

Connect

To other

Switchs

32

Packet Multiple Access Summary• Latency: Ratio of propagation delay to packet transmission time

• GEO example: Dp = 0.5 sec, packet length = 1000 bits, R = 1 MbpsLatency = 500 à very high

• LEO example: Dp = 0.1 secLatency = 100 à still very high

• Over satellite channels data rate must be very low to be in a low latency environment

• Low latency protocols• CSMA, Polling, Token Rings, etc. • Throughput ≈ 1/(1+aα), α = latency, a = constant

• High latency protocols• Aloha is insensitive to latency, but generally low throughput à

very little delays• Reservations system can achieve high throughput à delays for

making reservations• Protocols can be designed to be a hybrid of Aloha and

reservations à Aloha at low roads, reservations at high roads33

multiple access (lecture notes)

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