Süleyman Özekici

We consider a Markovian queueing model with abandonment where customer arrival, service and abandonment processes are all modulated by an external environmental process. The environmental process depicts all factors that affect the exponential arrival, service, and abandonment rates. Moreover, the environmental process is a hidden Markov process whose true state is not observable. Instead, our observations consist only of customer arrival, service, and departure times during some period of time. The main objective is to conduct Bayesian analysis in order to infer the parameters of the stochastic system, as well as some important queueing performance measures. This also includes the unknown dimension of the environmental process. We illustrate the implementation of our model and the Bayesian approach by using simulated and actual data on call centers.

We analyze mean time to failure and availability of systems that perform semi-Markov missions. The mission process is the minimal semi-Markov process associated with a Markov renewal process. Therefore, the successive phases of the mission follow a Markov chain, and the phase durations are generally distributed. The lifetimes of the non-identical components in the system are assumed to be generally distributed and are modeled using intrinsic aging concepts. Moreover, the lifetime parameters of the components and the configuration of the system change depending on the phases of the mission. We characterize the mean time to failure through solving a Poisson equation, and we analyze the system availability assuming that repair duration has a general distribution which is dependent on the phase of the mission during which the failure has occurred and on the deterioration level of the system.

We consider a device that is designed to perform missions consisting of a random sequence of phases or stages with random durations. The mission process is described by a Markov renewal process and the system is a complex one consisting of a number of components whose lifetimes depend on the phases of the mission. We discuss models and tools to compute system, mission, and phase reliabilities using Markov renewal theory. A simplified model involving a mission-based system with maximal repair is analyzed first, and the results are then extended to the case where there is no repair using intrinsic aging concepts. Our objective is to focus on computation of system reliability for these two possible extreme cases.

We consider the financial hedging of a random operational cash flow that arises in inventory operations with price and demand uncertainty. We use a variance minimization approach to find a financial portfolio that would minimize the total variance of operational and financial returns. For inventory models that involve continuous price fluctuations and price-dependent demand that arrives in continuous time, we characterize the minimum-variance hedging policies and numerically illustrate their effectiveness.

We analyze optimal replacement and repair problems of semi-Markov missions that are composed of phases with random sequence and durations. The mission process is the minimal semi-Markov process associated with a Markov renewal process. The system is a complex one consisting of non-identical components whose failure properties depend on the mission process. We prove some monotonicity properties for the optimal replacement policy and analyze the optimal repair problem under different cost structures.