1. University of Padova Department of Information Engineering On the Optimal Topology of Bluetooth Piconets: Roles Swapping Algorithms Med-Hoc-Net 2002, Chia (Italy), 6 September 2002 Daniele Miorandi & Andrea Zanella {daniele.miorandi, andrea.zanella}@dei.unipd.it

2. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Overview  Intro to Bluetooth system  Mathematical model  Stability issues & delay analysis  Optimal criterion for off-line topologies design  Suboptimal criterion for real-time network reconfiguration  Conclusion & discussion

3. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Background: BT system architecture Two up to eight active Bluetooth devices sharing the same FH channel form a piconet In each piconet, a unit acts as a master, the others act as slaves Channel access is based on a centralized polling scheme Full duplex is achieved by means of time division duplexing (TDD). active slave master parked slave standby slave1 slave2 slave3 master

4. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella System Model  Cluster of N+1 nodes (N  7)  Assumptions All nodes are in-range Independent Poisson traffic model  Definitions Δ={δ i,j }: End-to-end traffic matrix Λ={λ i,j }: Effective traffic pattern matrix k: master unit P={k, Δ}: piconet

5. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella System Model (2)  Stability condition for the PRR polling scheme:  Definition : A traffic matrix is admissible if there is a master choice k s.t. the stability condition holds (i.e. there is a stable topology).  Definition : A traffic matrix is fully admissible if the stability conditions hold for any choice of the master k.  Proposition : A traffic matrix is fully admissible if and only if the following conditions hold:  P roposition : A traffic matrix is admissible if and only if the following conditions hold:

6. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Optimal Criterion  Link delay:  Up to a randomization of the polling order the average packet delay may be expressed as:  Defining as the total offered traffic we have:  Criterion I : choose k s.t.

7. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Suboptimal Criterion  The effective offered traffic is given by:  Reasoning: The more the effective traffic, the closer we get to the stability limit. The closer to the stability limit, the higher the delay.  Criterion II : choose k s.t.

8. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Results (1) N=5, matrix entries uniformly distributed in (0,1).  At medium-to-high loads, both criterion offer a remarkable performance improvement.  The suboptimal criterion leads to results good, even if far from optimality.

9. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Results (2) N=5, matrix entries uniformly distributed in (0,1), average density of 0.4.  The delays are much lower in the sparse case.  Both criterion offer valuable performance improvement.

10. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Applications  Optimal design of a static Bluetooth piconet (e.g., sensor networks).  Dynamic reconfiguration of a Bluetooth piconet: Each node keeps an estimate of the traffic generated towards the other nodes. The suboptimal criterion is used to find “better” configurations. Connection admission control: for each request the master checks for admissibility of the resulting traffic matrix; if the answer is negative the request is dropped.

11. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Conclusion  An analytical settlement for the characterization of efficient piconet topologies has been proposed.  Two algorithms for the master choice (an optimal and a suboptimal with low computational complexity) have been presented.  Simulation have been performed to show the impact on network performance.  Some applications have been presented.  Next step: towards efficient scatternet topologies.

12. Med-Hoc-Net, Chia, 6 September 2002 D. Miorandi & A. Zanella Any Questions?