Lack of Information on Future Supply and Fuel Purchase Rush: Fuel market after the Great East Japan Earthquake

After the Great East Japan Earthquake, fuel customers rushed to gas stations in the affected area and formed long queues. We present a micro model, in which each customer chooses whether or not to join the queue on that day, based on the expected waiting time and the probability of fuel becoming sold out. Considering the dependence of those expectations on the present queue lengths, we show that there are two stable equilibria (ordinal and rush) and one unstable equilibrium. If the peoples' perceptions of the present status exceed the unstable threshold, the system converges toward the rush equilibrium. We explain the bias mechanism of congestion information in a multiple gas stations setting, and alert the possibility of early rush occurrences before all stations have the high possibility of being out of fuel. We also investigate the effect of several sales policies, such as the quota of sales, priority ticket distribution, and purchase limit, on rush occurrences and outcomes.