Hideaki Yamashita

Mean and variance of waiting time and their optimization for alternating traffic control systems

We analyze alternating traffic crossing a narrow one-lane bridge on a two-lane road. Once a car begins to cross the bridge in one direction, arriving cars from the other direction must wait, forming a queue, until all the arrivals in the first direction finish crossing the bridge. Such a situation can often be observed when road-maintenance work is being carried out. Cars are assumed to arrive at the queues according to independent Poisson processes and to cross the bridge in a constant time. In addition, once cars join the queue, each car needs a constant starting delay, before starting to cross the bridge. We model the situation where a signal controls the traffic so that the signal gives a priority to one direction as long as a new car from the same direction arrives in a fixed time. For this model, we get a closed form for the first two moments of the waiting time of cars arriving at the bridge, and then numerically obtain Pareto optimal solutions of holding times to minimize the mean waiting time and its standard deviation.

Existence of a Pure Strategy Equilibrium in Markov Games with Strategic Complementarities for Finite Actions and States

In this paper, we provide the sufficient conditions for a Markov perfect equilibrium in pure strategies to exist for a class of stochastic games with finite horizon, in which any stage game has strategic complementarities. In contrast to previous studies (e.g., Curtat (1996) and Amir (2002), we assume herein that the sets of actions and the set of states is finite and do not assume dominant diagonal conditions for payoffs and the transition probability, which yield the uniqueness of equilibria. The greatest equilibrium is monotonically increasing in the state. The main result is applied to a model of a Bertrand competition with investment.