EnergyEfficient Channel Access and Routing Protocols for MultiHop Wireless Networks

1
Energy-Efficient Channel Access and Routing
Protocols for Multi-Hop Wireless Networks

• Fikret Sivrikaya
• Rensselaer Polytechnic Institute
• Computer Science Department
• Nov 02, 2007

2
Wireless Sensor Networks

• A large number of tiny and limited-power sensor
  nodes (motes)
• Distributed, multi-hop, ad-hoc operation no
  infra-structure, no central control point
• Collect and process data from a target domain and
  transmit information to specific sites
• Some applications
• disaster recovery
• military surveillance
• health administration
• environmental monitoring

Mica2dot Motes by Crossbow Inc.
3
Wireless Mesh (Community) Networks

• WMNs try to close the gap between cellular
  networks and isolated wireless LANs (hotspots)
  for providing high-speed ubiquitous network
  access.

• Hybrid structure
• stationary mesh routers form a multi-hop network
  backbone,
• while mesh clients may roam and access data
  through various routers.
• May be much more efficient in sharing of local
  information, or collaborative access to data of
  common interest to a local community.

source research.microsoft.com/mesh
4
Multi-hop Wireless Networks

• WSNs and the router backbone of WMNs both
  constitute
• multi-hop wireless networks with stationary
  nodes.

Representation of the network as a graph
The wireless transmission range of a node
determines its neighbors
5
Common Terms Notations

• k-neighborhood of a node v
• ?k(v)
• k-neighborhood size of a node v
• ?k(v) ?k(v)
• max k-neighborhood size (in the network)
• ?k maxv ?k(v)
• n total number of nodes in the network

v
1-neighbors or neighbors of v

2-neighbors of v
6
Medium Access Control (MAC) Protocols

• Specify how nodes in a network access the shared
  communication channel.
• Three main classes
• Contention-based
• Contention-free
• Limited-contention (or hybrid)
• Slot Assignment
• Assign each node a time interval for channel
  access.
• Mainly used for Spatial Time Division Multiple
  Access (STDMA) MAC protocols.
• Existing approaches require a common view of time
  by all nodes, i.e. global time synchronization.

7
MAC Protocols for Wireless Networks

• Most of the initial work focused on
  contention-based schemes
• Mostly based on IEEE 802.11 (Wireless LAN)
  protocol or its variants.
• Duty/sleep cycles for energy savings.
• S-MAC Infocom02, T-MAC SenSys03, B-MAC
  SenSys04, Z-MAC (hybrid scheme) SenSys05
• Then contention-free MAC protocols start to
  emerge Mostly based on spatial TDMA (STDMA)
  scheme.
• Arumugam and Kulkarni, Self-stabilizing
  Deterministic TDMA for Sensor Networks ICDCIT
  2005
• Moscibroda and Wattenhofer, Coloring
  Unstructured Radio Networks SPAA 2005
• Herman and Tixeuil, A Distributed TDMA Slot
  Assignment Algorithm for Wireless Sensor
  Networks ALGOSENSORS 2004

8
Routing Protocols

• Specify how packets are delivered through the
  network from source to destination.
• Routing (network layer) resides above the MAC
  (link layer) in the communications protocol
  stack.
• MAC Routing protocols play a crucial role on
• network performance.

Application
Routing
MAC
PHY
9
Contributions Brief Talk Outline

• Contention-Free MAC Protocols for Asynchronous
  Wireless Networks
• LooseMAC
• ASAND
• TightMAC
• Minimum-Delay Routing Protocols for Networks with
  STDMA
• Spatially Limited Contention Scheme for Wireless
  Channel Access

10
Thesis Proposal (May06)
Progress
0
100
CONTENTION-FREE MAC PROTOCOLS
Weight
ROUTING
LIMITED CONTENTION MAC PROTOCOLS
MAC COMPARISON
11
CONTENTION-FREE MAC PROTOCOLS FOR ASYNCHRONOUS
WIRELESS NETWORKS
12
Asynchronous Slot Assignment

• Traditional slot assignment protocols rely on
  precise time synchronization.
• Time synchronization requires frequent message
  exchanges, causing extra communication and thus
  energy overhead.?

• We propose new STDMA protocols that do not
  require clock synchronization.

• Each node locally discretizes its local time.
• The number of slots in a time frame is called the
  frame size and denoted by ?.

• F. Sivrikaya and B. Yener, Time Synchronization
  in Sensor Networks A Survey, IEEE Network
  Magazine - special issue on Ad Hoc Networking
  Data Communications and Topology Control, Vol.
  18, Issue 4, pp. 4550, July/August 2004.

13
Static Slot Assignment

• Because of the hidden terminal problem, a node
  may contend with any neighbor in its
  2-neighborhood for channel access.
• A static slot assignment protocol should assign
  each node a time interval that is guaranteed to
  be collision-free in its 2-neighborhood.
• This corresponds to the coloring of G2, where G
  denotes the network graph.

b
a
c
Interference on node b (Hidden terminal problem)
14
Basic Approach
Select random slot ?
Report conflicts between neighbors
Transmit beacon at ?
Listen for ? slots
Conflict
YES
NO
Obtain slot ?
15
Basic Approach
Schedule nodes transmission times so that
neighbor nodes do not transmit at the same
time. ? Repeatedly select a random time slot
until it is collision-free in the 2-neighborhood.
?
u
w
v
16
A Collision Detection Primitive

• When a node transmits, it must be able to detect
  simultaneous transmissions of neighbor nodes.
• Divide each slot into 4 log n 8 mini slots.
• Generate a binary sequence b of 4 log n 8 bits
  based on unique node id.
• Transmit in mini slot j only if bu( j)1.
• Guarantees that each transmitting node can detect
  other transmissions during its current slot.

17
A Collision Detection Primitive
X idu Y idv
l idu log n
1 ? shift ? log n
shift log n 1
shift log n 2
log n 3 ? shift ? 2log n 2
shift 2log n 3
18
Handling Hidden Terminals - LooseMAC
u
w
v

• The 2-hop neighbors u and v are unaware that they
  have selected conflicting time slots (their
  transmissions collide on w).
• w acts as an arbitrator and reports the conflict
  between u and v, so that they select new random
  slots.

19
Algorithm LooseMAC
20
Convergence of LooseMAC

• If ? ? c??13, for some constant c, then with
  probability at least 1-1/n, starting from an
  arbitrary state I, every non-ready node will
  become ready in 2?log n time steps.?
• Each node sends at most O(log n) control
  messages.
• Each message has size O(log n) bits
• senders id (log n bits) fresh status
  conflict report ind.
• After convergence, all transmissions are
  collision-free, and we define throughput of each
  node to be the inverse of its frame size 1/?

• C. Busch, M. Magdon-Ismail, F. Sivrikaya, B.
  Yener, Contention-Free MAC Protocols for
  Wireless Sensor Networks, In Proc. 18th
  International Conference on Distributed Computing
  (DISC 2004), pp. 245-259, Amsterdam, The
  Netherlands, October 2004.

21
Asynchronous Slot Assignment and Neighbor
Discovery Protocol (ASAND)
Reporting Conflicts in ASAND

• Having observed a collision in its local time t,
  node w transmits at time t?, creating a spurious
  conflict with both u and v.
• This is called conflict reporting ? essentially
  reduces a conflict between hidden terminals to a
  conflict between neighbor nodes.
• After t?, u and v will be forced to select new
  slots

• F. Sivrikaya, C. Busch, M. Magdon-Ismail, B.
  Yener, ASAND Asynchronous Slot Assignment and
  Neighbor Discovery Protocol for Wireless
  Networks, OPNETWORK07, Washington DC, 27-31
  August 2007.

22
LooseMAC vs. ASAND - Reporting Collisions
LooseMAC
u
ASAND
w
v
23
Problem Chains of Conflict Reports
a
b
e
g
h
f
c
d
t3?

• Chain of messages goes on indefinitely and makes
  the time slot ? useless in this neighborhood.
• Nodes involved in the chain waste energy.
• Continuous collisions impose a problem for
  algorithm termination.

24
Remedy Probabilistic Conflict Reporting

• Upon detecting a collision at time t
• report the collision at t? with probability
  preport.
• otherwise, listen for collisions again at t?
  (with prob. 1?preport,).
• If a collision is detected again at t?, then
  report it at t2? with probability 2?preport
• In general, after c consecutive collisions,
  report with probability c preport
• A slot conflict is always reported after at most
  1/ preport frames.
• To obtain a slot, a node has to transmit 11/
  preport times in that slot.

Example (preport 0.2)
25
ASAND Protocol
At algorithm termination, a node discovers its
neighbors and a local schedule of their channel
access times
?
node i
v
x
w
i
u

• F. Sivrikaya, C. Busch, M. Magdon-Ismail, B.
  Yener, ASAND Asynchronous Slot Assignment and
  Neighbor Discovery Protocol for Wireless
  Networks, OPNETWORK07, Washington DC, 27-31
  August 2007.

26
An OPNET Implementation of ASAND
27
Collision Detection OPNET Modeler Implementation
28
The Effect of Conflict-Report Probability
29
Algorithm TightMAC
frame
time slot

• Allows nodes to have different frame sizes.
• Runs on top of a loose MAC with uniform frame
  sizes.
• Motivation tighten the frames to increase
  throughput in sparse areas of the network.

30
TightMAC Non-uniform Frame Sizes

• Node u selects a frame size proportional to ?u,
  where

max 2-neighborhood size among us 2-neighbors

• Each node selects a frame size which is an exact
  power of 2 ? coincidence set does not change.

31
Ready levels

• All 2-neighbors of a node i should be ready so
  that i can proceed to TightMAC phase.
• Introduce five ready levels
• ready-0 (or simply ready)
• ready-1
• ready-2
• ready-3
• ready-4
• When all neighbors of i are ready-k, i becomes
  ready-(k1).

32
Ready Levels Computing ?i
ready
send id
ready-1
send count ( of neighbors)
ready-2
send total
ready-3
send max
ready-4
?i ? max received
33
Algorithm TightMAC

• In the tight phase, the network stabilizes within
  O(2?log n) time slots, with probability at least
  1-1/n. Each node sends O(log n) messages, of size
  O(log n) bits.?

• C. Busch, M. Magdon-Ismail, F. Sivrikaya, B.
  Yener, Contention-Free MAC Protocols for
  Wireless Sensor Networks, In Proc. 18th
  International Conference on Distributed Computing
  (DISC 2004), pp. 245-259, Amsterdam, The
  Netherlands, October 2004.

34
Summary of Our MAC Protocols

• Asymptotically, TightMAC and ASAND have the same
  frame sizes.
• ASAND provides much smaller frame sizes in
  practical network sizes
• Networks with a highly non-uniform node
  distribution favors the use of TightMAC.

35
MINIMUM-DELAY ROUTINGOVER STDMA MAC
36
GreenWave Routing - Motivation
?
Two extreme cases
u
x
y
z
v
u
a
b
c
v
time
37
GreenWave Routing Auxiliary Graph
w(u,v)
u
v
w(u,v) (Fu(v) tu) mod ?
An example network with 6 nodes. On the right
local time frames of each node shown with their
relative alignment.
The auxiliary directed graph G corresponding to
the example network.
38
GreenWave Routing Data Fusion Case

• Data Fusion is the aggregation of data along the
  routing path, providing significant
  energy-savings in many sensor network
  applications.
• When data fusion/aggregation is used, it is
  assumed that there is no effect of congestion on
  end-to-end delays.

• Node u locally computes its outgoing edge
  weights, w(u,v).
• Then executes algorithm GreenWave at each time
  step.

39
GW Routing - OPNET Implementation
40
GW Routing - OPNET Implementation
CF MAC GW Routing
802.11 MAC SH Routing
41
Savings in Latency by GreenWave Routing
There is a significant decrease in the end-to-end
delays
Average single-hop delay remains almost constant
in spite of the increase in frame size.
42
GreenWave Routing with Congestion Control (GWCC)
No Data-Fusion Case

• No data fusion ? Must take into account
  congestion on relaying nodes.
• Formulate the problem as a Quadratic Integer
  Program (QIP).
• Present a lower bound algorithm and a heuristic.
• Design a distributed routing protocol based on
  the heuristic idea.

• F. Sivrikaya and B. Yener, Minimum Delay Routing
  for Wireless Networks with STDMA, to appear in
  the ACM/Springer Wireless Networks Journal
  (WINET).

43
GreenWave Routing with Congestion Control (GWCC)
44
QIP Formulation of the Problem
45
With vs. Without Data Fusion
Routing with data fusion no congestion
QIP Solution Routing without data fusion
congestion control
Sample Auxiliary Graph
46
GreenWave Routing with Congestion and Flow
Control (GWCF)

• Based on the heuristic idea Create a directed
  acyclic graph and incrementally solve the problem
  on this reduced graph.
• Implicit Flow Control (IFC) technique
• Congestion and flow control at no additional cost
• Utilizes overhearing in broadcast medium
• Creates a push back effect, regulating the
  injection and movement of data traffic in the
  network

47
GreenWave Routing with Congestion and Flow
Control (GWCF)

• Uses packet switching dynamically routes each
  packet hop-by-hop.
• Each node u discovers its du and hu values at
  network deployment,
• where du is the weighted shortest path distance
  and hu is the minimum path length from sensor u
  to a sink node.
• Then it builds a table which consists of a subset
  of its neighbors
• Nu v hv lt hu.
• For each neighbor v in its table, u stores the
  shortest distance to a sink node through v,
  denoted by duv dv w(u,v).

48
GreenWave Routing with Congestion and Flow
Control (GWCF)

• Also associated with node v ? Nu is a binary
  backlog value Buv

• All backlog values are initialized to 0.
• When u sends a packet to v, Buv is set to 1.
• When u overhears that v relays that its packet,
  Buv is reset to 0.
• Nodes can relay packets only to nodes in their
  routing table for which the backlog is 0. If
  theres no such node, the node blocks until a
  backlog entry in the routing table is cleared.

49
GreenWave Routing with Congestion and Flow
Control (GWCF)

• Demonstration of GWCF on a simple example.
• Node us routing table and the corresponding
  routing decision (red line) are given for three
  consecutive time frames.
• Transmission queues of the two relay nodes are
  also shown, where each entry is the node id of a
  packet source.

50
GWCF Performance Study
The average end-to-end delay values as the
simulation progresses for (a) GW / SH (b) GWCF
routing on a network of 500 sensor nodes and 3
sink nodes.
51
GWCF Performance Study
Total amount of traffic received at the sink
nodes per second as a function of the traffic
load at the sensor nodes.
52
SPATIALLY-LIMITED-CONTENTION SCHEME FOR WIRELESS
CHANNEL ACCESS
53
Recall the Hidden Terminal Problem
Interference on node b (Hidden terminal problem)
Because of the hidden terminal problem, a node
may contend with any neighbor in its
2-neighborhood for channel access.
54
Collision Avoidance (RTS/CTS) Scheme
ACK

• The overhead of collision avoidance is
  particularly high when the data payloads are
  small as is typical for sensor network
  applications.
• The default packet size in TinyOS is only 29
  bytes.
• Moreover, it is shown that the performance of
  collision avoidance scheme starts degrading
  quickly as the number of hidden terminals
  increase.?

• Y. Wang, J. J. Garcia-Luna-Aceves, Modeling of
  Collision Avoidance Protocols in Single-Channel
  Multihop Wireless Networks, Wireless Networks,
  10(5), pp. 495506, Sep. 2004.

55
Spatially-Limited Contention (SLICON)

• In Contention-Free MAC protocols, frame size may
  be arbitrarily large depending on the topology.
• In SLICON, we show that a small constant frame
  size is always sufficient to ensure that hidden
  terminals are eliminated. Only the direct
  neighbors may contend for the channel within each
  slot.

SLICON effectively reduces the contention-range
of a node from a circle of radius of 2r to a
radius r.
56
SLICON Media Access Scheme

• Definition (SLICON Media Access Scheme)
• Let G be the graph representing a given network
  topology and M a given MAC protocol.
• Further, let St denote a subset of nodes in G
  that are granted permission by M to contend for
  the channel at time t.
• Then M is said to implement the SLICON scheme if
  and only if St is an independent set in G2 -G for
  any time instant t.
• Considering the static slot assignment case for
  stationary networks, SLICON media access scheme
  corresponds to the coloring of graph G2 -G.

57
Coloring G2-G (SLICON Coloring)
Average vertex degree and number of colors used
in the greedy coloring of random graphs generated
with the G(n, p) and G(n, r) models
G(n, r) - random geometric graphs
G(n, p) general random graphs
58
Unit Ring Graphs

• Consider an undirected geometric graph G, and let
  d(u,v) denote the Euclidean distance between
  vertices u and v in G. Then G is called a unit
  ring graph if, for every edge (u, v) ? G, we have
  1 ? d(u, v) ? 2.
• Each vertex in G effectively has a surrounding
  ring (annulus) with inner radius of unit size and
  outer radius of 2 units, and is connected to
  every other node within its ring. (Note the
  analogy of the definition to that of unit disk
  graphs.)

59
Unit Ring Graphs Clique Number

• Lemma The clique number of any unit ring graph
  is at most 5.

• Proof is similar to Khullers proof for max
  independent set size in unit disk graphs.
• Since the distance between any two connected
  vertices in a unit ring graph is at most 2 units,
  all vertices in a clique must reside within a
  circle of unit radius.
• Suppose there is a clockwise ordering of vertices
  in this circle, and consider any two adjacent
  vertices, u and v, in this ordering.
• Then we have ?x gt ?/3 in the uxv triangle.

R2
60
Unit Ring Graphs Chromatic Number

• Lemma The chromatic number of any unit ring
  graph GR is at most 12.

• Proof is by construction. Use regular hexagons to
  tessellate the entire graph.
• All nodes within the same hexagon can be colored
  the same.
• The hexagons that are far enough from each other
  can use the same color.

61
Unit Ring Graphs

• Lemma Given a unit disk graph G, let H G2 -G.
  Then for any such H, there exists a unit ring
  graph GR such that H ? GR.

• Proof . Consider an edge (u,v) in H we have
• (u,v) ? E(G) ? d(u,v) gt 1,
• ? w such that d(u,w) ? 1 and d(w,v) ? 1
• So we have 1 ? d(u,v) ? 2, which implies (u,v) ?
  E(GR). Hence H ? GR.

G
HG2-G
GR
62
SLICON Scheme Scalability Result

• Lemma The chromatic number of any unit ring
  graph GR is at most 12.
• Lemma Given a unit disk graph G, let H G2 -G.
  Then for any such H, there exists a unit ring
  graph GR such that H ? GR.
• Theorem A constant frame size f, where f ? 12,
  is sufficient for assigning time slots to all
  nodes in a network using the SLICON scheme,
  regardless of network size and density.

63
Greedy SLICON Coloring Example
Example output of greedy SLICON coloring on a
network of 1000 nodes, where transmission radius
is set to 0.1 for all nodes. The color bar at
the bottom represents all colors used in the
greedy coloring as the slots in a time frame.
Nodes assigned to a specific color are
activated for channel access in the corresponding
slot.
64
SLICON Scheme
SLICON Frame

• In each slot ?, the nodes assigned to ? contend
  for the channel by a regular CSMA protocol.
• At the end of the slot, all involved nodes pause
  their operation, storing the current values of
  their local CSMA-related information (such as
  CWmin, CWmax, backoff timers).
• They resume from the saved state at the next
  occurrence (instance) of slot ?.
• If all instances of slot ? were to be adjoined,
  removing all other slots from the time line,
  there would be a set of independent groups of
  nodes executing a regular CSMA protocol in a
  single-hop network (i.e. no hidden terminals).

65
SLICON Scheme Analysis

• B channel bandwidth
• g traffic generation rate at a node (traffic
  load)
• f SLICON frame size (number of slots)
• Assume function SCSMA(i, g) ? normalized node
  throughput of a CSMA protocol in a single-hop
  network with i competing stations.
• Then the expected throughput of node v in the
  SLICON scheme can be expressed as
• where nv is the number of vs neighbors assigned
  the same time slot as v.

66
CSMA CSMA/CA Analysis

• CSMA slot size denoted by ?.
• Each node behaves according to a simple Markovian
  behavior.
• Initially in the idle state
• with probability g, generate a new packet and
  transition to wait state.
• In wait state
• with probability ?, sense the channel
• start transmission if the channel sensed idle
• If data transmission fails, go back to wait state
  to retry
• If succeeds, go back to idle waiting for new data
  arrival

67
CSMA Analysis
CSMA Markov chain model for a node
Markov chain model for the channel in a
single-hop network
68
CSMA Analysis
CSMA Markov chain model for a node
Markov chain model for the channel in a
single-hop network
69
CSMA Analysis
CSMA Markov chain model for a node
CSMA
N, g, ?, Ldata
S, D
Markov chain model for the channel in a
single-hop network
70
CSMA Analysis - Theory vs. Simulation
Average throughput S, and media access delay D
vs. data generation rate for a CSMA node,
comparing the analytical solution of the Markov
model to the simulation results. N 10 and
Ldata 50.
71
CSMA/CA Analysis
RTS
PIR
PRC
PRI
PII
PIC
IDLE
CTS
PCI
PCD
1
DATA
Markov chain model for the channel in a multi-hop
network
CSMA/CA Markov chain model for a node
72
CSMA/CA Analysis Theory vs. Simulation
Average throughput S, and media access delay D
vs. backoff rate for a CSMA/CA node, comparing
the analytical solution of the Markov model to
the simulation results. N 10, Ldata 100, g
0.1.
73
CSMA/CA Theory vs Simulation
Average throughput S, and media access delay D
vs. backoff rate for a CSMA/CA node, comparing
the analytical solution of the Markov model to
the simulation results. N 10, Ldata 20, g
0.1.
74
SLICON Scheme vs Collision-Avoidance (RTS/CTS)
Scheme

• Consider an arbitrary-size network with avg.
  neighborhood size of N.

• Using the hexagonal tessellation for the SLICON
  slot assignment, the average number of nodes
  within each hexagonal cell is
• Then the expected node throughput in the SLICON
  scheme can be expressed as

• Compare to SCA(N, g) ? normalized node throughput
  of a collision avoidance protocol in a multi-hop
  network with avg. neighborhood size of N.

75
SLICON vs Collision-Avoidance
Throughput and media access delay for different
access schemes versus traffic load for a small
packet size (Ldata 20?) and N20. Different
values of abstract MAC protocols with different
backoff schemes.
76
SLICON vs Collision-Avoidance
Throughput and media access delay for different
access schemes versus traffic load for a large
packet size (Ldata 200?) and N20. Different
values of abstract MAC protocols with different
backoff schemes.
77
SLICON vs Collision-Avoidance
Capacity analysis of different access schemes for
different data packet sizes.
78
IEEE 802.11 Simulations
Place 9N nodes uniformly at random in a circle of
radius 3r. Collect statistics of the center
node, which has N neighbors on average. Emulates
a large uniformly deployed multi-hop network
nodes further away have very weak effect on the
center node.
79
SLICON vs CA via 802.11 Simulations
Throughput and media access delay versus traffic
load. The average neighborhood size is N 20 and
data size is 400 bits (Ldata 20?). The upper
x-axis shows the value g in the analytical model
that corresponds to the packet interarrival time
on the lower x-axis.
80
SLICON vs CA via 802.11 Simulations
Data and control traffic overhead for each access
scheme for an average neighborhood size of N
20 and data size of Ldata 20?.
81
SLICON vs CA via 802.11 Simulations
Capacity analysis for different packet sizes.
82
Summary Future Work

• Designed efficient STDMA protocols that do not
  require global time synchronization.
• Presented routing protocols that minimize
  end-to-end delays in STDMA protocols, alleviating
  their high latency drawback.
• Proposed a new hybrid media access scheme that
  improves the channel access efficiency of
  collision avoidance scheme.
• Some future research venues are
• generalization of the SLICON scheme for
  multi-channel, multi-radio networks, and
  multicast transmissions,
• applying the GreenWave routing idea to more
  general underlying MAC protocols that may provide
  variable delay estimates to the upper layer,
  rather than certain values as in STDMA protocols.

83
Thank You!... Any Questions?
Relevant Publications

• F. Sivrikaya and B. Yener, Time Synchronization
  in Sensor Networks A Survey, IEEE Network
  Magazine - special issue on Ad Hoc Networking
  Data Communications and Topology Control, Vol.
  18, Issue 4, pp. 4550, July/August 2004.
• C. Busch, M. Magdon-Ismail, F. Sivrikaya, B.
  Yener, Contention-Free MAC Protocols for
  Wireless Sensor Networks, In Proc. 18th
  International Conference on Distributed Computing
  (DISC 2004), pp. 245-259, Amsterdam, The
  Netherlands, October 2004.
• F. Sivrikaya, C. Busch, M. Magdon-Ismail, B.
  Yener, ASAND Asynchronous Slot Assignment and
  Neighbor Discovery Protocol for Wireless
  Networks, OPNETWORK07, Washington DC, 27-31
  August 2007.
• F. Sivrikaya and B. Yener, Minimum Delay Routing
  for Wireless Networks with STDMA, to appear in
  the ACM/Springer Wireless Networks Journal
  (WINET).
• M. Magdon-Ismail, F. Sivrikaya, B. Yener,
  Problem of Power Optimal Connectivity and
  Coverage in Wireless Sensor Networks,
  ACM/Springer Wireless Networks Journal (WINET)
  Vol. 13 , Issue 4, pp. 537550, August 2007.
• M. U. Caglayan, F. Sivrikaya, B. Yener, What is
  the Optimum Length of a Wireless Link?, UPGRADE,
  The European Journal for the Informatics
  Professional, Vol. 5, Issue 1, February 2004.