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PDF[dist, x] gives the probability density function for the distribution dist evaluated at x. PDF[dist, {x1, x2, ...}] gives the multivariate probability density function for a distribution dist evaluated at {x1, x2, ...}. PDF[dist] gives the PDF as a pure function.

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A random access protocol with multi-packet reception (MPR) capability for infrastructure-less wireless autonomic networks is introduced and analyzed. In these networks mobile nodes may communicate with each other directly without a central entity (base station), where each mobile node either will be in a transmitting mode or in a receiving mode or in an idle mode. The throughput per node and the packet retransmission probability depend exclusively on the MPR capability and the ratio of the transmission probability and the receiving probability of each mobile node. For a given ratio of the transmission probability and the receiving probability of each mobile node, throughput-delay performance increases with the increase of MPR capability. In the proposed infrastructure-less networks, mobile nodes can control the network traffic very precisely by controlling the three parameters. These three parameters are transmission probability, receiving probability and idle mode probability of each mobile node. Since each mobile node can control the network traffic very precisely to obtain the maximum throughput, the network is autonomic, i.e., self-optimizing. The optimum transmission probability of each mobile node to obtain the maximum throughput is evaluated. The throughput utility increases with the increase of MPR capability. On the other hand, the cost per mobile node also increases with the increase of MPR capability. Therefore the MPR capability should be optimized to provide reasonable trade-off between the throughput per node and the cost per mobile node. The results of this study may be used for a system design of an infrastructure-less contention-based multiple access schemes with MPR capability.