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In this paper the problem of optimum slot size in Time Division Multiplexing (TDM) scheme in presence of per slot overhead has been addressed. Per slot overhead occurs in a variety of network structures. Messages are assumed t o be of random length, so they may need to be segmented into several slots, and are assumed t o be arriving according t o a Poisson process. Optimum slot size has been derived as a function of input rate, message length distribution, overhead per slot, and number of stations. It is also shown that how one will be penalized by deviating from this optimum slot size. Finally guidelines have been provided here as how t o assign unequal slot sizes in cases where different stations have different traffic characteristics. It is shown that this is a cun~bersonie nonlinear optimization programming problem in general, which will reduce to a Kuhn-Tucker optimization programming problem in light traffic situations.

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Sensor nodes in Wireless Sensor Networks (WSNs) operate with limited power resources such as small batteries which are difficult to be either recharged or replaced in some environments when depleted. Power consumption represents one of the most constraints impact the design of WSNs, leading to various protocols and algorithms aimed at minimizing the power consumption and extending batteries' lifetime. Sensor nodes in WSNs transmit their periodic packets continuously to central nodes (receivers) which are responsible for decoding packets and transmitting them to other communication networks. In addition, sensors usually follow various MAC strategies which allow accessing to wireless communication channels. However, sensors may attempt to access the wireless channels at the same time, potentially, leading to collisions among multiple nodes. In fact, central nodes in WSNs most often consume a large amount of power due to the necessity to decode every received packet regardless of the fact that the transmission may suffer from packets collision which impede the network performance. Therefore, in the receiver side of WSNs current collision detection mechanisms have largely been revolving around direct demodulation and decoding of received packets and deciding on a collision based on some form of parity bits in each packet for error control. From information theoretic prospective full decoding of received packets with error control bits at central nodes can achieve an efficient usage of network capacity, however, such an approach represents a major burden on power-constrained sensors. This drawback comes from the need to expend a significant amount of energy and processing complexity at sink nodes in order to fully-decode a packet, only to discover the packet is illegible due to a collision. In this paper, we propose a more practical power saving approaches which achieve a significant power saving with low-complexity at the expense of low throughput losses. Based on studying the statistics of received packets, central nodes can make a fast decision to detect a collision without the need for full-decoding of the whole received packets. Our novel approaches not only reduces processing complexity and hence power consumption, but it also reduces the delay incurred to detect a collision since it operates on only a small number of IQ samples in the beginning of a received packet. In such a paradigm, our approaches operate directly at the output of the receiver's Analog-to-Digital-Converter (ADC) and eliminate the need to pass the corrupted packets through the entire demodulator/decoder line-up. The performance gain of our proposed approach is illustrated through the comparison between the computational complexity of our Statistical Discrimination (SD) approaches and some existing Full Decoding (FD) algorithms (note 1). Our results show that the SD approaches has significant power savings and low computational complexities over existing FD algorithms with low False-Alarm and Miss probabilities, which qualify our SD approaches...