A probabilistic model of a conventional taxi service is formulated and analyzed. This model also applies to other queuing systems in which the servers must travel to the customers. The main assumptions are that demand is homogeneous and that the street network is uniform in a certain sense. Computer simulations incorporating these assumptions were made of both the taxi service and a many-to-many dial-a-bus system. It was found that small dial-a-bus vehicles (capacity 6–8) can serve 50 per cent more people than taxis with only a slight increase in travel-time. An attempt to carry more passengers leads to steadily greater travel-times. However dial-a-bus is generally less affected by changes in demand than taxis. The size of the region served has a pronounced effect on the efficiency of both dial-a-bus and taxi services.