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in the network Such estimations are also important to adjust the data injection rates and other requirements of ows at sources To provide accurate feedback, sinks must be able to compute the capacity of the network as functions of QoS parameters and the ow characteristics In the literature, capacity modeling of wireless multihop networks have been investigated with simple metrics The line of work pioneered by P R Kumar aims wireless network capacity in bit-meters per second [34] This approach has also stimulated similar analysis attempts with increasingly realistic communication models [35 38] The main shortcoming of these attempts lies in the oversight of an overarching goal of communication networks: Delivery of information to remote devices across a network under realistic conditions Furthermore, combined metrics do not represent individual metrics such as delay, throughput, and loss rates explicitly.

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Motivated by the lack of multimetric capacity modeling work for multihop networks, we have investigated the following problem [39]: Consider a dense sensor network deployed in a rectangular area, where sources and destinations are located along two opposite edges Assuming a Rayleigh fading channel, what is the maximum attainable throughput across the network given a delay bound for individual packets and a maximum tolerable bit error rate A corollary to this problem is the calculation of the minimum delay attainable if a particular throughput is required With the results of this analysis, it is possible to estimate the total capacity of the network for a given delay value Our analysis is based on a physical layer channel model that accounts for the effects of the noise as well as the interference from other simultaneous transmissions.

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The bit error rates are calculated as the probability of a signal to be below a given threshold based on the Rayleigh channel model With this comprehensive interference model, we analyze the effect of packets in the same data ow (intra ow interference) and other data ows (inter ow interference) As a rst step, we analyzed a data stream that traverses a linear path Based on a discrete time model where each packet transmission lasts one time unit, we modeled the behavior of the packets in the same ow Our analysis con rmed that every packet injected into the network slows down the progress of preceding packets To solve this problem, waiting times are introduced at the source while injecting packets into the network, allowing earlier packets to move forward before another packet (ie, an interferer) is introduced.

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To achieve the lowest end-to-end delay, a packet must exist in the network alone, which reduces the throughput to one packet per end-to-end delay Similarly, the maximum throughput can be achieved if packets are injected every time unit, which causes the delay to go to in nity as the network density approaches in nity Intermediate combinations are achievable by adjusting the interpacket waiting times The two-dimensional case is modeled as parallel linear ows In this case, every transmitted packet experiences inter ow as well as intra ow interference To increase the throughput, the distance between ows can be reduced Small inter ow separations increases the inter ow interference, causing packets to cover short distances every transmission time, which in turn increases the end-to-end delay If the ows are separated by larger distances, then the overall throughput decreases along with the end-to-end delay.

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The parameters that control this behavior are the interpacket delays,.

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relative packet injection times between ows, and the inter ow separations. Using nonlinear optimization techniques, it is possible to compute the maximum throughput for a given delay bound and parameters to achieve the desired performance. This study [39] is merely a rst step in this open research area, and it leaves out many important issues such as crossing paths, single destination ows, and non-timesynchronized systems. Furthermore, protocol-dependent effects on capacity are also left out for the sake of simplicity. We are hopeful that more accurate and comprehensive studies will follow this one that will address more realistic settings and that can be directly integrated to admission control and QoS feedback mechanisms.