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Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN En Línea: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i8.10
pages 1-15

Markov Models of Queuing-Inventory Systems with Different Types of Retrial Customers

Agasi Zarbali ogly Melikov
Institute of Control Systems of National Academy of Sciences of Azerbaijan, Baku
Leonid A. Ponomarenko
International Research and Training Center of Information Technologies and Systems of National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kiev, Ukraine
Ismail Alakper ogly Aliyev
Baku State University, Baku (Azerbaijan)

SINOPSIS

Consideration is given to queuing-inventory system with two types of retrial customers and instantaneous service time. It is assumed that if at the time of high priority customer arrival the inventory level is above zero then it receives inventory and leaves the system. A low priority customer receives inventory if at the time of its arrival the inventory level is above a certain critical level, otherwise this customer according to Bernoulli scheme 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 retrial customer arrival the inventory level is above the critical one, then it instantly receives the required inventory and leaves the orbit; otherwise according to Bernoulli scheme it either leaves the orbit or remains in it. Consideration is given to three inventory replenishment policies: two-level policy, a variable replenishment size policy and the policy in which an order for inventory supply is made 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 of servicing customer 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 there was constructed the corresponding two-dimensional Markov chain and the algorithm was given for finding its generating matrix. Joint distribution of the system inventory level and the number of customers in orbit as well as the formulas for calculating the averaged characteristics of the studied models were developed.

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