AbstractIn this paper, the queuing problem characterised by Poisson arrivals and a wide class of service time distribution has been solved by applying the phase method under the condition of limited waiting space. This problem is already solved by Finch, but he gave only explicit solution for the case of exponential distribution. The phase method has an advantage of giving the solution in a form which is easily computable. Tables are presented for the operational parameters for exponential and 2‐Erlang service time distribution