Chap 4 Multiaccess Communication(Part 1)

Ling-Jyh Chen

Overview

Ethernet and Wi-Fi are both “multi-access” technologies Broadcast medium, shared by many hosts Simultaneous transmissions will result in collisions

Media Access Control (MAC) protocol required Rules on how to share medium

Media Access Control Protocols

Channel partitioning Divide channel into smaller “pieces” (e.g., time slots,

frequency) Allocate a piece to node for exclusive use E.g. Time-Division-Multi-Access (TDMA) cellular network

Taking-turns Tightly coordinate shared access to avoid collisions E.g. Token ring network

Contention Allow collisions “recover” from collisions E.g. Ethernet, Wi-Fi

Contention Media Access Control Goals

Share medium If two users send at the same time, collision results in no

packet being received (interference) If no users send, channel goes idle Thus, want to have only one user send at a time

Want high network utilization TDMA doesn’t give high utilization

Want simple distributed algorithm no fancy token-passing schemes that avoid collisions

Evolution of Contention Protocols

Developed in the 1970s for a packet radio networkAloha

SlottedAloha

Improvement: Start transmission only at fixed times (slots)

CSMA

CSMA = Carrier Sense Multiple AccessImprovement: Start transmission only if no transmission is ongoing

CD = Collision Detection

Improvement: Stop ongoing transmission if a collision is detected (e.g. Ethernet)

CSMA/CD

4.2 Idealized slotted multiaccess model

m transmitting nodes and one receiver

1. Slotted systema) packets are of the same length

b) each packet requires one time unit for transmission

c) the reception of each packet starts at an integer time and ends before the next integer time

2. Poisson Arrivalsoverall arrival rate of the system: λindividual rate of each node: λ/m

3. Collision or Perfect Receptiona) If just one node sends a packet in a given

slot, the packet is correctly received.b) If two or more nodes send a packet in a

given time slot, then there is a collision and the receiver obtains no information about the contents or the source of the transmitted packets.

4. 0,1,e Immediate Feedback Assuming each node obtains feedback from

the receiver at the end of each slot

5. Retransmission of Collisions Assuming each packet involved in a collision

must be retransmitted in some later slot. A node with a packet that must be

retransmitted is said to be backlogged.

6. Two addition assumptionsa. No buffering

If one packet at a node is currently waiting for transmission or colliding with another packet during transmission, new arrivals at that node are discarded and never transmitted.

This assumption provides the lower bound to the delay for systems with buffering and flow control!

b. Infinite set of nodes (m=∞): This assumption provides the upper bound!

Slotted ALOHA

The basic idea: Each unbacklogged node simply transmit a

newly arriving packet in the first slot after packet arrival.

Slotted ALOHA risks occasional collisions but achieves very small delay if collisions are rare.

Contrast to TDM systems, which avoids collisions at the expense of large delays.

Collisions in S-ALOHA

1.1 1.2

TransmissionDelay

Station 1

2.1Station 2

3.1 3.2

Station 3

Broadcastchannel

2.2

1.3

CompleteCollision

Slotted ALOHA (cont.)

When a collision occurs, each node sending one of the colliding packets discovers the collision at the end of the slot and becomes backlogged.

Such nodes wait for some random number of slots before retransmitting.

Slotted ALOHA (cont.)

Using infinite-node assumption, the total number of retx and tx in a given slot is a Poisson random variable with parameter G, where G> λ.

The prob. of a successful transmission in a slot is

In equilibrium, the arrival rate, λ, should be the same as the departure rate, Ge-G.

GG

GeeG

nP

!1

]1[1

Slotted ALOHA (cont.)

Using GNUPlotset xr [0:5]plot x*exp(-x)

Slotted ALOHA (cont.)

The MAX departure rate occurs at G=1 and is 1/e ≈ 0.368.

If G<1, too many idle slots are generated. If G>1, too many collisions are generated.

Slotted ALOHA (cont.)

Markov Chain for Slotted ALOHA State: the number of backlogged packets Increases by the number of new arrivals

transmitted by unbacklogged nodes Decreases by one each time if a packet is

transmitted successfully.

Slotted ALOHA (cont.)

qr: the prob. of a backlogged node retx in the next slot i.e., the number of slots from a collision until a

given node involved in the collision retx is a geometric R.V. having value i>1 with prob. qr(1-qr)i-1

qa: the prob. of an unbacklogged node transmits a packet in the given slot i.e. qa=1-e-λ/m

Slotted ALOHA (cont.)

Qa(i, n): the prob. that i unbacklogged nodes transmit packets in a given slot

Qr(i, n): the prob. that i backlogged nodes transmit.

ir

inrr

ia

inmaa

qqi

nniQ

qqi

nmniQ

)1(),(

)1(),(

Slotted ALOHA (cont.)

1),,1(),0(

0)],,1(1)[,0(),0(),1(

1)],,0(1)[,1(

)(2),,(

,

inQnQ

inQnQnQnQ

inQnQ

nminiQ

P

ra

rara

ra

a

inn

),1(),0(),0(),1( nQnQnQnQP rarasucc

Slotted ALOHA (cont.)

Dn: “drift” in state n, i.e. the expected change in backlog over one slot time

G(n): the expected number of attempted transmissions in a slot

If qa and qr are small, )()( nGsucc enGP

Slotted ALOHA (cont.)

The “drift” is the difference between the throughput curve (Ge-G) and the straight line:

Slotted ALOHA (cont.)

Using infinite-node assumption:

Using no-buffering assumption:

4.2.3 (optional)

rnqnG )(

ra nqqnmnG )()(

Unslotted ALOHA

Unslotted ALOHA (a.k.a. Pure ALOHA) was the precursor to slotted ALOHA.

In Pure ALOHA, each node transmits a new packet immediately upon receiving, rather than waiting for a slot boundary.

If a packet is involved in a collision, it is retransmitted after a random delay.

Collisions in (Pure) ALOHA

1.1 1.2

TransmissionTime

(F)

Station 1

2.1Station 2

3.1 3.2Station 3

Broadcastchannel

2.2

1.3

CompleteCollision

PartialCollision

Unslotted ALOHA (cont.)

Frame which collideswith start of red frame

Frame

t0-F t0 t0+F

VulnerablePeriod of red frame

Time

Frame which collideswith end of red frame

A frame (red frame) will be in a collision if and only if another transmission begins in the vulnerable period of the frame

Vulnerable period has the length of 2 frame times

Unslotted ALOHA (cont.)

Since arrivals are independent, Psucc=e-2G

Since attempted transmissions occur at rate G(n), the throughput = Ge-2G

The MAX throughput of a Pure ALOHA system = 1/(2e), achieved when G=0.5.

If λ is very small and the mean retx time is very large, the system can be expected to run for long periods w/o major backlog buildup.

The main adv. of pure ALOHA is that it can be used with variable-length packets.

Comparison of ALOHA and S-ALOHA

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

R

Thr

ough

put

(ALO

HA

)

Slotted ALOHA: Re-R

Pure ALOHA: Re-2R

Ideal (no collisions): R