The Double-Ended Queue with Bulk Service and Limited Waiting Space

The double-ended queue involving taxis and customers at a taxi-stand has been considered under the assumption that there is limited waiting space both for customers and for taxis, and that the taxis "serve" the customers in bulk. The arrivals of customers and taxis are taken as general and Poisson respectively. Two separate probability generating functions have been defined for the cases when i taxis are waiting and ii when customers are waiting and their Laplace transforms L.T.'s as well as that of the probability for empty state have been obtained by using the supplementary variable technique. Cases of Erlangian and Poisson arrivals of customers and of single-seated taxis are considered as particular cases.