Balaji Prabhakar

Stochastic network theory seeks models that explain the behavior of large data networks. This work draws upon ideas from queueing theory, information theory, interacting particle systems, percolation, statistical physics and random graph theory. One major theme of research concerns the resolution of conjectures regarding the existence, uniqueness and attractiveness of fixed points for queueing operators. This work shows how packet processes behave in large queueing tandem networks and how the entropy of these processes changes as they pass through certain queues. Another major theme concerns the behavior of large ad hoc wireless networks, modeled as random geometric graphs: what is the optimal trade-off in interference and power in such networks as their size increases?

Publications

1. El Gamal, J. Mammen, B. Prabhakar, D. Shah, “Optimal throughput-delay trade-off in wireless networks – Part II: Constant-size packets,” IEEE Transactions on Information Theory, 52(11):5111-5116, November 2006.
2. El Gamal, J. Mammen, B. Prabhakar, D. Shah, “Optimal throughput-delay scaling in wireless networks - Part I: The fluid model,” IEEE Transactions on Information Theory, 52(6):2568-2592, June 2006.
3. A. El Gamal, J. Mammen, B. Prabhakar, D. Shah, “Throughput-delay scaling in wireless networks with constant-size packets,” Proceedings of the IEEE International Symposium on Information Theory, pp.1329-1333, September 2005.
4. A. Montanari, B. Prabhakar, D. Tse, “Belief propagation based multi-user detection,” Proceedings of the 43rd Allerton Conference on Communication, Control and Computing, September 2005.
5. P. Gupta, B. Prabhakar, S. Boyd, “Near-optimal depth-constrained codes,” IEEE Transactions on Information Theory, 50(12):3294-3298, December 2004.
6. A. El Gamal, J. Mammen, B. Prabhakar, D. Shah, “Throughput-delay trade-off in energy constrained wireless networks,” Proceedings of the IEEE International Symposium on Information Theory, p.439, June 2004.
7. Best Paper Award. A. El Gamal, J. Mammen, B. Prabhakar, D. Shah, “Throughput-delay trade-off in wireless networks,” Proceedings of IEEE INFOCOM Conference on Computer Communications, 23(1):464-475, March 2004.
8. B. Prabhakar, R. Gallager, “Entropy and the timing capacity of discrete queues,” IEEE Transactions on Information Theory, 49(2):357-370, February 2003.
9. A.J. Ganesh, N. O’Connell, B. Prabhakar, “Invariant rate functions for discrete-time queues,” Annals of Applied Probability, 13(2):446-474, May 2003.
10. B. Prabhakar, “The attractiveness of the fixed points of a ·/GI /1 queue,” Annals of Probability, 31(4):2237-2269, October 2003.
11. J. Mairesse, B. Prabhakar, “The existence of fixed points for the ·/GI /1 queue,” Annals of Probability, 31(4):2216-2236, October 2003.
12. B. Prabhakar, R. Gallager, “Entropy and the timing capacity of discrete queues,” Proceedings of the IEEE International Symposium on Information Theory, p.228, June 2001.
13. B. Prabhakar, N. Bambos, T.S. Mountford, “The synchronization of Poisson processes and queueing networks with service and synchronization nodes,” Advances in Applied Probability, 32(3):824-843, September 2000.
14. A.J. Ganesh, N. O’Connell, B. Prabhakar, “Invariant rate functions for discrete time queues,” Proceedings of the 37th Annual Allerton Conference on Communication, Control and Computing, pp.288-296, September 1999.
15. Invited. R. Gallager, B. Prabhakar, “Entropy and the Shannon capacity of queueing systems,” Proceedings of the IEEE Information Theory and Communications Workshop, p.1, June 1999.
16. Invited. R. Gallager, B. Prabhakar, “The entropies of queue arrivals and queue departures,” Proceedings of the IEEE Information Theory and Networking Workshop, p.42, June 1999.
17. Invited. A.J. Ganesh, N. O’Connell, B. Prabhakar, “A large deviations characterization of the fixed point of a ·/G/1 queue,” Proceedings of the IEEE Information Theory Workshop, pp.143-144, June 1998.
18. B. Prabhakar, N. Bambos, “On a singular feature of critical G/M/1 queues,” Systems & Control Letters, 28(5):239-245, September 1996.
19. B. Prabhakar, T.S. Mountford, N. Bambos, “Convergence of departures in tandem networks of ·/GI /∞ queues,” Probability in the Engineering and Informational Sciences, 10:487-500, October 1996.
20. B. Prabhakar, N. Bambos, “The entropy and delay of processes in ATM networks,” Proceedings of the IEEE Information Theory Workshop on Information Theory, Multiple Access and Queueing, pp.448-453, 1995.
21. B. Prabhakar, N. Bambos, “Entropy methods for high speed communications,” Proceedings of the Conference on Information Sciences and Systems, pp.448-453, March 1995.
22. T.S. Mountford, B. Prabhakar, “On the weak convergence of departures from an infinite series of ·/M/1 queues,” Annals of Applied Probability, 5(1):121-127, February 1995.
23. N. Bambos, B. Prabhakar, “On infinite queueing tandems,” Systems & Control Letters, 23(4):305-314, October 1994.
24. B. Prabhakar, T.S. Mountford, N. Bambos, “The asymptotics of traffic processes in large queueing networks,” Proceedings of the 32nd Annual Allerton Conference on Communication, Control and Computing, pp.563-572, September 1994.