Optimal Staffing Policy - A Service System with Stochastic Travel Times

Abstract

Abstract:Private sector operators of response services such as ambulance, fire or police etc. are often regulated by targets on the distribution of response times. This may result in inefficient overstaffing to ensure those targets are met. In this paper, we use a network chain of M/M/K queues to model the arrival and completion of jobs on the system so that quantities such as the expected total time waiting for all jobs can be calculated. The Markov nature enables us to evoke the Hamilton Jacobi Bellman equation (HJB) principle to optimize the required number of staff whilst still meeting targets.