1. Department of Information Engineering University of Padova, ITALY Performance Analysis of Limited–1 Polling in a Bluetooth Piconet A note on the use of these ppt slides: We’re making these slides freely available to all, hoping they might be of use for researchers and/or students. They’re in PowerPoint form so you can add, modify, and delete slides (including this one) and slide content to suit your needs. In return for use, we only ask the following: If you use these slides (e.g., in a class, presentations, talks and so on) in substantially unaltered form, that you mention their source. If you post any slides in substantially unaltered form on a www site, that you note that they are adapted from (or perhaps identical to) our slides, and put a link to the authors webpage: www.dei.unipd.it/~zanella Thanks and enjoy! A note on the use of these ppt slides: We’re making these slides freely available to all, hoping they might be of use for researchers and/or students. They’re in PowerPoint form so you can add, modify, and delete slides (including this one) and slide content to suit your needs. In return for use, we only ask the following: If you use these slides (e.g., in a class, presentations, talks and so on) in substantially unaltered form, that you mention their source. If you post any slides in substantially unaltered form on a www site, that you note that they are adapted from (or perhaps identical to) our slides, and put a link to the authors webpage: www.dei.unipd.it/~zanella Thanks and enjoy!

2. Department of Information Engineering University of Padova, ITALY Performance Analysis of Limited–1 Polling in a Bluetooth Piconet {daniele.miorandi, andrea.zanella}@dei.unipd.it Daniele Miorandi, Andrea Zanella CITSA’05, Orlando, 14-17 July 2005 Special Interest Group on NEtworking & Telecommunications

3. CITSA05, Orlando (Florida), 14-17 July, 2005 Outline of the contents  Motivations & Purposes  Bluetooth Basic  System Model  Performance Analysis  Concluding Remarks

4. CITSA05, Orlando (Florida), 14-17 July, 2005 What and Why… Motivations & Purposes

5. CITSA05, Orlando (Florida), 14-17 July, 2005 Motivations  Analytical models for Bluetooth systems permit  Performance estimation (packet delay statistics)‏  Buffer dimensioning (queue length statistics)‏  Segmentation and reassembly strategy (packet type selection)‏  Recently, some models have been proposed for simple scenarios with multi-slot packets [Bruno,Misic]  Approximate delay estimation using M/G/1 queues with vacations  Exact analysis for symmetric systems (equally loaded nodes) only  Literature still lacks a mathematical model that takes into consideration multislot packets and asymmetric traffic load among nodes

6. CITSA05, Orlando (Florida), 14-17 July, 2005 Aim of the study  Providing an approximate performance analysis in case of  Use of multi-slot packets  Asymmetric and unbalanced traffic matrix

7. CITSA05, Orlando (Florida), 14-17 July, 2005 What the standard says… Bluetooth basic

8. CITSA05, Orlando (Florida), 14-17 July, 2005 Bluetooth piconet piconet  Two up to eight Bluetooth units sharing the same channel form a piconet  In each piconet, a unit acts as master, the others act as slaves centralized polling scheme  Channel access is based on a centralized polling scheme Time-division- duplex  Full-duplex is supported by Time-division- duplex (TDD), with time slots of T=0.625 ms active slave master parked slave standby slave1 slave2 slave3 master

9. CITSA05, Orlando (Florida), 14-17 July, 2005 Multi-slot packets  Data packets can be:  1, 3, or 5 slot long  Unprotected or 2/3 FEC protected  Unprotected packet formats (DH)  higher data capacity  more subject to errors  Protected packet formats (DM):  medium data capacity  higher protection against errors

10. CITSA05, Orlando (Florida), 14-17 July, 2005 Mathematical Model System Model for Ideal Channels

11. CITSA05, Orlando (Florida), 14-17 July, 2005 Downlink master queues (one per slave)‏ Uplink slaves queues System Model  Number of units  N-1 slaves and 1 master  System model  2N-2 interacting queues  Traffic model  Packets arrive at link i,j as a marked Poisson process of rate λ i,j and weights  ij (l), l=1,3,5  Only single-hop communications  Pure Round Robin (PRR)‏  One packet polling cycle  One packet per queue is served per polling cycle random duration  Polling cycle has a random duration depending on the size of the packets found waiting at each queue-head N-1

12. CITSA05, Orlando (Florida), 14-17 July, 2005 Cycle Time Queue service time (B 0,1 )‏ Queue service time (B 1,0 )‏ Cycle Time (T C )‏ B i,j : part of the cycle time spent in serving queue (i,j)‏ T C : time required to complete a polling cycle P i,j (0): probability of empty (i,j) queue  i,j : load factor of (i,j) queue Little’s law

13. CITSA05, Orlando (Florida), 14-17 July, 2005  According to the head of the queue packet type we have  Empty queue: B ij = 1 slot (POLL or NULL packet)‏  DH1 or DM1: B ij = 1 slot  DH3 or DM3: B ij = 3 slots  DH5 or DM5: B ij = 5 slots  Taking expectations we get  Average service time for (i,j) queue: b ij =E[B ij ]  Average cycle time  Putting pieces together, we get a system of 2N-2 equations Cycle Time Statistics

14. CITSA05, Orlando (Florida), 14-17 July, 2005 Average cycle time  Solving the system we easily get

15. CITSA05, Orlando (Florida), 14-17 July, 2005 Delay time Slave 1 Slave 2 Slave k Vacancy delay (V i,j )‏ Slave 1 Slave 2 Slave k Queue delay (Q ij )‏ Slave 1 Slave 2 Slave k Transmission time (Z i,j )‏ Cycle Time (T C )‏

16. CITSA05, Orlando (Florida), 14-17 July, 2005  Let W ij be the access delay for link (i,j), i.e., the time spent in the queue before entering the service  The access delay W ij can be expressed as where  V i,j : vacancy time time between the packet arrival and the instant the queue gets the service  Q i,j : queue delay time for getting rid of all the packets found in the queue  Hence, the packet delay D ij for link (i,j) will be given by Packet Delay

17. CITSA05, Orlando (Florida), 14-17 July, 2005  The queue delay Q ij can be expressed as follows  where  L i,j : number of queued packets at the packet arrival epoch  U ij (k): inter-visit time for the k-th queued packet at (i,j) queue time for getting rid of all the packets found in the queue  NOTE: U ij (k) is a special polling cycle, since it refers to the specific case in which at least a packet is waiting in the (i,j) queue  Assuming U ij (k) to be independent of packet index k we get Queue Delay Queue service time obtained with

18. CITSA05, Orlando (Florida), 14-17 July, 2005 Equivalent load factor  Once again we get a system of equations  that solves for

19. CITSA05, Orlando (Florida), 14-17 July, 2005 Laplace-Stieltjes Transform (LST)‏  Applying LST & assuming delay components to be independent we get  Packet service time  Number of queued packets  Queue delay  Queue service time  Inter-visit time  Access delay The LST of the vacancy time is still missing…

20. CITSA05, Orlando (Florida), 14-17 July, 2005 Vacancy Time  The LST of the vacancy time, V * i,j (s) can be  either derived extending the method proposed by Ibe&Cheng [COMM89]… random look theory  or approximated by applying the random look theory (much easier!)‏  This approximation allows to get a closed form expression of the average packet delay

21. CITSA05, Orlando (Florida), 14-17 July, 2005 Results (1)‏  We checked the accuracy of our approximated model for balanced scenarios, for which exact solution is known  N=4,  (1)=  (3)=1/9,  (5)=7/9  Queues are equally loaded  Symmetric Traffic  Remark: the proposed model closely approximates the exact result also for high traffic loads

22. CITSA05, Orlando (Florida), 14-17 July, 2005 Results (2)‏  Balanced asymmetric scenarios  N=4,  (1)=  (3)=1/9,  (5)=7/9  Queues are equally loaded  Download Traffic only  Remark: the accuracy of the proposed model is even more clear for asymmetric scenarios

23. CITSA05, Orlando (Florida), 14-17 July, 2005 Results (3)‏  Unbalanced scenarios  N=4,  (1)=  (3)=  (5)=1/3   0,1 =  1,0 =  0,2 =  2,0 =0.3   0,3 =  3,0 =0.9

24. CITSA05, Orlando (Florida), 14-17 July, 2005 Conclusions & Future work  Summary  Simple mathematical model for ideal Bluetooth links with unbalanced load has been presented  Average packet delay estimations given by the model closely approximates the exact results in balanced scenario, largely improving the models previously presented in the literature  The model seems to offer rather good performance estimation also in unbalanced scenarios  Next steps  Model can be extended to error-prone links  A fading channel model might be considered  Remark: this might exacerbate the interdependency among the queues, making the model less accurate

25. CITSA05, Orlando (Florida), 14-17 July, 2005 That’s all! Thanks for your attention!