Matrix geometric solutions in stochastic models

Human endeavors are often planned to be completed at some predefined times. In reality, these tasks are completed either before or after the planned times. In this paper, we define a stochastic process called the due date process which models the times at which these tasks are completed. Our main concern is the deviation of the completion times from the planned times. We derive conditions under which this process is stable. An interesting application of the due date process is to represent arrival processes associated with the assembly queue in manufacturing. Under this formulation, it is easy to characterize the transient and steady state behavior of the assembly queue. We also characterize a single server, exponential service queueing problem in which the arrivals are from a due date process.