Analisis Sistem Antrean Pelayanan Rawat Jalan Menggunakan Model M/M/1 di Rumah Sakit Islam

Abstract

This study aims to analyze the outpatient service queue system using the M/M/1 queuing model at an Islamic Hospital. The queuing system is an important factor in determining the effectiveness of healthcare services because patient waiting time can affect service quality and patient satisfaction. This study uses a quantitative method with a case study approach. Research data were obtained through observations of the number of patient arrivals and patient service times in the outpatient unit over five working days. The analysis was conducted using the M/M/1 queuing model by calculating system performance parameters, including the system utilization rate (ρ), the average number of patients in the queue (Lq), the average waiting time of patients in the queue (Wq), the average number of patients in the system (Ls), and the average time patients spend in the system (Ws).

The results showed that the patient arrival rate (λ) was 6.2 patients/hour and the patient service rate (μ) was 9.68 patients/hour, with a system utilization value (ρ) of 0.64 or 64%. This value indicates that the queuing system is in a stable condition because the value of ρ < 1. The analysis also showed that the average number of patients in the queue was 1.14 patients, the average waiting time in the queue was 10.8 minutes, the average number of patients in the system was 1.78 patients, and the average time patients spent in the system was 17.2 minutes.

Based on the results of the study, it can be concluded that the outpatient service queuing system at the Islamic Hospital has been operating quite effectively. However, continuous evaluation and improvement of service efficiency are still needed to maintain service quality.

Keywords— queuing system, M/M/1 model, outpatient service, hospital, patient waiting time