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Lecture on Multi Access Communication

- For many applications (e.g.,satellite, radio

broadcast, Ethernet), users share the same

channel. The received signal is the sum of the

transmitted signal from the source that is

intended, the transmitted signals from several

other sources that are not intended, and noises. - Data Link Control Layers job is to construct a

reliable virtual bit pipe. To accomplish that

job, we need another layer between the DLC Layer

and the Physical Layer. We call this Medium

Access Control (MAC) Layer.

DLC

Layer 2

MAC

Physical

Layer 1

Queuing Problem in Multiple Access

- Each node has a queue of packets to be

transmitted and channel is a common and shared

resource (i.e., server). - In the above model,
- Information is distributed.
- The server does not know which nodes contain

packets. - Nodes are unaware of packets at other nodes.

Node 1

Node i1

Channel

Node 2

Node i2

. . .

. . .

Node i

Node m

Extreme Solutions

- We may consider the following two extreme

solutions. The actual solution will be somewhere

in between. - Free for all multiple access.
- Nodes send packets whenever they need

to, hoping for no interference or collision. - An important question is how and when to

retransmit when collisions occur. - Scheduled (dynamically or not) multiple access.
- A certain schedule is given for packet

transmission in order to avoid a collision. An

important question here is how to fix the

scheduling. We must also consider how to transmit

to the nodes the information about the schedule.

Example of Multiple Access Media

Satellite

- 1. Satellite Channel
- Separate antennas are needed for different

geographical areas. We may consider for one area,

TDM can be used while FDM can be used for others.

However, this is very inefficient use of the

expensive channel. We can reduce the delay and

increase utilization by sharing the medium on a

per demand basis. We, however, need a mechanism

of mediating the potential collisions.

Area 1

Area k

Area 1

Ground Stations

- 2. Multi drop telephone lines.
- This is also known as party lines.
- 3.Multi tapped bus.
- Each node can receive signals sent by other

nodes. Simultaneous transmissions causes a

collision.

Primary

Secondaries

- 4. Packet radio network
- Each node is in the reception range of some sub

network of nodes. For example, the nodes marked

with can transmit simultaneously. A mechanism

to mediate collisions is complex.

Example of Multiple Access System Slotted Aloha

Network

- Basic Assumptions
- Each packet requires one time unit or slot for

transmission. - There are m nodes each generating packets

according to a Poisson process with rate ?/m. - Over the defined medium, there are only two

possibilities collision or perfect reception. - There is a mechanism for immediate feedback.

Immediately after any time slot, every node

learns the results of the previous time slot

(0,1,e) where 0 implies no packet was

transmitted, 1 implies one packet was

transmitted, and e implies there was a collision. - Each packet involved in a collision will be

retransmitted later until it is received

correctly. - 6. A node with packets for retransmission is said

to be back logged. One of the following two is

true - If a packet is waiting for transmission or

collided with another packet(s), all new arrivals

are lost. - There exists an infinite set of nodes and new

arrivals arrive a new node each time.

slot

t

Slotted Aloha

- Each node sends its packet in the first slot

after the packet arrival. - Slotted Aloha will potentially reduce the delay.
- Slotted Aloha has a significant of collision

risk. - TDM has on the average m/2 slots of delay.
- When a collision occurs, the nodes involved will

know at the end of slot, and become backlogged. - Those collided nodes cannot re-send packets

immediately since it creates a certain

collision. - It is required to wait for a random number of

slots and retransmit.

Analysis

- Assume the infinite node case, i.e., 6b.
- Consider the total number of packets transmitted

in the next time slot. - The combine new arrival is Poisson with rate ?.
- There are also retransmissions from backlogged

nodes. - Assume that the total number of packets to be

transmitted in the next time slot to be Poisson

with rate G (gt?). - The transmission is successful only if there is

exactly one packet transmitted in a time - slot, and therefore,
- because the transmission in the next time slot is

Poisson with rate G, i.e.,

- At equilibrium,
- Arrival rate departure rate
- Maximum

throughout 1/e ? 0.368 - Problem with this approach is that G is a

function of the number of backlogged nodes, which

is not reflected in this model.

More Precise Model

- Assume the no buffering case of 6a.
- Define
- qr probability that a backlogged node

retransmit in a time slot - X number of slots from collision until a

backlogged node retransmits - n number of backlogged nodes
- m total number of nodes generating packets
- m-n nodes are not backlogged, and they will

transmit any fresh arrival takes place before the

beginning of the next time slot.

- Let the probability that an unbacklogged node has

a packet be qa. - Since n is the number of backlogged nodes of the

system (i.e., the state), from one to next time

slot, n is increased by the number of new

arrivals and is decreased by at most one if one

packet is transmitted successfully.

- We can solve the above equations for pn where pn

is the steady state probability of being in state

n.

0

1

2

3

- We want to determine whether or not the system is

stable. - (The term stability will be defined later.)
- We want qr to be large to avoid unnecessary

delays. - If nqr gtgt1, then collision will occur in every

slot and the system remains heavily - backlogged.
- Determining qr involves tradeoffs.
- Define
- Dn expected changes in the number of backlogged

node in one slot - Psucc expected number of successful

transmissions in one slot - Then, since

(m-n)qa is the expected number of new arrivals in

one time slot. Therefore, Dn can be viewed as

the expected drift of the state from n in one

time slot.

- Let G(n) be the packet transmission attempt rate,

i.e., at state n, the sum of new arrival rate and

the retransmission rate from the backlogged

nodes. - G(n) expected number of attempted

transmissions in a time slot - when the system is

in state n. - (m-n)qa nqr ()
- Using () and () together, Psucc G(n)e-G(n).
- In the above, we used the fact that

for small x. - Then, Probability of idle slot .

- One desired stable state, one unstable state, and

one undesired stable state. - Maximum Psucc maximum departure rate 1/e

- If we use assumption 6b instead,
- One desired stable state, and one unstable state.

Stability Problem with Slotted Aloha

- If qr is increased, retransmission delay is

reduced. - Attempt rate G(n)(m-n)qa nqr increases with n

faster for a larger qr . - G(n) scale is contracted.
- Fewer packets are required to exceed unstable

equilibrium. - If qr is decreased, retransmission delay

increases. - ?G(n) scale is expanded.
- Only one stable point remains.
- Backlog is a large fraction of m.
- Large delay
- Many packets may be discarded.

Definitions

- Definition
- A multi access system is stable for a given

arrival rate if the average delay per packet is

finite. - Definition
- Maximum throughput is the least upper bound of

arrival rates for which system is stable. - Slotted Aloha is unstable for any rate greater

than zero,. Therefore, the maximum throughput of

Slotted Aloha is zero.

Stabilizing Slotted Aloha Pseudo-Bayesian

Algorithm

- New arrivals are considered backlogged upon

arrival. If there are n backlogged packets, the

attempt rate is . - Probability of successful transmission
- Algorithm keeps as estimate of backlog n in

the beginning of each slot. - Backlogged packets are then transmitted with

probability - This makes Gnqr to be near 1.
- Updating
- estimated backlog in beginning of kth slot.

Note

- Adding ? to previous backlog is due to new

arrivals. - max is to ensure the estimate is never less

than the number of new arrivals. - For successful transmission 1 is subtracted from

previous backlog due to successful departure. - Subtract 1 for idle to avoid too many idle

slots. - Add (e-2)-1 on collision to avoid too many

collisions. - For large , if n, each of n backlogged

nodes retransmits with probability - By Poisson approximation

Delay Analysis

- Define Wi be the delay from the arrival of ith

packet until the beginning of ith successful

transmission. In FIFO, Wi is the queuing delay of

ith arrival. - Average of Wi over all i is the average delay.
- Ri residual time to the beginning of next slot.
- ni number of backlogged packets just before ith

arrival. - tj time interval from end of (j-1) successful

transmission to end of jth success. - yi time until beginning of next successful

transmission after those ni transmissions. - For each interval tj, backlog is at least two

(i.e., ni ith arrival) - Thus each slot is successful with probability

1/e. - (Assume that Psucc 1/e for n ? 2 and Psucc 1

for n1)

delay

Splitting Algorithms

- Most often collision is between two users.
- It is advantageous to inhibit new arrivals from

transmission until a collision is resolved. - To resolve a collision, each node involved in

the collision would retransmit in the next - slot with probability 1/2.
- Collision is resolved in
- Two slots with probability 1/2.
- Three slots with probability 1/4.
- Four slots with probability 1/8.
- i slot with probability 2-(i-1).
- Expected number of slots for sending two packets

equals 3 - throughout for this period 2/3.
- In essence, the set of colliding nodes are split

into two sets those that transmit - in the next slot and those that do not.
- Splitting Algorithms

Tree Algorithm

- Splitting algorithm has a tree structure when

collision occurs. - All nodes not involved in collision go into

waiting mode. - The first subnet transmits in the next slot.
- If this transmission is successful or idle, the

second subject transmits in the following slot. - If collision occurs in the retransmission, then

the subset is split and so on.

LRRL success

success LRRR

idle LRL

- Mechanics
- A counter is set to 0 or 1 at the beginning of a

collision for each packet. - If it is 0, packet is transmitted.
- If it is non zero, it is incremented by 1 for

each collision, and decreased by 1 for each

success or idle.

collision

LRR

success

collision

LL

LR

idle

collision

R

L

collision

Issue

- What do we do with packets that arrived while

collision was being resolved? - A Collision Resolution Period (CRP) starts as

soon as one ends. If many packets arrived in the

meantime, they will collide immediately and have

to be split and so on. - Solution At the end of a CRP, split the set of

nodes with new arrivals into j subjects with j

such that the expected number of packets in each

subsets is slightly larger than 1. - These new packets are now transmitted via a tree

structure. - Maximum throughput for optimized j 0.43 packets

per slot.

Improvement for Tree Algorithm

- The splitting at node A creates two subsets one

of which is empty (i.e, left subset). - This causes another collision in the next time

slot (at right subset). - 1st Improvement
- Omit transmission of the 2nd subset after an idle

time slot, preceded by a collision. Split the 2nd

subset before transmission. Throughput 0.46

packets per slot

idle

collision

success

collision

collision

node A

idle

collision

2nd Improvement

- Suppose one collision follows another. Let
- x number of packets in the first collision
- xr number of packets in the right subset
- xl number of packets in the left subset
- Assume x xr xl is Poisson.

2nd Improvement When there is a collision,

regard the 2nd subset as new arrivals that have

not been involved in collision previously.

Unslotted Aloha

- There is no slot for timing.
- Packets are transmitted as they arrive.
- Collided packets are re-transmitted a random

time later. - Assume infinite number of nodes (6b Assumption).
- Let ? time until attempted retransmission.
- Suppose ? is exponential with probability density

function xe-?x where x is node retransmission

attempt rate. - Let ? overall Poisson arrival rate.
- If n nodes are backlogged, there is also an

arrival of rate nx from backlogged nodes - which we assume to be Poisson.
- Total attempted transmission is Poisson with rate

G(n) ? nx.

Let ?i duration of interval between ith and

(i1)st transmissions. The ith transmission is

successful if ti-1 gt 1 and ti gt 1.

- Maximum throughput 1/2e at G1/2.
- Pure Aloha (i.e., Unslotted Aloha) is unstable.

Carrier Sensing Multi Access (CSMA)

- In some multi-access systems, a node can hear

when other nodes are transmitting. - Detection is possible after a propagating and

detection delay which is small compared to - packet transmission time.
- Detection delay is the time it takes for the

node to determine if other nodes are

transmitting. - ? propagation and detection delay in seconds
- C bits per second rate in the channel
- L average number of bits per packet
- Feedback is not instantaneous, but it is with a

maximum delay of ß in packet transmission - unit.
- If a slot is idle, then the slot terminates

after ß time units and a new slot begins. - ? ? ?C/L
- Slots are not of equal length.
- Idle slots have length ?.
- Other slots have length 1.

CSMA Slotted Aloha

- Idle slot duration ?
- If a packet arrives at a node while a

transmission is in progress in the channel (by

any node), the packet is regarded as backlogged. - Backlogged packets begin transmission with

probability qr after each subsequent idle slot. - Non Persistent CSMA Packets arriving during

idle slots are transmitted in the next slot - Persistent CSMA All arrivals during a busy

period transmit at the end of that slot. - P-Persistent CSMA Collided packets and new

packets use different probabilities for

transmission.

Analysis of CSMA Slotted Aloha

- Each busy slot (success or collision) is

followed by an idle slot. - Node can only transmit after an idle slot.
- We want to evaluate the maximum throughput such

that the drift is negative. - Drift ? Dn
- expected number of arrivals

expected number of departures - E(number of arrivals) Psucc
- Define
- State number of backlogged packets
- State transition time end of idle slot
- We want to evaluate the drift at the state

transition times. - Time between state transitions
- ? if the slot is idle
- 1 ? if a busy slot is followed by idle

slot

- Suppose the system is in state n.

Expected number of departures between state

transitions from state n where

(No Transcript)

- CSMA Slotted Aloha is unstable.
- It can be stabilized for all rates

. - Stability is not as a severe problem as in

ordinary Aloha - Expected idle time a backlogged node must wait

before transmission is ?/qr as oppose to 1/qr

for ordinary aloha. - For small ? ,qr can be very small without

causing much delay. - n must very large before backlog appears.

Satellite Reservation Systems

Amv

- Round trip delay 2?
- Duration of reservation slot v
- Reservation period A mv
- 2? is many times larger than A.
- TDM is used to make reservations.
- Duration of data packet has general distribution

with mean and second moment

1 2 m

reservation interval

Data intervals

arrival

res data res data res data

Wait for reservation

Wait for assigned data slot

Delay Analysis of Satellite Reservation System

- Consider the ith packet arriving into system.
- The ith packet must wait for
- residual time Ri (for the transmission or

reservation currently in progress), - transmission time of Ni packets already in

queue for which reservations have been made - two reservation periods.

- Satellite reservation system is an M/G/1 queue

with vacation where reservations correspond to

vacations.

- As v ? 0, the same queuing delay as M/G/1.
- W is finite for ? lt1.
- Every packet must be delayed by at lest 2? (gtgtA)

in order for the reservations to be made. - We need W gt 2?. ? This formula is only valid

for ? ? 1. - NoteThe use of variable frame size is

undesirable. - If the frame length is variable, errors made

during a reservation period requires

resynchronization on the next reservation period.

This is not easy. - Busy nodes can lock out less frequent nodes.
- ? Fixed frame length should be used.
- Since all nodes are aware of all reservations,

any queuing discipline can be used as long as - a packet is sent whenever the queue (which is

common) is not empty.

Approximate Analysis of Delay

- Consider the following scheme
- A fraction ? of bandwidth is set aside for making

reservations. - TDM is used within this bandwidth.
- Each node gets one reservation slot in each round

trip delay which is 2?.

- The arrival process of packets (with

reservations) to the common queue is

approximately - Poisson.
- Number of arrivals in different reservation

slots are independent and have Poisson - distribution.
- A packet in common queue has the service time
- Where is the service time with full

bandwidth. - The common queue is M/G/1 with

data data

1-r

1 2 3 m

r

frame

- Assume
- The total queuing delay
- For small ?, large and needless delay for making

reservation takes place. - To reduce the number of data slots wasted in

each frame, use an unscheduled contention - mode. If a packet gets through before the

reservation time, cancel its reservation.

Local Area networks Ethernet

nodes

- Model
- Propagation delay is very small.
- Nodes are connected to a common cable.
- When one node transmits all other nodes (which

are silent) can hear that transmission. - It is possible for a node to listen while

transmitting. - If two nodes start transmit almost

simultaneously, they will shortly detect a

collision and - stop transmitting (CSMA/CD).
- If one node starts transmission and during the

propagation delay and no other node starts - transmission, then no other node will start

transmission and the node transmitting is

guaranteed the transmission without collision.

Ethernet cable

Slotted CSMA/CD

- Visualize Ethernet in terms of slots and

mini-slots. - ? Slots have duration of 1.
- ? Mini-slots have duration of ?.
- ? ? is the maximum propagation delay time in

slot unit. - Nodes are synchronized into mini-slots.
- If only one node starts transmitting, the other

nodes can hear and will not transmit until - the transmitting node has finished the

transmission. - If two nodes or more start transmission, they

will detect a collision by the end of the - mini-slot and both will stop transmission.
- Mini-slots are used in a contention mode and

when a successful transmission occurs, - the transmitting node reserves the channel

for the slot for the completion of the packet.

Analysis

- Assumptions
- Each backlogged node will transmit with

probability qr after an idle mini-slot. - n number of backlogged node.
- Number of nodes transmitting after an idle slot

is Poisson with parameter G(n) ?? nqr - Consider state transitions after each idle

mini-slot. - No transmission idle slot ends after ? .
- One transmission next idle slot ends after 1?

. - More than one transmission next slot ends

after 2?.

idle

idle

?

?

State transition

Packet transmission

idle

idle

1

?

?

State transition

idle

idle

idle

?

?

?

State transition

State transition

- Like Slotted Aloha

- ? is usually very small in LAN.
- It is very difficult to synchronize all nodes on

short mini-slots - Unslotted CSMA/CD makes more sense.

Token Ring

1

nodes

9

2

Interface units

3

8

4

7

5

6

- A collection of ring interfaces are connected in

a ring topology. - Nodes are connected to the ring through the

interfaces. Token ring is more like a collection

of point-to-point links. - There is uni-directional transmission around the

ring. - Each bit arriving at an interface is copied into

a one-bit buffer and then copied out into the

ring again. - The arrived bit can be inspected and modified

before being written out. - There is a one-bit delay at each interface.

Model

- A special bit pattern called token circulates

around the ring whenever all nodes are idle. - Token can be a flag indicating the end of

packets, e.g., 01111110. (We need bit stuffing.) - A node that does not have any packet to transmit

simply passes the token to the next - node with one bit delay.
- When a node wants to transmit, it seizes the

token and inverts the last bit of the token - and transmits. The token now becomes

01111111 (i.e., busy token). After this busy

token, the packet follows. - Since there is only one token, the channel

access problem is resolved. - Ring interface has two modes
- Listen
- Transmit
- If the packet length is longer than the round

trip delay, then when the busy token bits - propagated around the ring, they are removed

from the ring. - IEEE 802.5 Standard 24 bit token, 4 or 10 Mbps

Notes

- Ring is susceptible to failures
- Ring breaks down if cable or any interface

breaks down. - Use a star configuration.
- Nodes can be by passed or added from the central

site

Delay Analysis

- Assumptions
- This is called the exhaustive multi user

reservation system.

- If each node can only transmit one packet at a

time, then, - This is called the partially gated multi user

reservation system.

Fiber Distributed Data Interface(FDDI)

2 fiber rings

- Defined by American National Standard Institute

(ANSI) - Dual ring is constructed on optical fibers.
- Transmission rate 100Mbps.
- Uses 4 bits to 5 bits encoding.
- A group of 4 bits is encoded into a character

which is 5 bits long. - 16 characters represent 4 bits of data each.
- Other characters are special communication or

control characters. - 5-bit long characters contain at most 2

successive 0s. - To provide guaranteed service for high priority

traffic (e.g., digitalized speech, video), - we need to impose constraints on traffic.
- Question How much of high priority traffic can

each node send per received token?

Model

- There are m nodes labeled as 0,1,2,,m-1.
- ?i for i 0,1,2,, m-1, is the amount of time

node i can send high priority traffic, including

delay to reach the next node. - If a token is received at time t by node i, and

node i sends ?i high priority traffic, and token

reaches node i1 at t ?i. - When the ring is initialized, there is a

parameter ?, called target token rotation time. - ? is used by nodes in deciding when to send low

priority traffic. - ? is the upper bound on the time average

inter-token arrival time.

Distributed Queue Dual Bus (DQDB)

bus A

- Standardized as IEEE 802.6
- There are two buses running.
- Uses 53 byte long ATM frames.
- Frames contain two special bits.
- Busy bit B
- Request bit R
- B 1 if frame is busy.
- B 0 if frame is idle.
- Slots are used.
- Left most node on bus A generates slots for

transmission on bus A. - Right most node on bus B generates slots for

transmission on bus B.

nodes

bus B

Packet Radio Networks

- This is a multiple access network where not all

nodes can hear transmissions of other nodes. - Network topology is represented by a graph

containing nodes and links. - Nodes are the sources and destinations of

packets. - Links are ordered pair of nodes (i, j) indicating

transmission from i can be heard at j. - Packets from i will be correctly received by j if
- There is a link between i and j.
- j or js neighbors are not transmitting.
- In the above diagram, if nodes 2 and 3 are

transmitting simultaneously, nodes 1 and 5 will

receive correctly, but node 6 will not. - More links does not necessarily imply greater

throughput.

- Definition Collision Free Set is a set of links

that can carry packet simultaneously - without collision at the end of the link.
- Example) In the previous diagram, (1,2), (4,5),

(4,6) and (2,1),(5,3),(5,4) are collision free

sets. - Definition Collision Free Vector (CFV) is a

vector of 0s and 1s where the ith component is

1 iff the ith link is in the collision free set. - (1,2) (2,1) (2,6) (3,5) (3,6) (4,5) (4,6) (5,3)

(5,4) (6,2) (6,3) (6,4) - 1 0 0 1 1 0

0 0 0 0 0 0 - 1 0 0 0 0 1

1 0 0 0 0 0 - 1 0 0 0 0 0

0 1 1 0 0 0 - Once a collection of the collision free sets are

known, we can assign a time slot for each set and

cycle through like TDM. In the ith slot of TDM,

all links in the ith collision free set can carry

packets.

- f is a convex combination of CFVs.
- Any convex combination can be achieved by TDM.
- Any link utilization achievable by other

allocation algorithms (e.g., collision resolution

algorithms) can be achieved by TDM. - TDM has an issue of long delay.
- A more difficult problem with TDM is for

dynamic networks (i.e., one with changing

topology like mobile networks). - FDM can be used in stead of TDM.

Collision Resolution (Aloha)

- When an unbacklogged node receives a packet to

transmit (from outside or other nodes), - it sends the packets in the next slot.
- If no acknowledgement is received within a time

out period, the node is backlogged and - will retransmit after a random time.
- Consider heavy loading

- We can get through from qij.
- In design, we have a set of desired throughputs

and want to find qij. - Suppose fs are the desired throughputs.
- Algorithm for design