Social welfare optimisation in a Hotelling model with two double-sided queues

We study the problem of the optimal number of taxis in a Hotelling queue model, with two taxi stations: one at each end of a linear market. Each station is modelled as a double-sided queue and an equilibrium location divides taxi drivers into two parts to join either station. We find that customer utility increases with the number of customers, but decreases with the buffers of stations, the unit transportation cost and unit waiting cost of taxi drivers. The profit of each taxi driver increases with the number of customers but decreases with the unit transportation cost. Interestingly, the profit of each taxi driver increases and then decreases with the unit waiting cost and the buffers of the stations.