Stability and Capacity of Wireless Networks with Probabilistic Receptions : Part II — Regular Networks

We study the stability and capacity problems inregular wireless networks. In Part I, we characterized the stability and the capacity regions, and introduced policies sufficient to achieve every rate in these regions. In this part, we obtainclosed 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 performance loss due to suboptimal protocols (such as slotted ALOHA and random walk), and the effects of link fading and increasing connectivity.

[1]  Alex Reznik,et al.  On the transport capacity of a broadcast Gaussian channel , 2002, Commun. Inf. Syst..

[2]  Stuart C. Schwartz,et al.  Optimal decentralized control in the random access multipacket channel , 1989 .

[3]  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.

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

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

[6]  Erdal Arikan,et al.  Some complexity results about packet radio networks , 1983, 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]  John A. Silvester.  On the spatial capacity of packet radio networks , 1981, Perform. Evaluation.

[9]  Suhas Diggavi,et al.  Even one-dimensional mobility increases capacity of wireless adhoc networks , 2002 .

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

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

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

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

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

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

[16]  Philip A. Whiting,et al.  Cdma data qos scheduling on the forward link with variable channel conditions , 2000 .

[17]  R. M. Loynes,et al.  The stability of a queue with non-independent inter-arrival and service times , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[18]  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).

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

[20]  Anthony Ephremides,et al.  On the stability of interacting queues in a multiple-access system , 1988, IEEE Trans. Inf. Theory.

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

[22]  Edmund M. Yeh,et al.  Throughput and delay optimal resource allocation in multiaccess fading channels , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

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

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

[25]  R. Srikant,et al.  Stable scheduling policies for fading wireless channels , 2005, IEEE/ACM Transactions on Networking.

[26]  Leandros Tassiulas,et al.  Scheduling and performance limits of networks with constantly changing topology , 1997, IEEE Trans. Inf. Theory.

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

[28]  Lang Tong,et al.  Random scheduling medium access for wireless ad hoc networks , 2002, MILCOM 2002. Proceedings.

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

[30]  Leandros Tassiulas,et al.  Linear complexity algorithms for maximum throughput in radio networks and input queued switches , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[31]  Alexander L. Stolyar,et al.  Scheduling algorithms for a mixture of real-time and non-real-time data in HDR , 2001 .

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

[33]  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..

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

[35]  Lang Tong,et al.  A multiqueue service room MAC protocol for wireless networks with multipacket reception , 2003, TNET.

[36]  Sergio D. Servetto,et al.  Lattice quantization with side information , 2000, Proceedings DCC 2000. Data Compression Conference.

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

[38]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

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

[40]  Moshe Shaked,et al.  Stochastic orders and their applications , 1994 .

[41]  P. R. Kumar,et al.  Internets in the sky: The capacity of three-dimensional wireless networks , 2001, Commun. Inf. Syst..

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

[43]  Wojciech Szpankowski,et al.  Stabilty Conditions for Some Multiqueue Distributed Systems: Buffered Random Access Systems , 1992 .

[44]  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.

[45]  Venkat Anantharam.  The stability region of the finite-user slotted ALOHA protocol , 1991, IEEE Trans. Inf. Theory.

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

[47]  Matthew Andrews,et al.  Providing quality of service over a shared wireless link , 2001, IEEE Commun. Mag..

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

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

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

[51]  P. Viswanath,et al.  Upper bounds to transport capacity of wireless networks , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[52]  Wei Luo,et al.  Stability of N interacting queues in random-access systems , 1999, IEEE Trans. Inf. Theory.

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

[54]  Lang Tong,et al.  Stability of Queues in Slotted ALOHA with Multiple Antennas , 2002 .