As we saw in the last lesson, queuing models describe the expected lines. They have many applications but in business the most important is:

  • Don’t lose money by having many impatient people in the queue.
  • Don’t lose money by paying employees in the cash register that are idle without customers to attend.

In these situations, it is very interesting to answer the questions: what is the percentage of time that there will be “n” people in a queue? What percentage of time will be the seller idle?


The answers to these questions can be obtained through Markov Model.

Markov Chain is a random process that undergoes transitions from one state to another on a state space. It’s required to possess a property that is usually characterized as “memoryless”: the probability distribution of the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of “memorylessness” is called the Markov property.

More info:

  • An Introduction to Markov Chains: https://www.youtube.com/watch?v=AaP8Zr0yoF4
  • Book: Problemas y Modelos Matemáticos para la Administración y Dirección de Empresas, Cortés López, J. Carlos. This book was written by one of the supervisors I had in the Final Thesis of my Degree here in Universidad Politécnica de Valencia and there you can find interesting solved problems about Markov Chain Model and so on.

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