Forecasting Air-to-Ground Munitions Demand in Military Operations Using Markov-Modulated Poisson Process

Abstract

In this paper, we examine the problem of modeling and forecasting the air-to-ground munitions demand in military operations. We consider a continuous state space time series approach and we model the munitions demand as a non-homogeneous Poisson process with intensity function that depends on a continuous-time Markovian operational tempo process. This approach is known in stochastic process as a Markov-Modulated Poisson Process (MMPP) and has successfully been applied to queuing and communication network problems. We consider four operational tempo states, corresponding to the different intensity levels of military operations. We apply the maximum likelihood estimation method to derive the MMPP model parameters, assuming that the Markov chain states are observed. We illustrate the method with an example using two time series data sets of different trends. This study provides military planners with a decision support method for forecasting munitions requirements in the face of abrupt changes in demand. An extension of the model would be to use Bayesian approach for inferring the MMPP parameters through application of a Forward-Backward type algorithm to capture potential hidden states.