International Journal of Multidisciplinary Research and Human Factors

IISSN: 3043-579X

Published: 23rd  November, 2024

DOI: https://doi.org/10.66419/WJPE2715

 

Application of Queuing Theory on Customer Management
in Supermarket

 

 

Magdalene A. Dodo
S. E. Chaku
M. U. Adehi 
Abubakar Muhammad Auwal

 

Abstract


The formation of a waiting line is a prevalent scenario when the immediate demand for a service surpasses the current capacity to provide that service. This study investigates the application of queuing theory on customer management in supermarkets using the Markov chain process across three consecutive months, represented by transition matrices. Each matrix outlines the probabilities of transitioning between four states (0, 1, 2, 3) over time. The dataset was analysed using TORA software and the following estimates were obtained. The transition matrix for the first month reveals that state
0 is absorbing, while other states show varied probabilities of transitioning to other states. In the second month, state 1 consistently transitions to state 3 with a probability of 1.04, highlighting a significant shift in state dynamics. The third month’s matrix continues to reflect these transitions, with state 0 remaining absorbing and other states exhibiting notable probabilities of either remaining in their current state or transitioning to others. These findings demonstrate the evolving nature of the system’s state transitions over time, offering insights into the behaviour and stability of the Markov process.


Keywords : Service surpasses, Transition matrix, Markov process, Queuing theory, Customers time management, Markov chain model