Local area networks designed to carry a variety of traffic such as data, voice, facsimile, and video should be able to implement low latency virtual circuits to meet the demands of periodic traffic. We have designed a partially distributed algorithm to efficiently schedule voice traffic on a unidirectional bus system called Fasnet. Virtual channels are allocated for the duration of a talk spurt and relinquished during the intervening silent intervals. Conversations already in progress, but without an assigned circuit, take precedence over newly arriving calls. Unused voice capacity may be utilized by data stations when required. Simulations of the system indicate that performance is close to that obtained by an ideal TASI multiplexer. While the algorithm is unfair, this is not a significant factor unless the network is loaded very heavily. Further, except for a "sojourn" time unused voice capacity is utilized by the data stations.