Some Parameterized Dynamic Priority Policies for Two-Class M/G/1 Queues

Completeness of a dynamic priority scheduling scheme is of fundamental importance for the optimal control of queues in areas as diverse as computer communications, communication networks, supply/value chains, and manufacturing systems. Our first main contribution is to identify the mean waiting time completeness as a unifying aspect for four different dynamic priority scheduling schemes by proving their completeness and equivalence in two-class M/G/1 queues. These dynamic priority schemes are earliest due date based, head of line priority jump, relative priority, and probabilistic priority. We discuss major challenges in extending our results to three or more classes. In our second main contribution, we characterize the optimal scheduling policies for the case studies in different domains by exploiting the completeness of the above dynamic priority schemes. The major theme of the second main contribution is resource allocation/optimal control in revenue management problems for contemporary systems such as cloud computing, high performance computing, ans so forth, where congestion is inherent. Using completeness and the theoretically tractable nature of relative priority policy, we study the impact of approximation in a fairly generic data network utility framework. Next, we simplify a complex joint pricing and scheduling problem for a wider class of scheduling policies.