Matrix-geometric method to study queueing-inventory system with feedback and destructive customers

Authors

DOI:

https://doi.org/10.18372/2073-4751.67.16192

Keywords:

queueing-inventory system, feedback, spending customers, repeated customers, destructive customers, matrix-geometric method

Abstract

In this paper, we propose a Markov model of a queueing-inventory system with instant service, feedback, primary and repeated spending customers of various types, and destructive customers. Primary orders form a Poisson flow and, if stocks are available, they instantly receive stocks. If at the moment of receipt of the initial request the stock level is equal to zero, then this request, according to the Bernoulli scheme, either leaves the system or goes into an infinite buffer to repeat its request in the future. The intensity of repeated requests is constant, and if at the moment of receipt of a repeated request the level of reserves is zero, then this request, according to the Bernoulli scheme, either leaves orbit or remains in orbit to repeat its request in the future. Destructive customers also form a Poisson flow, however, unlike spending customers, they do not require servicing, since at the moment such a customer arrives, the inventory level instantly decreases by one. The system has adopted a replenishment policy, according to which, at the time of receipt, the system's warehouse is completely filled. Lead time is a random variable that has an exponential distribution. It is shown that the mathematical model of the system under study is a two-dimensional Markov chain with an infinite state space. An algorithm for calculating the elements of the generating matrix of the constructed chain has been developed and the ergodicity condition for this chain has been found. To calculate the stationary probabilities of states, a matrix-geometric method is used. Formulas are found for calculating the main characteristics of the system.

References

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Published

2021-10-12

How to Cite

Aliyeva, S. (2021). Matrix-geometric method to study queueing-inventory system with feedback and destructive customers. Problems of Informatization and Management, 3(67), 4–10. https://doi.org/10.18372/2073-4751.67.16192

Issue

Vol. 3 No. 67 (2021)

Section

Статті

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