A stochastic model to predict the routability of field-programmable gate arrays

Field-Programmable Gate Arrays (FPGAs) have recently emerged as an attractive means of implementing logic circuits as a customized VLSI chip. FPGAs have gained rapid commercial acceptance because their user-programmability offers instant manufacturing turnaround and low costs. However, FPGAs are still relatively new and require architectural research before the best designs can be discovered. One area of particular importance is the design of an FPGA’s routing architecture, which houses the user-programmable switches and wires that are used to interconnect the FPGA’s logic resources. Because the routing switches consume significant chip area and introduce propagation delays, the design of the routing architecture greatly influences both the area utilization and speed-performance of an FPGA. FPGA routing architectures have already been studied using experimental techniques in [1] [2] and [3]. This paper describes a stochastic model that facilitates exploration of a wide range of FPGA routing architectures using a theoretical approach. In the stochastic model an FPGA is represented as an N x N array of logic blocks, separated by both horizontal and vertical routing channels, similar to a Xilinx [4] [5] [6] FPGA. Each routing channel comprises a number of tracks and each track consists of a set of short wire segments. Routing switches are available to connect the pins of the logic blocks to the wire segments, and to connect one wire segment to another. The number of routing switches and their distribution over the wire segments are parameters of the stochastic model. A circuit to be routed is represented by additional parameters that specify the total number of connections, and each connection’s length and trajectory. The stochastic model gives an analytic expression for the routability of the circuit in the FPGA, which is defined as the percentage of the circuit’s connections that can be accommodated by the FPGA’s routing architecture. Practically speaking, routability can be viewed as the likelihood that a circuit can be successfully routed in a given FPGA. The routability predictions from the model are validated by comparing them with the results of a previously published experimental study on FPGA routability.