Queueing systems with phase-type service

In this thesis, service times in the queueing systems are modelled by using phase-type distribution. All the systems have the structure of quasi-birth-death process. By means of the advantage of this process, the stationary distributions of the systems are obtained by using matrix geometric method. All studied queueing systems have phase-type service times, however each queueing model presented is designed for a special real-life application, such as healthcare systems, working vacation, Markovian arrival process and crowdsourcing. Firstly, the service process in a geriatric department is characterized as a queueing system. In this context, three different models are studied. The main difference among these models comes from the capacity of the system. The models have no waiting space, infinite buffer and finite buffer, respectively. Secondly, queueing model with phase-type service is studied with working vacation policy. The server does not remain idle during the vacation period and the system operates at a lower rate. Finally, four queueing models are analyzed in the context of crowdsourcing useful in service sectors. In these models, the arrival and service processes are modeled by Markovian arrival process that allows correlated arrivals and phase-type distribution, respectively. The first model has a single server whereas the second model has multi-server. Then, the single-server queueing model with crowdsourcing is developed by working vacation and pure vacation policies. In the working vacation model, the server offers services to customers arriving during a vacation at a lower rate while the server doesn't work during a vacation period in the pure vacation model.