Nov. 15 2002 Chung-Hsien Hsu 1

Round Robin with Look Ahead: A New Scheduling Algorithm for Bluetooth Daqing Yang, Gouri Nair, Balaji Sivaramakrishnan,

Harishkumar Jayakumar and Arunabha SenICPPW’02. 2002 IEEE

Speaker: Chung-Hsien Hsu

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Outline

Introduction Bin Packing Problem Scheduling Algorithm

– Look Ahead– Look Ahead Round Robin

Simulation Conclusion

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Introduction

SCO: Synchronous Connection Oriented

ACL: Asynchronous Connectionless Links

frame

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Introduction

Objective:– To achieve high channel utilization.

(throughput).

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Bin Packing Problem

Bin Packing Problem:– A set of objects L = { a1,…,an} with a size s(ai)

– A set of bins with a fixed capacity B– Objective:

• To pack the objects ai, 1<=i<=n, into as few bins as possible.

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Bin Packing Problem (cont.)

Off-line bin packing problem:– Have the complete knowledge of all elements

and their sizes.• Efficiently pack the objects in the bins.

Online bin packing problem:– Limited amount of future knowledge.– The scheduling algorithm for Bluetooth

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Bin Packing Problem (cont.)

M

S1 S2

MQ1 ( 5,5,5,5,5) MQ2 ( 1,1,1,1,1)

SQ1 ( 5,5,5,5,5) SQ2 ( 1,1,1,1,1)

CMSQ1 ( 10,10,10,10,10) CMSQ2 ( 2,2,2,2,2)

Bluetooth:

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Bin Packing Problem (cont.)

Supposition:– The number of slots between every SCO slot

pair is 10.• Frame size = 10

• As a bin with capacity 10.

The packets in the CMSQ can be viewed a objects.

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Scheduling Algorithm

Definition:– Asymptotic worst-case performance ratio

The minimum number of bins required to pack list L

The number of bins used by packing list L

Scheduling Algorithm AL = (a1,a2,…,an) : the packets being scheduled by algorithm A

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Scheduling Algorithm (cont.)

Theorem:– For the Round Robin scheduling algorithm A in

Bluetooth, RA = 5/3Proof:Bin sizes: 10Item sizes: 2, 4, 6, 8, 10.The Round Robin algorithm A guaranteed that any neighboring pair of bins packed item sizes at least 12.If OPT(L) = n the packets need to be packed have size at most 10n.A(L) <= 20n/12RA = 5/3

The Round Robin algorithm A compared with any scheduling algorithm B in Bluetooth, A is at most 5/3 worse than B.

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Scheduling Algorithm (cont.)

Look Ahead Look Ahead Round Robin

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Look AheadStep 1: Examine the (Head-Of-the-Line) packets CMSQ1,…CMSQx for all the active slaves in the piconet.

Step 2: Prioritize slaves in order of non-increasing size of their HOL packets in CMSQ (the slave with the largest HOL packet has the highest priority).

Step 3: If possible, schedule the highest priority slave in the current frame.

Step 4: If HOL packet of the highest priority does not fit, search through HOL priority list for highest priority that will fit the current frame.

Step 5: If none fits, wait for the start of a new frame and put the HOL packet in the new frame. Repeat step 1 through 5.

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Look Ahead (cont.)

Drawback – Computational overhead may be unacceptably

high.• If N slaves, it can be computed in O(log N) amount

of computation.

– Starvation.

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Look Ahead Round Robin

Round Robin + Look Ahead.– To avoid the starvation.– To reduce the computational complexity.

Different from RR:– When the current packet does not fit,

the algorithm looks ahead and attempt to schedule a packet from next slave in line.

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Look Ahead Round Robin (cont.)

Step 1: The algorithm will fill the current frame with the HOL packets in a Round Robin fashion, if the HOL packet can fit in the frame.

Step 2: If the HOL packet of the queue being serviced is too large to fit in the current frame, following Round Robin fashion, find the queue whose HOL packet will fit in the current frame. If no such queue exists, wait for the start of a new frame and schedule the HOL packet in the new frame. Repeat steps 1 and 2.

Note:

The information (size of the HOL packet in the slave) may be conveyed to the master by slaves using the unused fields in the header of the immediately preceding packet.

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Look Ahead Round Robin (cont.)

Example 1:Support the number of packets in each queue is n.Queue 1: L1 = (6, 6, 6, 6, 6, …)Queue 2: L2 = (8, 8, 8, 8, 8, …)Queue 3: L3 = (4, 4, 4, 4, 4, …)Queue 4: L4 = (2, 2, 2, 2, 2, …)

Round Robin algorithm : 3n frames.Round Robin with 1-look-ahead algorithm : 2n frames.

Performance comparison ratio: 3/2

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Look Ahead Round Robin (cont.)

Example 2:Support the number of packets in each queue is n.Queue 1: L1 = (6, 6, 6, 6, 6, …)Queue 2: L2 = (6, 6, 6, 6, 6, …)……Queue 2k-1: L2k-1 = (6, 6, 6, 6, 6, …)Queue 2k: L2k = (8, 8, 8, 8, 8, …)Queue 2k+1: L2k+1 = (4, 4, 4, 4, 4, …)Queue 2k+2: L2k+2 = (4, 4, 4, 4, 4, …)……Queue 4k-1: L4k-1 = (4, 4, 4, 4, 4, …)Queue 4k: L4k = (2, 2, 2, 2, 2, …)

Round Robin algorithm : 3kn frames.Round Robin with (2k-1)-look-ahead algorithm : 2kn frames.

Performance comparison ratio: 3/2

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Look Ahead Round Robin (cont.)

Example 3:Support the number of packets in each queue is n.Queue 1: L1 = (6, 6, 6, 6, 6, …)Queue 2: L2 = (6, 6, 6, 6, 6, …)……Queue 2k: L2k = (6, 6, 6, 6, 6, …)Queue 2k+1: L2k+1 = (8, 8, 8, 8, 8, …)Queue 2k+2: L2k+2 = (4, 4, 4, 4, 4, …)Queue 2k+3: L2k+3 = (4, 4, 4, 4, 4, …)……Queue 4k+1: L4k+1 = (4, 4, 4, 4, 4, …)Queue 4k+2: L4k+2 = (2, 2, 2, 2, 2, …)

Round Robin algorithm : (3k+1)n frames.Round Robin with 2k-look-ahead algorithm : (2k+1)n frames.

Performance comparison ratio: (3k+1)/(2k+1)

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Simulation

Special situations– Round Robin with k-look-ahead can reduce the

number of frames by 50% over just Round Robin.

General situations:– Turned to simulation.

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Simulation (cont.)

Environment:– Developed in Java

• Create pseudo-parallel packet generation and scheduling.

• Assume packet arrival at the master and the slaves followed a Poisson process.

• Packet size: 1, 3, 5

• Packet be drawn from a uniform distribution.

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Simulation (cont.) Variables:

– The number of slaves in the piconet.• 1 ~ 7

– Packet arrival rate.• 0.1 ~ 1.0

The simulation was carried out for 1000 units of times.

Each experiment was repeated 500 times to compute average frame savings.

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Simulation (cont.)

Number of Slaves

Average % Savings from RR

LARR

LA

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Simulation (cont.)

Arrival rates

Average % Savings from RR

LARR

LA

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Simulation (cont.)

Arrival rates

Average % Savings from RR

LARR

LA

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Simulation (cont.)

Arrival rates

Average % Savings from RR

LARR

LA

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Conclusion

Present two scheduling algorithms for BT.– Look Ahead algorithm– Look Ahead Round Robin algorithm.

LA and LARR perform significantly better than the RR algorithm.

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Conclusion (cont.)

LARR better than LA– Computational complexity is smaller.– To avoid starvation.

Currently Examining the efficacy of these two algorithms from the power consumption point of view.