Allocation in a Vertical Rotary Car Park

Abstract

We consider a vertical rotary car park consisting of l levels with c parking spaces per level. Cars arrive at the car park according to a Poisson process, and if there are parking spaces available, they are parked according to some allocation rule. If the car park is full, arrivals are lost. Cars remain in the car park for an exponentially distributed length of time, after which they leave.We develop an allocation algorithm that specifies where to allocate a newly-arrived car that minimises the expected cumulative imbalance of the car park. We do this by modelling the working of the car park as a Markov decision process, and deriving an optimal allocation policy. We simulate the operation of..