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Carrier sense multiple-access (CSMA) protocols are widely used in local area networks (LAN's) to control access to a shared communications channel such as a coaxial cable or radio frequency band. CSMA protocols are designed to exploit the property that the signal propagation time across the LAN is much smaller than the packet transmission time. Consequently, their performance depends on the exact timing of a sequence of asynchronous events originating at different points in the network. Previous models of CSMA protocols have not captured this essential space-time characteristic. Instead, the system has been reduced to a 1-dimensional model (i.e., a sequence of events on a single time line) by assuming either that events are synchronous (i.e., "slotted" operation of the protocol) or that all stations are mutually equidistant (so it can be assumed that each station's time line is identical). The novelty in our work is to describe the system state in terms of an ( )-dimensional "ribbon" of space-time, allowing us to faithfully model the exact timings of events for LAN's where the stations are distributed over a fully connected region in -space. For example, an Ethernet-like "bus" network can be viewed as a 1-dimensional LAN, a terrestrial packet radio network can be viewed as a 2dimensional LAN, and so on. First we highlight some of the key properties exhibited by such a model in the general case, including the notion of an embedded Markovian sequence of "idle points," and the decomposition of the space-time ribbon into cycles (each of which can be further decomposed into a number of "regions"). Then we present extensive results for the interesting special case of a 1-dimensional LAN, i.e., an Ethernet-like "bus" network. Our results show that previous models of bus LAN's can significantly underestimate their performance.