Year: 2026 | Month: October | Volume: 13 | Issue: 10 | Pages: 253-262
DOI: https://doi.org/10.52403/ijrr.20261024
Queueing System Analysis and Customer Service Optimization in Retail Business Using a Multi-Channel Model
Nurcahya Yulian Ashar1, Agista Surya Bawana2, Humam Rosyadi3
1,2Department of Mathematics, Faculty of Sciences and Mathematics, Diponegoro University, Semarang, Indonesia.
3Department of Accounting, Politeknik Negeri Semarang, Semarang, Indonesia.
Corresponding Author: Agista Surya Bawana
ABSTRACT
This study aims to analyze the performance of the queuing system and determine customer service optimization strategies for Marni’s Grocery Store in Bangetayu Wetan, Semarang City. Research data were obtained through observation and interviews over a five-day period (July 9–13, 2023), tracking customer arrivals and service delivery between 08:30 and 11:30 WIB. Analysis was conducted using queuing theory based on the M/M/2 model, while distribution goodness-of-fit was assessed via the Kolmogorov-Smirnov test using IBM SPSS Statistics 26. Subsequently, queuing system performance metrics were calculated mathematically and verified using WinQSB 2.0 software. The results indicate that Marni’s Grocery Store employs a multi-channel, single-phase service structure with two service facilities, utilizing both First Come, First Served and Priority Service queuing disciplines. Customer arrival rates follow a Poisson distribution, and the system operates in a steady state. With two servers, the service facility utilization rate is 51%; on average, there is one customer in the queue and two in the system, with an average waiting time in the queue of 0.42 minutes and an average total time in the system of 2 minutes. A simulation involving the addition of a third server showed a reduction in waiting time to 0.06 minutes but increased the likelihood of facility idleness. Thus, the use of two servers is considered optimal in terms of balancing service levels and facility utilization.
Keywords: Queuing System, Queuing Theory, M/M/2, Service Optimization.
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