¹Department of Mathematics G.B.S College Mauranipur India 

²Department of Mathematical Sciences and Computer Applications Bundelkhand University Jhansi UP India

The double-ended queue involving trains and passangers at a Railway station has been considered under the assumption that there is limited waiting space both for trains and for passangers. The arrival distribution of trains is simulated by means of an arrival timing channel consisting of j phases. The arrivals of passangers are assumed to be Poisson distributed. In the time dependent case we obtain an expression for the Laplace transform of the probabilities that there are n units in the queue. The cases of exponential and 2-Erlang arrival distributions for trains have been considered as particular cases. In the steady state, for a 2-Erlang arrival distribution for trains, we have evaluated the probabilities that the waiting space for passangers or trains is full in different particular cases. Their values are also shown by means of graphs.