Stability and capacity of regular wireless networks

We study the stability and capacity problems in regular wireless networks. In the first part of the paper, we provide a general approach to characterizing the capacity region of arbitrary networks, find an outer bound to the capacity region in terms of the transport capacity, and discuss connections between the capacity formulation and the stability of node buffers. In the second part of the paper, we obtain closed-form expressions for the capacity of Manhattan (two-dimensional grid) and ring networks (circular array of nodes). We also find the optimal (i.e., capacity-achieving) medium access and routing policies. Our objective in analyzing regular networks is to provide insights and design guidelines for general networks. The knowledge of the exact capacity enables us to quantify the loss incurred by suboptimal protocols such as slotted ALOHA medium access and random-walk-based routing. Optimal connectivity and the effects of link fading on network capacity are also investigated.

[1]  Sanjeev R. Kulkarni,et al.  A deterministic approach to throughput scaling in wireless networks , 2002, IEEE Transactions on Information Theory.

[2]  Leandros Tassiulas.  Scheduling and performance limits of networks with constantly changing topology , 1997 .

[3]  Robert B. Ellis.  Discrete Green's functions for products of regular graphs , 2003, math/0309080.

[4]  Andrea J. Goldsmith,et al.  Performance, optimization, and cross-layer design of media access protocols for wireless ad hoc networks , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[5]  E. Modiano.  A dynamic adaptive multi-receiver random access protocol for the code division multiple access channel , 1995, Proceedings of 6th International Symposium on Personal, Indoor and Mobile Radio Communications.

[6]  Bruce E. Hajek,et al.  Link scheduling in polynomial time , 1988, IEEE Trans. Inf. Theory.

[7]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1990, 29th IEEE Conference on Decision and Control.

[8]  Massimo Franceschetti,et al.  Closing the gap in the capacity of random wireless networks , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[9]  L. Kleinrock,et al.  Spatial reuse in multihop packet radio networks , 1987, Proceedings of the IEEE.

[10]  Michael Gastpar,et al.  On the capacity of wireless networks: the relay case , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[11]  Panganamala Ramana Kumar,et al.  A network information theory for wireless communication: scaling laws and optimal operation , 2004, IEEE Transactions on Information Theory.

[12]  Lang Tong,et al.  A dynamic queue protocol for multiaccess wireless networks with multipacket reception , 2004, IEEE Transactions on Wireless Communications.

[13]  Alexander L. Stolyar,et al.  Scheduling for multiple flows sharing a time-varying channel: the exponential rule , 2000 .

[14]  Leandros Tassiulas,et al.  Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks , 1992 .

[15]  Lang Tong,et al.  Stability and delay of finite-user slotted ALOHA with multipacket reception , 2005, IEEE Transactions on Information Theory.

[16]  Lang Tong,et al.  Stability of slotted ALOHA with spatial diversity , 2003, IEEE International Conference on Communications, 2003. ICC '03..

[17]  Eytan Modiano,et al.  Dynamic power allocation and routing for time varying wireless networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[18]  W. Rudin.  Real and complex analysis , 1968 .

[19]  Andrea J. Goldsmith,et al.  Capacity regions for wireless ad hoc networks , 2003, IEEE Trans. Wirel. Commun..

[20]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[21]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

[22]  Lang Tong,et al.  Exploiting decentralized channel state information for random access , 2005, IEEE Transactions on Information Theory.

[23]  David Tse,et al.  Mobility increases the capacity of wireless adhoc networks , 2002 .

[24]  John A. Silvester,et al.  On the Capacity of Multihop Slotted ALOHA Networks with Regular Structure , 1983, IEEE Trans. Commun..

[25]  David Tse,et al.  Power control and capacity of spread spectrum wireless networks , 1999, Autom..

[26]  P. Kumar,et al.  Capacity of Ad Hoc Wireless Networks , 2002 .

[27]  Rajesh K Pankaj,et al.  Two multi access algorithms for channels with multiple reception capacity , 1989, Fourth IEEE Region 10 International Conference TENCON.

[28]  Erdal Arikan,et al.  Some complexity results about packet radio networks , 1983, IEEE Trans. Inf. Theory.

[29]  David Tse,et al.  Mobility increases the capacity of ad hoc wireless networks , 2002, TNET.

[30]  Leandros Tassiulas,et al.  Dynamic server allocation to parallel queues with randomly varying connectivity , 1993, IEEE Trans. Inf. Theory.

[31]  Z.J. Haas,et al.  On the scalability and capacity of wireless networks with omnidirectional antennas , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[32]  Panganamala Ramana Kumar,et al.  Towards an information theory of large networks: an achievable rate region , 2003, IEEE Trans. Inf. Theory.

[33]  W. Szpankowski.  Stability conditions for some distributed systems: buffered random access systems , 1994, Advances in Applied Probability.

[34]  Lang Tong,et al.  Stability and Capacity of Wireless Networks with Probabilistic Receptions : Part II — Regular Networks , 2003 .

[35]  Lang Tong,et al.  Multipacket reception in random access wireless networks: from signal processing to optimal medium access control , 2001, IEEE Commun. Mag..

[36]  Nader Mahravari.  Random-access communication with multiple reception , 1990, IEEE Trans. Inf. Theory.

[37]  David J. Aldous,et al.  Lower bounds for covering times for reversible Markov chains and random walks on graphs , 1989 .

[38]  Stuart C. Schwartz,et al.  Stability properties of slotted Aloha with multipacket reception capability , 1988 .

[39]  John A. Silvester.  On the spatial capacity of packet radio networks , 1981, Perform. Evaluation.

[40]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.