Petri Net Model and Max-Plus Algebra on Queue in Clinic UNS Medical Center

Abstract

Patients come to the clinic UNS (Universitas Sebelas Maret) Medical Center to get a medical treatment. The clinic provides two health services include dental polyclinics and general polyclinics. Majority of patients do not know exactly how long the process of service from patient registration to getting medicine. Moving queues to each service is an event and people who queue up at each service are state. It is clear that the sum of all possible states is finite. This problem includes a Discrete Event System (DES). One of the uses of petri net is to model a DES. In this research, service flow was built in the clinic using Petri Net and service scheduling was modeled using Max-Plus Algebra. Furthermore, a coverability tree was built to determine the liveness and deadlock of the patient service queue and analyze the petri net flow. The selection of service start time can be chosen randomly to simulate the scheduling and length of service time.