МАРКОВСЬКІ МОДЕЛІ СИСТЕМ ОБСЛУГОВУВАННЯ–ЗАПАСАННЯ ІЗ РІЗНОТИПНИМИ ПОВТОРНИМИ ВИМОГАМИ

• Datum: 2025
• Hauptverfasser: Melikov, A.Z., Ponomarenko, L.A., Aliev, I.A.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Schlagworte: системи обслуговування–запасання; марковська модель; повторна заявка; політика поповнення запасів
• Online Zugang: https://jais.net.ua/index.php/files/article/view/674
• Назва журналу: Problems of Control and Informatics

In this paper, models of queuing-inventory systems with two kinds of retrial customers and instantaneous service time are considered. It is assumed that if at the time of arrival of a high-priority customer the inventory level is greater than zero then it receives an inventory and leaves the system. Customers of low priority receive inventory if at the time of its arrival the inventory level is above a certain critical level; otherwise, this customer, according to the Bernoulli trials, either goes into orbit or does not receive an inventory and leaves the system. The sojourn time of customers in an infinite orbit is a random variable with an exponential distribution function. If at the time of receipt of the repeated customer the inventory level is more than a critical level, then it instantly receives the required inventory and leaves the orbit; otherwise, according to the Bernoulli scheme, it either leaves the orbit or remains in orbit. Three replenishment policies are considered — a two-level policy, a variable order size policy, and a policy in which an order is made to supply inventory after each inventory release act. The main characteristics of the system are the average inventory level, the average intensity of orders, the probability of failure in servicing customers of each type when entering the system, the average number of customers in orbit, the average intensities of successful and unsuccessful repetition of customers from orbit. For the mathematical analysis of the system under study, a corresponding two-dimensional Markov chain was constructed and an algorithm was given for finding its generating matrix. Joint distribution of the system's inventory level and the number of customers in orbit as well as formulas for calculating the averaged characteristics of the studied models are developed.