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The interest on firefly approaches to the problem of synchronizing the nodes of a wireless ad hoc communication network is rising, because of its efficiency and efficacy. In this paper we show that it is enough to have an indirect interaction among nodes, either spatially (through multi-hop paths), or temporally (through mobility) to achieve synchronism among them. As the interactions among nodes increases, global synchronization emerges faster.

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In a wired multi-hop path, the concepts of end-to-end bandwidth (BW) and end-to-end available bandwidth (ABW) are clearly defined and widely accepted as the capacity of the narrow link and the unused bandwidth of the tight link, respectively. This consensus has led to clever estimation techniques based on active probing measurements. However, these concepts do not apply directly to wireless ad hoc networks (manets) because the idea of a point-to-point link does not exist as an independent communication resource between a pair of neighbor nodes given the shared nature of the transmission medium and the random nature of multiple access protocols. Furthermore, the overhead is no longer a constant small header appended to each packet, but a random variable that depends on many phenomena and makes both BW and ABW largely dependent on packet length. In this paper we provide new definitions for BW and ABW of a multi-hop path in a manet, which extend the wired concepts and capture their random shared nature and their packet length dependency. Indeed, within the new definitions, we replace the concept of a point-topoint link with the concept of a spatial channel as the independent unit of communication resource, so that the new definitions become natural extensions of the widely accepted ones. Simulations validate the analytical model and the accuracy of these new concepts and definitions.