Stochastic Model of Waiting Time: A Case of Two Selected Banks in the Sekondi-Takoradi Metropolis
- 1 Department of Mathematics, Statistics and Actuarial Science, Takoradi Technical University, Takoradi, Ghana
- 2 Department of Mathematics, Statistics and Actuarial Science, Takoradi Technical University, Takoradi, Ghana
- 3 Department of Mathematics, Statistics and Actuarial Science, Takoradi Technical University, Takoradi, Ghana
- 4 Department of Mathematics, Statistics and Actuarial Science, Takoradi Technical University, Takoradi, Ghana
Abstract
Queue is an act of joining a line to be served and it is part of our everyday human involvement. The objectives of the study focused on using a mathematical model to determine the waiting time of two selected banks as well as compare the average waiting time between the banks. The study uncovered the extent of usage of queuing models in achieving customer satisfaction as well as permitting to make better decisions relating to potential waiting times for customers. The study adopted a case study and observational research with the source of data being primary. Purposive sampling technique was used to select the two banks under study with the target population comprising of all the customers who intended to transact businesses with the banks within the period of 11 am to 12 pm. The sample sizes for the first, second and third day of the first bank are twenty-eight (28), seventeen (17) and twenty (20) respectively with three servers on each day whereas that for the first, second and third day of the second bank is twenty (20), nine (9) and seventeen (17) with two servers on each day. A multiple server (M/M/s) Model was adopted, and Tora Software was the statistical tool used for the analysis. Findings of the study revealed that the second bank had a higher utilization factor than the first bank. Also, the number of customers in the banking hall of the second bank was higher than that of the first bank during the entire period of observation. Finally, it takes customers of the first bank lesser minutes to complete their transaction than the second bank. In conclusion, the three days observations revealed different banking situations faced by customers in both banks which had effect on waiting time of customer service. The waiting time of customer service has effect on the number of customers in the queue and system, the probability associated with the emptiness of the system and the utilization factor. Based on the results, the study recommended, inter alia , that the management of the second bank should adopt a three-server (M/M/3) model.
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