1February 20, 2008

Spatio-Temporal Bandwidth Reuse: A Centralized Spatio-Temporal Bandwidth Reuse: A Centralized Scheduling Mechanism for Wireless Mesh NetworksScheduling Mechanism for Wireless Mesh Networks

Mahbub Alam

Prof. Choong Seon Hong

Introduction

• Broadband wireless access (BWA) network is a promising technology in providing better end user services.

• Designing a scheduling algorithm that fairly allocates bandwidth to the end users while maximizes the overall network throughput is a challenging task.

• We present a fair and efficient scheduling mechanism for IEEE 802.16 based Wireless Mesh Networks.

Introduction (Contd.)

• IEEE 802.16 provides fixed BWA with QoS guarantee and supports two operational modes:

– Point-to-multipoint and the optional mesh mode.

• The wireless mesh network adopts the Time Division Multiple Access (TDMA) method between SSs and between SSs and BS

• The mesh mode supports two different types of scheduling:

– centralized and distributed scheduling

• In centralized scheduling the BS acts as a scheduler and determines transmission and reception slots for each SS

Fair Scheduling in Wireless Mesh Networks

• Due to the multihop nature, throughput of different connections can vary depending on the location of the SSs to whom they are connected.

• If SS is few hop away from BS, then a connection of this SS may not send or receive traffic at all – which is not only unfair but undesirable as well.

• Therefore, the main challenge of scheduling in a mesh network is two folds: – To ensure that every connection gets equal access from the

network irrespective of their locations

– To achieve optimum bandwidth utilization to increase the overall network throughput.

System Models and Assumptions

BS

SS1

SS2SS3 SS4

SS5

SS6

SS7

SS8 SS9

11c

12c

13c23c

14c

15c25c

18c28c

16c

17c

19c29c

System Models and Assumptions (Contd.)

• The network is used to connect clients to the Internet. – traffic flows from SSs to BS and BS to SSs

• All traffics from SSs to the BS are termed as uplink traffic

• The traffic from a particular connection of a particular SS towards the BS is defined as uplink flow

• We assume that the SSs are static and so the topology of the access network does not change frequently

• Scheduling is done separately for uplink and downlink flows. – a single scheduling mechanism is applicable to both types

of flows

Fair and Efficient Scheduling in Mesh Networks

Fairness in Scheduling

• Definition (Fair Scheduling): A scheduling mechanism is defined as fair if all the flows achieve equal throughput in all time interval (t1, t2) and is given by

• If BS assigns fixed number of slots to a link for one connection then the throughput of connection, if 1 hop away from BS

• If the SS is h hop away from the BS, then the BS has to assign S slot in all h links during (t1, t2)

1 2 1 2( , ) ( , ) , , , | ( , ) , ,j yi x i xW t t W t t i j x y i x j y

22 1

( , )ji i

S bW t t

t t

Fairness in Scheduling (Contd.)

• The fixed amount of data (S × b) that BS receives from a connection is termed as Transmission Unit (TU)

• The duration of time when BS receives one TU from each flow is a Transmission Round or a cycle

• Number of TU in one cycle is

1 1

iCN

r i di j

t h S t

1 1

iCN

ii j

T h

Load of a Link

• Scheduling mechanism either uses link-based transmission rights assignment or node-based assignment.

• We choose to assign transmission rights to the links

• Definition (Load of a Link): The load of a link is defined as the number of connections for which the link forwards data.

– In other words, is the number of transmission units the link is assigned in a transmission round.

Network Throughput

• Throughput of a connection in a transmission round is

• Then system throughput in a round is

• Network throughput is inversely proportional to T• therefore the system throughput can be maximized if

we can minimize T

( )ji r

d

S bW t

T t

1 1 1 1

i iC CN Nj

ii j i j d

S bW W

T t

Throughput Maximization

• Throughput of the network is increased exploiting the spatial reuse of the bandwidth

– scheduling multiple non-contending links simultaneously (STDMA)

• STDMA reduces the length of a transmission round in terms of transmission units

• We introduce a spatio-temporal bandwidth reuse technique

– Which provides further improvement in reducing the length of a transmission round.

Link Scheduling Matrix (LSM) and Graph

0 0 0 0 0 0 0 1 1

0 0 0 0 0 1 1 0 0

0 0 0 1 1 1 1 0 0

0 0 1 0 0 0 0 1 1

0 0 1 0 0 0 0 1 1

0 1 1 0 0 0 1 1 1

0 1 1 0 0 1 0 1 1

1 0 0 1 1 1 1 0 0

1 0 0 1 1 1 1 0 0

LSM

2,1

7,6

8,7 5,4

4,1

9,7

6,0

3,2

1,0

(a) Link Scheduling Matrix (LSM) (b) Link Scheduling Graph (G)

rows in LSM correspond to links (1,0), (6,0), (7,6), (2,1), (4,1), (3,2), (5,4), (8,7) and (9,7) respectively.

Scheduling by Clique Construction

• Clique construction method using Link scheduling graph (G), can be used to maximize the throughput.

• This technique achieves better throughput compared to conventional TDMA through spatial reuse of bandwidth

• The scheduling mechanism selects a set of cliques such that

– the set of cliques covers each link in G only once and includes all the links in G

– maximizes the gain

• The gain of a clique is defined as the number of transmission units that the scheduling mechanism can save by using frequency reuse

Does the Clique Construction Mechanism provide Optimum Throughput?

Fig. Scheduling using clique construction. This figure is taken from the paper “A Fair Scheduling for Wireless Mesh Networks” by Naouel Ben Salem and Jean-Pierre Hubaux

Throughput Maximization

• The gain will be maximum in scheduling by clique construction only if each link has the same load

• In multihop mesh networks, links closer to BS forward the traffic of the upstream nodes and so have higher load than a distant link.

– links have different loads depending on their location in the network or distance from the BS

Fair Scheduling with Spatio-Temporal Bandwidth Reuse

• If link li,j is closer to BS and link lx,y is far away from BS.

– Then for mesh networks Li,j >> Lx,y

– And a clique construction algorithm creates a clique of cardinality 2.

• But there exists many other links far away from BS, say link lm,n, which does not contend with li,j but may contend with lx,y.

• Also it may be true that

Li,j ≥ Lx,y + Lm,n

Spatio-Temporal Bandwidth Reuse (Contd.)

• There exists many cliques of cardinality 2 that have common links and the common link is the mostly loaded link of the cliques.

• Links li,j, lx,y and lm,n form a complete bi-partite graph where

– one partition has only one vertex (and so one link) and it is the mostly loaded link

– the other partition can have as many vertices as possible satisfying the condition

1 1 2 2, , , ,..........p pi j x y x y x yL L L L

Spatio-Temporal Bandwidth Reuse (Contd.)

• Definition (Spatio-Temporal Bandwidth Reuse): If n links are individually non-contending with a particular link li,j but the links are pairwise contending (or form an independent set) and the combined load of the n links are less than or equal to the load of li,j,

• Then a special scheduling is possible where n links are scheduled in different time with respect to each other but spatially scheduled with li,j, achieving a combination of both spatial and temporal bandwidth reuse.

Spatio-Temporal Bandwidth Reuse (Contd.)• Observation 1: Combined scheduling of more than one

cliques of cardinality 2, where – Each clique has a common vertex and it is the mostly loaded vertex

in each clique,

– Allows both spatial and temporal reuse of bandwidth

– And maximizes the bandwidth reuse over the individual scheduling of each clique.

lI, j

la1, b1 la2, b2 la3, b3 lan, bn

links

Transmission unit

li, jla1, b1

la2, b2

la3, b3

lan, bn

Spatio-Temporal Bandwidth Reuse (Contd.)

• Observation 2: If n cliques of cardinality 2 have a common vertex and the remaining vertices form an independent set,

– then these n cliques always produce a complete bi-partite graph.

• Number of transmission units required to schedule all the links of a complete bi-partite graph is equal to the sum total of the loads of the mostly loaded partition.

Spatio-Temporal Bandwidth Reuse (Contd.)

• Observation 3: For a complete r-partite graph, where number of vertices in partition i is xi, and load of the mostly loaded partition is dr, then number of transmission units require to schedule all the links in the r-partite graph is dr.

• Load of a partition,

• Load of the mostly loaded partition

• Gain of complete r-partite graph

1 2, ,.... rx x xK

,

,i

i j i

P i jl P

L L

, ,...,1 2

max ( )i

i x x xr

r PP K

d L

1 2, ,...,1

( ) ( )n i

r

x x x P ri

K L d

g

Scheduling Algorithm

• Different sets of complete r-partite graphs, where each set satisfies the following two conditions

– Each set si of complete r-partite graphs covers all the vertices in the link contention graph.

– In each set si a vertex does not appear in more than one r-partite graph, that is, a set of r-partite graphs includes a vertex only once.

Scheduling Algorithm (Contd.)

• Optimum scheduling solution can be found from the following optimization problem

1 2, ...,1 2,

1 2 1 2 1 2 1 2

, ,...,

1 2 1 2, ,..., , ,..., , ,..., , ,...,,

rx x xr

r r r r

i

i

x x xK s

x x x x x x x x x x x x

or

T

subject to

K U

K K K K s

maximize g

minimize

Example Scheduling

8,7

9,7 1,0 (a)

2,1

7,6

5,4

4,1

6,0

3,2

(b)

2,1

7,6 4,1

(b) 5,4 6,0

3,2

(a)

links

Transmission units

(1,0)

(2,1)

(3,2)

(4,1)

(5,4)

(6,0)

(7,6)

(8,7)

(9,7)

1 transmission round = 19 transmission units

2,1

7,6

8,7 5,4

4,1

9,7

6,0

3,2

1,0

Conclusion

• We present a centralized fair scheduling algorithm which ensures per connection fairness and enhance throughput

• Throughput enhancement is achieved through spatio-temporal bandwidth reuse.

• However, Proposed algorithm is computationally expensive.

• So greedy approach or heuristics are better to find the optimal solution.