Tradeoffs between performance guarantee and complexity for distributed scheduling in wireless networ

1
Tradeoffs between performance guarantee and
complexity for distributed scheduling in wireless
networks

• Saswati Sarkar
• University of Pennsylvania

Communication and Complexity Workshop
August 31, 2006
2
Performance Goals in Multihop Wireless Networks

• Multi-hop wireless networks
• Ad hoc networks (disaster recovery, battlefields,
  communication in remote terrains)
• Sensor networks (environmental monitoring,
  agriculture, production and delivery,
  surveillance)
• Commercial deployment (mesh networks)
• Performance Goal
• Network Stability
• Bounded expected queue lengths
• Seek to design a policy that stabilizes the
  network if some policy stabilizes the network
• Throughput Maximization

3
Scheduling Challenges in Multi-hop Wireless
Networks

• Need to dynamically decide when to transmit and
  whom to transmit to
• Decisions of each node affect the outcomes of
  transmissions of other nodes
• Nodes are geographically separated
• Key questions
• Attainability
• Does there exist a policy that maximizes the
  throughput?
• Centralized or Distributed
• Minimization of computation time and resources
  per scheduling decision

4
Attainability (Tassiulas and Ephremides, TAC 92)

• Key result
• A back-pressure based scheduling policy
  stabilizes an arbitrary wireless network provided
  some policy stabilizes the network
• Interference constraints modeled by considering
  that only certain subsets of nodes can be
  simultaneously scheduled
• Weight of any such allowed subset is the sum
  of the queue lengths at the nodes in the subset
• Schedule the allowed set that has the maximum
  weight
• Computation time per scheduling decision is
  exponential in the number of nodes in the network
  (n)

5
Attainability Through Linear Complexity
Computation (Tassiulas, Infocom 98)

• Randomized scheduling policy
• Select an allowed set randomly in each slot
• Compare the weights of the sets selected in the
  current and previous slots
• Schedule the set that has the higher weight among
  the two
• Requires only linear computation time (O(n)) per
  scheduling decision
• Distributed Implementation
• Naïve broadcasts
• Rumor routing (Zussman, Shah, Modiano, Sigmetrics
  2006)
• Computation time for both implementations is
  linear in the number of nodes in the network

6
Throughput Guarantees for Specific Interference
Models

• Node exclusive interference model
• A node can be involved in at most one
  communication.
• A set of links can be simultaneously scheduled if
  and only if they constitute a matching
• Models only primary interference
• Maximal matchings
• A set of links constitute a maximal matching if
  addition of any other link to the set violates
  the matching property
• Maximal matchings can be computed in O(log n)
  time using randomized computations

7
Throughput Guarantees using Maximal Matching (Dai
and Prabhakar, Infocom 2000)

• A policy that schedules some maximal matching in
  each slot attains at least half the maximum
  throughput region.
• Input queued switches Dai and Prabhakar. Infocom
  2000
• Wireless networks with single-hop sessions and
  node-exclusive interference model Lin and
  Shroff. Infocom 2005
• Wireless networks with multi-hop sessions and
  node-exclusive interference model Wu and
  Srikant, CDC 2005

8
Throughput Guarantees using Logarithmic
Computation Time Arbitrary Interference Models

• Pair-wise Interference Relations
• Represent links as nodes in the interference
  graph
• There exists an edge between two nodes in the
  interference graph if and only if they can not
  simultaneously transmit successfully
• Models both primary and secondary interference
  (e.g., IEEE 802.11)
• Can consider arbitrary transmission patterns,
  directional antennas, networks with multiple
  channels

9
Maximal scheduling

• An independent set is a set of nodes such that
  there does not exist an edge between any two
  nodes in the set.
• Any independent set in the interference graph is
  a valid schedule.
• An independent set is maximal if addition of a
  node in the set destroys the independence
  property.
• A maximal scheduling is one that schedules a
  maximal independent set in the interference graph
  in each slot.
• A maximal independent set can be computed in
  O(log n) time using randomized computations.

10
Performance guarantees using maximal scheduling
for arbitrary interference models (Chaporkar,
Kar, Sarkar, Allerton 2005)

• Interference Degree of a wireless network
• Maximum number of transmitter receiver pairs that
  interfere with any particular transmitter-receiver
  pair, but do not interfere with each other
• Key results
• Maximal scheduling reduces the throughput region
  by at most a factor of the interference degree
• There exists maximal schedulings that reduce the
  throughput region by a factor of exactly the
  interference degree.

11
Some insights on the interference degree

• Node exclusive spectrum sharing model
• Interference degree is at most 2
• There exists networks with interference degree
  exactly 2.
• Explains the ½ performance guarantee earlier
  obtained for node exclusive spectrum sharing
  model
• Shows that the ½ performance guarantee is tight
  for maximal matching for node exclusive spectrum
  sharing model

12
Some insights on the interference degree

• Bidirectional equal power model
• Communication is bidirectional
• Nodes use equal power to transmit
• Two links (u,v) and (x,y) interfere with each
  other if either u or v falls within the range of
  either x or y
• IEEE 802.11
• Interference degree is at most 8
• There exists networks with interference degree
  exactly 8.
• Implications
• Logarithmic computations approximate the maximum
  throughput region within a constant factor (1/8).
• There exists maximal schedulings that attain a
  penalty factor of exactly 8.

13
Some insights on the interference degree

• Unirectional equal power model
• Communication is unidirectional
• Nodes use equal power to transmit
• Asymmetric interference relation
• Given any constant Z, there exists a network
  whose interference degree exceeds Z.
• Implication
• Arbitrary maximal schedulings can not attain
  constant factor approximation guarantees.

14
Can the approximation factor be improved while
retaining logarithmic computation time?

• Approximation guarantees for arbitrary maximal
  schedulings can not be improved beyond the
  interference degree.
• Improved approximation guarantees may be attained
  using specific maximal schedulings.
• All maximal schedulings can not be computed in
  O(log n) time.
• There exists a maximal scheduling that can be
  computed in O(log n) time and attains at least
  2/3 of the maximum throughput region when the
  topology is a tree and the interference model is
  node exclusive spectrum sharing (Sarkar, Kar,
  Luo, Allerton 2006)