Patients come to SoloPeduli Clinic to get medical treatment. Medical treatment at SoloPeduli Clinic is divided into two parts namely outpatient and inpatient health services. Patients generally do not know how long it will take for service from arrival to discharge at the clinic. The queue flow is called a system, while the patients queuing at each service are called states, the number of states cannot be limited as health services must be available 24 hours a day. This issue includes a Discrete Event System which can be modeled with a Petri Net. Petri Net is a mathematical model that can be used to describe certain events in a Discrete Event System. In this research, service flow is modeled using Petri Net which is then represented in the form of a matrix. Coverability Tree was created to define life and deadlock. Scheduling is modeled using Max-Plus Algebra. Service times will be randomly selected to facilitate scheduling and length of service time.