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Lecture on Multi Access Communication

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Title: Lecture on Multi Access Communication


1
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
2
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
3
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.

4
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
5
  • 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
6
  • 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.



7
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
8
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.

9
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.,

10
  • 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.

11
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.

12
  • 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.

13
  • We can solve the above equations for pn where pn
    is the steady state probability of being in state
    n.

0
1
2
3
14
  • 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.

15
  • 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 .

16
  • One desired stable state, one unstable state, and
    one undesired stable state.
  • Maximum Psucc maximum departure rate 1/e

17
  • If we use assumption 6b instead,
  • One desired stable state, and one unstable state.

18
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.

19
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.

20
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.

21
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

22
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)

23

24
delay
25
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

26
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
27
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.

28
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
29
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.
30
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.

31
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.
32
  • Maximum throughput 1/2e at G1/2.
  • Pure Aloha (i.e., Unslotted Aloha) is unstable.

33
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.

34
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.

35
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

36
  • Suppose the system is in state n.

Expected number of departures between state
transitions from state n where
37
(No Transcript)
38
  • 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.

39
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
40
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.

41
  • Satellite reservation system is an M/G/1 queue
    with vacation where reservations correspond to
    vacations.

42
  • 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.

43
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?.

44
  • 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
45
  • 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.

46
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
47
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.

48
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
49
  • Like Slotted Aloha

50
  • ? is usually very small in LAN.
  • It is very difficult to synchronize all nodes on
    short mini-slots
  • Unslotted CSMA/CD makes more sense.

51
Token Ring
1
nodes
9
2
Interface units
3
8
4
7
5
6
52
  • 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.

53
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

54
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

55
Delay Analysis
  • Assumptions
  • This is called the exhaustive multi user
    reservation system.

56
  • If each node can only transmit one packet at a
    time, then,
  • This is called the partially gated multi user
    reservation system.

57
Fiber Distributed Data Interface(FDDI)
2 fiber rings
58
  • 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?

59
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.

60
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
61
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.

62
  • 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.

63
  • 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.

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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

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  • 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
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