Distributed Dynamic Scheduling for EndtoEnd Rate Guarantees in Wireless Ad Hoc Networks Using Asynch

1
Distributed Dynamic Scheduling for End-to-End
Rate Guarantees in Wireless Ad Hoc
Networks(Using Asynchronous TDMA)

• T. Salonidis L. Tassiulas
• Presented by Jon Leighton
• jtleight_at_udel.edu

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What exactly does that mean?

• There are no central algorithms, and no global
  network knowledge is required.
• Changes in network topology (mobility), and
  session demand are supported.
• Each flow over the network is assigned a
  guaranteed rate. (MMF)
• Nodes communicate using TDMA, but without
  synchronizing their clocks.

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Outline of Presentation

• Asynchronous TDMA architecture
• Dynamic Link Scheduling
• Local feasibility conditions
• Distributed coordination system
• Distributed link scheduling algorithm
• End-to-end Fairness and Rate Guarantees
• Experiments and Results
• Conclusions

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Asynchronous TDMA

• Each node communicates on at most one link at a
  time.
• No hidden terminal problem
• Use orthogonal channels
• Use directional antennae
• Each node uses its own clock to divide time into
  fixed size full duplex slots.
• Nodes transmit and receive on their adjacent
  links according to their own local schedule of
  period Tsystem slots.
• On each link, one node is the master and the
  other the slave.
• Master node controls the reference time on a link.

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Asynchronous TDMA

• The network can be modeled as a directed graph
  G(N,E), with master nodes pointing to slaves.
• Any distinct pair of linked nodes may communicate
  simultaneously.
• A node may be the master on some of its links,
  and the slave on its other links.
• Time slots on master and slave nodes will not, in
  general, be aligned.

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Asynchronous TDMA

• If the master node assigns tl consecutive time
  slots to link l, then the slave must assign tl
  1 time slots to accommodate the lack of
  synchronicity.

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Asynchronous TDMA

• Questions
• What happens if the number of slots assigned to a
  particular link needs to change?
• How do the endpoint nodes on a link find and
  agree on what slots to use for that link?
• How can we be sure that no node is asked to
  create a schedule that is not feasible?

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Dynamic Link Scheduling

• Local feasibility conditions.
• Given global knowledge, the question of whether
  or not a particular set of slot demands for each
  link is feasible, in a period of Tsystem slots,
  is NP-complete.
• To ensure feasibility solely on the basis of
  local knowledge, you must either control the
  topology or under utilize the network.
• For uncontrolled topologies, feasibility can be
  guaranteed if every node offers no more than
  ?Tsystem /3? slots to all its adjacent links.
• For bipartite topologies, feasibility can be
  guaranteed if every node offers no more that
  ?Tsystem /2 ? slots to all its adjacent links.
• For either topology, you will find that there are
  many cases where you can offer many more slots
  than allowed by these bounds, however, in general
  you can only guarantee an offer that meets these
  bounds.

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Dynamic Link Scheduling

• Local feasibility conditions (cont.)
• What is the best we can hope to do? That is, how
  many of the Tsystem slots can we hope to offer in
  the best case?
• We can offer enough slots that the busiest node
  will utilize all Tsystem slots.
• In general, this cannot be accomplished.
• It turns out that it can be accomplished for tree
  topologies.

where
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Dynamic Link Scheduling

• Summary of topology based conditions for local
  determination of feasibility.

where
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Dynamic Link Scheduling

• Distributed coordination mechanism
• At any given time, several links may be
  asynchronously triggered for rate adjustment in
  parallel.
• Link rate adjustment is triggered when an
  endpoint node is notified of a change in the link
  demand, or is notified of a schedule change by an
  adjacent node.
• Each node can only be involved in one link rate
  adjustment at a time. Upon initiation, both
  nodes set their busy bit, exchange their
  current schedules, and one node determines the
  new schedule.
• The updated schedule is stored but not
  implemented until notification has been sent to
  all affected neighbors and they have acknowledged
  the modification.
• The busy bit is then cleared on both nodes.
• During the rate adjustment process, the current
  TDMA schedule is maintained, and control packets
  are sent using these slots.

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Dynamic Link Scheduling

• Link Scheduling Algorithm (tree topologies)
• The link scheduling algorithm is invoked in
  response to a need to adjust link rates.
• Each node knows only its own parent/child
  relationships, and the current demand on each of
  its adjacent links.
• The algorithm may start from any TDMA schedule,
  and will converge to a new schedule satisfying
  the current demand requirements.
• Each node tries to satisfy all its child links.
• Satisfaction means
• Each child link is scheduled in a single window
  of time slots.
• The size of the window exactly meets the demand.

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Dynamic Link Scheduling
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Dynamic Link Scheduling

• Consider a node u
• The window of slots required for the parent link
  is chosen by the parent node and enforced on node
  u.
• Node u then selects and enforces a slot window
  for each of its unsatisfied child nodes.
• Each child link is assigned a priority based on
  the order its slots occur in node us current
  schedule.
• Node u checks its children for satisfaction in
  order of decreasing priority.
• If all children are satisfied, the link
  scheduling algorithm terminates.
• If a child is found not to be stabilized, it and
  all lower priority children are rescheduled.

t (2, 2, 2, 3, 3)
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Dynamic Link Scheduling

• Rescheduling a child of node u.
• The schedule for us parent, and all children
  with higher priority than the current child, are
  considered fixed.
• The minimum allocation needed to satisfy all
  lower priority children is determined based on
  the current demands, and is reserved at the end
  of the schedule.
• The available window for scheduling this child is
  all remaining slots.
• The child is scheduled in the window so that the
  fewest links are affected on node u and the child.

t (2, 2, 2, 6, 3)
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End-to-End Fairness and Rate Guarantees

• Finding Feasible Session Rates
• Maximum radio transmission rate is 2R bps.
• Rate for session i is ?i R. (half duplex)
• Network must be able to allocate ti ?ri/R
  Tsystem? slots at every link on sessions path.
• On intermediate nodes we must include slots for
  both the incoming and outgoing links. Thus, if
  F(u) is the set of all sessions passing through
  node u, then the local feasibility conditions for
  session rates are

where
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End-to-End Fairness and Rate Guarantees

• The link demands are found from the session
  demands by
• Link demands which meet these conditions are
  enforceable by the link scheduling algorithm.

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End-to-End Fairness and Rate Guarantees

• How are the session rates ?i chosen?
• There are many ways to choose which flow gets
  what portion of the available bandwidth.
• In this case we use the max-min fairness (MMF)
  objective.
• MMF in simple terms
• Locate the node(s) with the most flows passing
  though it and evenly distribute the bandwidth
  among the flows. This is the enforced session
  rate for these flows.
• Remove the node and its flows from the network,
  and reduce the bandwidth of all other nodes that
  these flows passed through by their session
  rates.
• Repeat until all flows have been removed.

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End-to-End Fairness and Rate Guarantees
Tsystem 50
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End-to-End Fairness and Rate Guarantees

• Finding the MMF rates
• Note that some nodes cannot allocate all 50 slots
  due to their roll as slaves on some links. Their
  bandwidth is correspondingly reduced from the
  full link bandwidth. For example, while node A
  has the full bandwidth available, node G has only
  47/50 94 of the full bandwidth available.
• Node A has the greatest number of sessions, at 8.
  Evenly sharing its bandwidth gives each flow 1/8
  of the full bandwidth.
• Removing node A and all the flows through it,
  leaves node B with the greatest number of
  sessions, at 3. The full bandwidth of B is
  reduced by the bandwidth allocated to the 3 flows
  it had in common with node A, leaving 1 3/8
  5/8 of the full bandwidth. Evenly sharing this
  bandwidth gives the three remaining flows 5/24
  0.208 of the full bandwidth.
• Removing node B and the three flows through it,
  leaves node G with the only remaining flow. The
  three flows removed with node B do not pass
  through node G, so node Gs bandwidth is reduced
  only by the five flows it shared with node A,
  giving an available bandwidth of 0.94 5/8
  0.315 of the full bandwidth. This is allocated
  to the one flow.
• There are no flows remaining, so the MMF rates
  have been determined (as fractions of the full
  link rate), to be
• S1 S2 S3 S7 0.125, S4 S6 0.208, S5
  0.315

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End-to-End Fairness and Rate Guarantees

• Some details of implementing distributed MMF
• Algorithm is based on similar work done in ATM
  networks.
• Control packets are injected and circulated along
  each session path. They carry the current
  estimate of the MMF rate for that flow.
• Upon receiving a control packet, a node adjusts
  its estimate of the MMF rate for that flow based
  on an update algorithm, updates the packet
  information, and forwards the packet.
• As the estimated MMF rates change for each flow,
  the corresponding link demands also change, and
  these changes are conveyed to the nodes adjacent
  to these links.

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End-to-End Fairness and Rate Guarantees

• It can be shown that the process will converge to
  the MMF rates in a finite number of iterations,
  for any topology.
• While this process is converging towards the MMF
  rates, the Link Scheduling algorithm is trying to
  meet the changing link demands.
• Once the MMF rates have stabilized, the link
  demands have also stabilize, and the link
  scheduling algorithm will now converge.

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Experiments

• Simulated a Bluetooth network using ns.
• Bluetooth
• Is a multi-channel asynchronous TDMA wireless
  network.
• Uses orthogonal channels based on frequency
  hopping.
• For each link it assigns master and slave rolls
  to the adjacent nodes.
• Supports using two half duplex slots to simulate
  full duplex communication.
• Supports a transmission rate of 172.8kbps in each
  direction.
• Handles the issues of node discovery, frequency
  assignment, and time slot reference.

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Experiments

• Ran the simulation once with each node as the
  root of the tree.
• Simulation duration was 25 sec.
• Reported time for link demands to stabilize, DS,
  and time for link scheduling to converge once the
  link demands were stable, DL.

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Results
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Results (cont.)
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Conclusions

• Proposed an asynchronous distributed MMF
  algorithm applicable to any network topology.
• Showed that tree topologies can achieve the
  maximum utilization possible given the underlying
  asynchronous TDMA architecture.
• Introduced a link scheduling algorithm that
  enforces the MMF end-to-end rates for tree
  topologies.
• Presented an implementation of this framework
  over Bluetooth.
• A natural extension of this work is to
  investigate link scheduling algorithms for more
  general topologies than trees.

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Questions?
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Homework
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B
S3
Tsystem 20
2
19
H
C
19
3
5
10
S2
18
11
1
7
6
S1
19
19
A
J
F
D
I
17
20
S6
8
4
9
S5
19
20
E
G
S4

• Find the MMF session rates for sessions S1 S6
  in the network shown above, as a fraction of the
  max 1-way link bandwidth, R. The bold numbers
  are the link numbers, and the numbers next to
  each node indicate the number of time slots
  available for scheduling in a period of length
  Tsystem.
• Briefly answer the three questions on slide 7
  (in the context of distributed MMF rate
  guarantees and tree topologies).