An abstract model for transmission scheduling Sample Clauses

An abstract model for transmission scheduling. We will now develop a mathematical model for analysis and design of transmission schedules in WirelessHART based on the short description above. The model considers a single superframe in isolation – the problem of merging multiple superframes into one conflict-free superframe is not considereded in this report. ∈ { } We assume that the devices are static and represent the network topology with a graph G = (V, E) where vertices v V = v0, v1, . . . , vN represent devices and edges in E denote device pairs that can communicate with each other. ⊆ We focus on communication from devices to the gateway and assume that all such traffic is routed along a spanning tree T = (V, Ej) with Ej E rooted at GW . We refer to T as the routing topology of the network to stress that it could potentially be very different from the actual physical placement of the devices. For every device vi we let fi denote its parent and chi be the set of its children in T . Time is synchronized and slotted with standardized length that allows the transmission of one data packet and its associated acknowledgement. Transmission opportunities in a given time slot on a given channel are dedicated and can only be assigned to one device pair. Devices are equipped with a half-duplex radio trasceiver, which means that devices cannot transmit and receive in the same time slot. There maximum number of concurrent transmissions is equal to the number of channels C available for communication.
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