Analysis of multiclass Markovian polling systems with feedback and composite scheduling algorithms

We consider multiclass Markovian polling systems with feedback and analyze their average performance measures. Scheduling in polling systems has many applications in computer and communication systems. We utilize the framework that has been effectively used to analyze various composite scheduling algorithms in many types of multiclass queues systematically in conjunction with the functional computation method (Hirayama in Naval Research Logistics 50:719-741, 2003; Journal of the Operations Research Society of Japan 48:226-255, 2005; Advances in queueing theory and network applications, pp. 119-146, Springer, New York, 2009a; Journal of Industrial and Management Optimization 6:541-568, 2010). We define the conditional expected values of the performance measures such as the sojourn times as functions of the system state and find their expressions by solving some equations. Then from these expressions, we derive the average numbers of customers and the average sojourn times for all service stages of customers circulating the system. We consider their application to a packet scheduling problem where multiple categories of packets share a resource.