ANALISIS TEORI ANTREAN MODEL M/M/5 PADA BARBERSHOP FLOBAMORA

Abstract

Barbershop Flobamora Solution in Jayapura City runs with five active barbers serving an average of 13 customers per day across eight working hours. On paper, nothing looks alarming. But when researchers visited the site directly, especially on weekday afternoons and weekends, customers were visibly waiting sometimes 10 to 20 minutes before getting called. This study tries to examine how well the M/M/5 model explains that gap, and why the model predicts a waiting time of just 11 seconds while real customers experience something much longer. Primary data were collected through direct observation and service time recording, then processed using POM-QM for Windows. Results show λ = 1.63 customers/hour, μ = 1.2 customers/hour per barber, server utilization ρ = 27%, Lq = 0.01, Wq = 11.19 seconds, W = 50.19 minutes (average total time in the system from arrival to completion of service), and P₀ = 26%. The gap between model output and field reality stems from the M/M/s assumption that customer arrivals are evenly distributed throughout the day something that simply does not hold in practice. Sensitivity analysis identifies s = 4 as the most balanced configuration (Wq = 1.2 minutes, ρ = 34%), with recommendations for time-segmented scheduling and digital queue management.