The stochastic processes provide the basis for modeling a variety of uncertain behaviors that we face in our daily life. Especially, the renewal processes play an important role in understanding the discrete event systems arising in queueing theory, production and inventory control, design of communication systems, performance evaluation in computer science and product warranty estimation, as well as reliability and maintenance modeling. In fact, most standard textbooks on the stochastic processes spend many pages on renewal theory, so its important to have a high-level understanding.

Question-

Discuss Stochastic operations research. You may also discuss the application of Stochastic OR in terms of the medical example provided and provide a background in the application and form of the Stochastic approach using the Renewal process.