Performance Analysis of the M/M/1 Queuing System in Barber Shop Services Using an Analytical Approach

Pebi Mina Husania; Rani Chantika; Puji Sri Alhirani; Uli Salsabila Hasibuan

doi:10.61132/mars.v3i6.1283

Authors

Pebi Mina Husania Universitas Islam Negeri Sumatera Utara
Rani Chantika Universitas Islam Negeri Sumatera Utara
Puji Sri Alhirani Universitas Islam Negeri Sumatera Utara
Uli Salsabila Hasibuan Universitas Islam Negeri Sumatera Utara

DOI:

https://doi.org/10.61132/mars.v3i6.1283

Keywords:

M/M/1 queueing model, service performance, barbershop, analytical approach, waiting time

Abstract

Queueing systems play an important role in evaluating service performance, especially in small-scale businesses such as barbershops, where fluctuating customer arrival patterns and limited service capacity often lead to long waiting times. This study aims to analyze the performance of barbershop services using the M/M/1 queueing model and an analytical approach based on experimentally tested arrival (λ) and service (μ) rates. The model was selected because it represents a single-server system with Poisson arrivals and exponentially distributed service times, closely matching real barbershop operational characteristics. Using assumed realistic parameters, the analysis shows that when λ = 12 customers per hour and μ = 6 customers per hour, the system becomes unstable with a utilization rate (ρ) exceeding 1, indicating continuous queue growth. Further simulations with increased service rates demonstrate significant improvements: at μ = 15, the system achieves ρ = 0.8 with an average waiting time of 16 minutes, while at μ = 13, the system remains stable but experiences a long waiting time of approximately 55 minutes. These findings emphasize that barbershop performance is highly sensitive to service speed and that even small increases in μ can produce substantial improvements in queue stability and customer waiting times. The study concludes that barbershops must ensure adequate service capacity—either through optimizing service duration, improving worker efficiency, or adding servers—to maintain service quality and enhance customer satisfaction.

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