It is possible that more than one node of the network wants to use the channel at the same time. For such a protocol it can be shown that 36% of the slots can contain successful packets. This is because a significant portion of the transmit power is fed back to the receiver.

The network product under this saturation assumption is called the saturation throughput. There have been many other analytical studies on the saturation capacity of the 802·11 DCF protocol. See (Cali et al 1998; Carvalho & Garcia-Luna- Aceves, 2003) for more approximate models for protocol throughput.

Remember that in the infrastructure mode of the 802·11 network, the wireless nodes (STAs) must connect through an access point (AP), i.e. in the above scheme the AP is passive in that it does not influence the decision of the STA . . Here, each STA specifies its throughput request and the transmission rates with which it can associate with each of the APs in the network.

An algorithm for max-min fair allocation of the STAs to the APs is described (Bejerano et al 2004).

## Ad hoc Internets

This is only a sample of some of the literature in the area and not a complete list. The capacity of the network and the connectivity are therefore important issues and we will discuss them in different settings. It is therefore reasonable to analyze networks by assuming that the location of the nodes is arbitrary.

Two issues are addressed: (1) maximizing the capacity of the network and (2) controlling the transmission ranges and hence the topology of the network. In this way, the connections and the transmission power for activating the connections are determined for all nodes. To characterize this set of F, it should be noted that an activation vector can be represented by a corner of the L-dimensional unit hypercube.

Note that in the above algorithm, the source of the packets is not important and the routing is done automatically. We now consider arbitrary networks specified by the spatial distribution of the nodes in the operational area and a transmission radius or 'cutoff'. It is easy to see that the randomness of the coordinates of the node in the distribution area introduces randomness into the graph.

Two important quantities are of interest—. i) The topological properties of the network in function of the most important property of being connected. ii) Network communication properties - the set of communication requirements that the network can support. 20 can be derived as a special case of the probability of the existence of a component in the flowing network (Godehardt & Jaworski 1996). The exponential distribution of node locations implies that the node spaces are also independent and have an exponential distribution, i.e.

Thus, the probability of network connectivity is just the probability that Yi < r fori = 1,. An interesting property of the exponential network is that if λr <∞then it can be shown that limn→∞Pc(n) <1, where Pc(n) is the probability that the n-node network is connected. For example, we will say that the carrying capacity of the network is one bit-meter per second if one bit moves one meter to the destination in one second.

Recall that the transmission range of the nodes must be O to connect the network. The above result is interesting because it shows how the mobility of the nodes in the network can be leveraged to increase capacity.

## Ad hoc wireless sensor networks (WSNs)

It can be shown that in the physical model, if there were only direct transmissions with no transmissions, then λ(n)= O(n−1/(1+α/2)) (Grossglauser & Tse 2001). Since nodes are assumed to be mobile, either relay or source nodes will eventually be "near" the destination. In the absence of a centralized control, this entire process of self-organization must be carried out in a distributed manner.

Thus, here we are interested in the aspect of self-organization of distributed instruments of ad hoc wireless sensor networks. Each device has one or more sensors, corresponding to the modality to be monitored. Given the sensitivity and range of the sensors, a certain number of sensors will need to be deployed in order to have adequate coverage of the area to be monitored.

Another option is to reduce the computations to simple calculations that can be performed distributed across network nodes. See Giridhar & Kumar (2005) and (Giridhar & Kumar 2006) for an analysis of general function computation in random networks and Khude et al (2005) for the time and energy complexity of maximal function computation in random networks. v) Distributed computing should be implemented over an ad hoc wireless network. Such a computer network will have to be self-organized from RF transmitters in nodes.

A topology must be defined and then a packet scheduling algorithm (MAC (medium access control)) determines how packet transmissions are scheduled on the network. In the survey (Santi 2005) and the book (Zhao & Guibas 2004), the focus is on network topologies that use very little energy in communication. Finally, in the operational network, measurements are made, distributed computations are done at the nodes, and the wireless ad hoc network moves the computations between the nodes, ultimately resulting in the desired conclusions being drawn.

The results are in the form of scaling laws 'in probability' as the number of nodes in a fixed area increases. On the other hand, in the tree algorithm the maximum is calculated recursively as the data propagates towards the root. In the wavelet algorithm, nodes exchange their current maximum estimate with their neighbors.

## Summary

Cyairci Erdal, Tezcan Hakan, Dogan Yasar, Coskun Vedat 2004 Wireless Sensor Networks for Underwater Surveillance Systems. Gui Chao, Mohapatra Prasant 2005 Virtual Patrol: A New Energy Conservation Design for Surveillance Using Sensor Networks. Iannone Luigi, Benbadis FARid, de Amorium Marcelo Dias, Fdida Serge 2004 Some applications of wireless sensor networks.

Jiang Chunyu, Dong Guozhu, Wang Bin 2005 Detection and tracking of region-based evolving targets in sensor networks. Kar K, Kodialam M, Lakshman TV, Tassiulas L 2003 Routing for network capacity maximization in power-constrained ad hoc networks. Karnik Aditya, Kumar Anurag 2004b Iterative localization in ad hoc wireless sensor networks: one-dimensional case.

WiOpt'04: Modeling and Optimization in Cellular, Ad Hoc and Wireless Networks Cambridge, UK Kasbekar G, Kuri J, Nuggehalli P 2006 Internet connectivity policies in IEEE 802·11 WLAN networks. Khude Nilesh, Kumar Anurag, Karnik Aditya 2005 Time and Energy Complexity of Distributed Computing in Wireless Sensor Networks. Kumar A, Altman E, Miorandi D, Goyal M 2005 New insights from a fixed-point analysis of single-cell IEEE 802.11 WLAN.

Li B, Battiti R 2003 Supporting service differentiation with improvements to the IEEE 802.11 MAC protocol: models and analysis. Prasanthi Venkata K, Kumar Anurag 2006 Optimizing delay in sequential change detection over ad hoc wireless sensor networks. Ramaiyan V, Kumar A, Vasudevan N 2005b Fixed-point analysis of the saturation throughput of IEEE 802.11 WLANs with capture.

Shakkottai Srinivas, Altman Eitan, Kumar Anurag 2006 An example of non-cooperative user-to-access point multihoming in IEEE 802.11 WLANs. Tickoo O, Sikdar B 2004 Queuing Analysis and Delay Mitigation in IEEE 802.11 MAC Random Access Wireless Networks. Wattenhofer R, Li L, Bahl P, Wang Y M 2001 A distributed topology for energy-efficient operation in multi-hop wireless ad hoc networks.