Optical Networks

Poompat Saengudomlert

Session 19

Aloha-Based MAC for Broadcast PONs

P. Saengudomlert (2017) Optical Networks Session 19 1 / 12

6.2.3 MAC Protocols for Broadcast PONsBrief Reviews on Slotted Aloha

Aloha is one of the first MAC protocols for broadcast networks.

Underlying assumptions for slotted Aloha

Time is divided into slots of equal length.

Each packet length is equal to 1 time slot.

A transmitting user gets a feedback on the transmission success or apacket collision before the beginning of next time slot.

Operations of slotted Aloha

When ≥ 1 data packet is available, a user transmits a packet in nexttime slot.

Upon finding a collision, a user retransmits the packet after waiting arandom number of time slots, e.g., retransmit in subsequent timeslots each with probability qr until success.

P. Saengudomlert (2017) Optical Networks Session 19 2 / 12

Illustration of Slotted Aloha

2 users assumed for simplicity

Retransmissions can still collide.

Random retransmissions are necessary to avoid repeated collisions.

user 1 user 2

1 6 11 time slot

S S

C

S S S

C C

C: collisionS: success

Two key performance parameters: throughput and delay

We focus on throughput next (delay analysis beyond our scope).

P. Saengudomlert (2017) Optical Networks Session 19 3 / 12

Throughput of Slotted Aloha

To approximate the throughput, assume that

Packet arrivals from each of N users form a Poisson process.N is large and thus successive packets (transmissions andretransmissions) come from different users.

Let G be the total transmission rate (i.e., sum of transmission andretransmission rates) in packet/time slot

In each time slot,

Pr{success} = Pr{one arrival} = Ge−G

yielding the throughput of

Ge−G (in packet/time slot).

P. Saengudomlert (2017) Optical Networks Session 19 4 / 12

Maximum Throughput of Slotted Aloha

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4

G

GGe−

1/e

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4

G

GGe−

1/e

By solvingd

dG(Ge−G ) = 0, the throughput is maximized by G = 1.

⇒ max throughput is1

e≈ 0.37 packet/time slot.

NOTE: To maintain G ≈ 1, some dynamic adjustment of qr is needed. Such

dynamics is beyond our scope of discussion.

P. Saengudomlert (2017) Optical Networks Session 19 5 / 12

Unslotted Aloha

Unslotted Aloha does not divide time into slots.

A user transmits a packet immediately when it arrives.

As an approximation, consider that time is divided into very smallminislots each of with duration of ∆ ≪ 1 time slot.

Each transmission occurs at the beginning of a minislot.

time

(1) Exactly 1 packet arrives in slot marked by (2) No packet arrives in slots marked by

For a successful packet transmissionin time slot marked by "S"

S

P. Saengudomlert (2017) Optical Networks Session 19 6 / 12

Throughput of Unslotted Aloha

Let G be the total transmission rate (i.e., sum of transmission andretransmission rates) in packet/time slot

In each minislot,

Pr{success} = Pr{one arrival}×Pr{no arrival in 1/∆− 1 minislots before and after}

= ∆Ge−G∆ × e−G(2−2∆)

= ∆Ge−G(2−∆) (in packet/minislot)

= Ge−G(2−∆) ≈ Ge−2G (in packet/time slot).

The maximum throughput, obtained from solving ddG (Ge

−2G ) = 0, is

1

2e≈ 0.19 , which is half of that for slotted Aloha.

Roughly speaking, collisions are more likely for unslotted Aloha.

P. Saengudomlert (2017) Optical Networks Session 19 7 / 12

SA/SA Protocol for WDM PONs

Slotted Aloha/slotted Aloha (SA/SA) is slotted Aloha modified to operatewith WDM PONs.

Assumptions

A dedicated control wavelength channel with fixed transmitter andfixed receiver at each user

Each user has one tunable transmitter and one tunable receiver totransmit/receive data packets.

A control packet lasts for one minislot while a data packet lasts for Lminislots with L > 1, where L minislots last for one time unit.

P. Saengudomlert (2017) Optical Networks Session 19 8 / 12

SA/SA operations

When data packet is available, user selects data wavelength withequal probabilities, transmits control packet in next minislot, andtransmit data packet on selected wavelength in minislot after.

Upon finding a collision, a user retransmits in each subsequentminislot with probability qr until success.

user 1

user 2

0 time

control wavelength

λ1

λ2

user 3

NOTE: Data packet follows even after collision of control packets.

P. Saengudomlert (2017) Optical Networks Session 19 9 / 12

Throughput Analysis of SA/SA

Approximations

Assume that packet arrivals from each of N users form a Poissonprocess.

Assume N is large and successive transmissions tend to come fromdifferent users. As a result, the probability of a collision at anyreceiver is negligible, i.e., dominated by other events.

Notations

G : is the total transmission rate in packet/time unit.

∆: is the length of a minislot in time unit.

g = ∆G be the total transmission rate in packet/minislot.

L: packet length (in minislot)

W : number of data wavelength channels

P. Saengudomlert (2017) Optical Networks Session 19 10 / 12

In each minislot,

Pr{success}= Pr{1 control packet, no collision on data channel,

no collision at receiver}≈ Pr{1 control packet, no collision on data channel}= Pr{1 control packet} · Pr{no collision on data channel|1 control packet}= ge−g · Pr{no data on same wavelength in L− 1 minislots

before and after}

= ge−g ·(e−g/W

)2L−2

The throughput is

ge−g(1+2(L−1)/W ) in packet/minislot

= Lge−g(1+2(L−1)/W ) packet/time unit

=Lg

We−g(1+2(L−1)/W ) packet/time unit/wavelength

P. Saengudomlert (2017) Optical Networks Session 19 11 / 12

Maximum throughput (from differentiation over g)

TSA/SA =L

We(1 + 2(L−1)

W

) ≈ 1

e(2 +W /L)

NOTE: Max throughput above is always below 12e .

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2

L=10,W=10

L=5,W=10

L=10,W=5

g

( )1 2( 1)g L WLge

W− + −

P. Saengudomlert (2017) Optical Networks Session 19 12 / 12