Network Theory
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 tradeoff in interference and power in such networks as their size increases?
Publications

El Gamal, J. Mammen, B. Prabhakar, D. Shah,
“Optimal throughputdelay tradeoff in wireless networks – Part II: Constantsize packets,”
IEEE Transactions on Information Theory, 52(11):51115116, November 2006.

El Gamal, J. Mammen, B. Prabhakar, D. Shah,
“Optimal throughputdelay scaling in wireless networks  Part I: The ﬂuid model,”
IEEE Transactions on Information Theory, 52(6):25682592, June 2006.

A. El Gamal, J. Mammen, B. Prabhakar, D. Shah,
“Throughputdelay scaling in wireless
networks with constantsize packets,”
Proceedings of the IEEE International Symposium
on Information Theory, pp.13291333, September 2005.

A. Montanari, B. Prabhakar, D. Tse, “Belief propagation based multiuser detection,”
Proceedings of the 43rd Allerton Conference on Communication, Control and
Computing, September 2005.
 P. Gupta, B. Prabhakar, S. Boyd,
“Nearoptimal depthconstrained codes,”
IEEE Transactions on Information Theory, 50(12):32943298, December 2004.

A. El Gamal, J. Mammen, B. Prabhakar, D. Shah,
“Throughputdelay tradeoff in energy constrained wireless networks,”
Proceedings of the IEEE International Symposium on Information Theory, p.439, June 2004.

Best Paper Award. A. El Gamal, J. Mammen, B. Prabhakar, D. Shah,
“Throughputdelay tradeoff in wireless networks,”
Proceedings of IEEE INFOCOM Conference on
Computer Communications, 23(1):464475, March 2004.

B. Prabhakar, R. Gallager,
“Entropy and the timing capacity of discrete queues,”
IEEE Transactions on Information Theory, 49(2):357370, February 2003.

A.J. Ganesh, N. O’Connell, B. Prabhakar,
“Invariant rate functions for discretetime
queues,” Annals of Applied Probability, 13(2):446474, May 2003.

B. Prabhakar,
“The attractiveness of the ﬁxed points of a ·/GI /1 queue,” Annals of
Probability, 31(4):22372269, October 2003.

J. Mairesse, B. Prabhakar,
“The existence of ﬁxed points for the ·/GI /1 queue,” Annals of
Probability, 31(4):22162236, October 2003.

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.

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):824843, September 2000.

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.288296, September 1999.

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.

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.

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.143144, June 1998.

B. Prabhakar, N. Bambos,
“On a singular feature of critical G/M/1 queues,” Systems &
Control Letters, 28(5):239245, September 1996.

B. Prabhakar, T.S. Mountford, N. Bambos, “Convergence of departures in tandem
networks of ·/GI /∞ queues,” Probability in the Engineering and Informational Sciences,
10:487500, October 1996.

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.448453, 1995.

B. Prabhakar, N. Bambos, “Entropy methods for high speed communications,”
Proceedings of the Conference on Information Sciences and Systems, pp.448453, March
1995.

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):121127, February 1995.

N. Bambos, B. Prabhakar,
“On inﬁnite queueing tandems,” Systems & Control Letters, 23(4):305314, October 1994.

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.563572, September 1994.
