Police staffing and workload assignment in law enforcement using multi-server queueing models

Criminal activities have been posing threat to human societies. In many countries, police officers have been serving as one major solution in addressing crime. However, some countries suffer from a scarcity of police officers and the unbalanced distribution of police forces. In this research, we study the law enforcement problem to address the aforementioned situation by dividing it into two sub-problems, i.e., the police staffing problem and the workload assignment problem. To improve staffing efficiency and service quality, we propose a double-resource queueing model (DRQM) with referral and a single-resource queueing model (SRQM) with inner classification. We solve the problems of police staffing and workload assignment by optimizing the referral threshold in the DRQM and the inner classification criterion in the SRQM. Results show that the SRQM with inner classification can always achieve higher staffing efficiency than the DRQM with referral. On service quality, dependent on the optimal referral threshold in DRQM or the optimal inner classification criterion in SRQM, either DRQM or SRQM is preferred.