Üniversite Hastanelerinde Hasta Bekleme Sürelerinin Kuyruk Teorisi ile Analizi: M/M/c ve M/G/c Modelleri

Year 2025, Volume: 40 Issue: 4, 1252 - 1286, 01.10.2025

Alkan Durmuş

https://doi.org/10.24988/ije.1599052

Abstract

Bu çalışma, bir üniversite hastanesinin ortopedi polikliniğinde hasta bekleme sürelerini analiz ederek hizmet süreçlerini iyileştirme ve kaynak kullanımını optimize etme amacıyla gerçekleştirilmiştir. Kuyruk teorisi modelleri olan M/M/c ve M/G/c kullanılarak sistemin mevcut performansı değerlendirilmiş ve yoğunluk artışı senaryoları incelenmiştir. M/M/c modeli, hizmet sürelerinin üstel dağıldığını varsayarak sistemin düşük yoğunluk koşullarında verimli çalıştığını göstermiştir. Kuyruk bekleme süresi 17,85 dakika, toplam sistem bekleme süresi ise 34,02 dakika olarak hesaplanmıştır. Model, mevcut doktor sayısıyla hasta taleplerinin karşılandığını ortaya koymuştur. M/G/c modeli, hizmet sürelerindeki varyasyonları dikkate alarak daha gerçekçi sonuçlar sunmuştur. Kuyruk bekleme süresi 9,06 dakika, toplam bekleme süresi ise 25,22 dakika olarak hesaplanmıştır. Ancak yoğun saatlerde hizmet süresi değişkenliği bekleme sürelerinde artışa neden olmuştur. Senaryo analizlerinde, hasta giriş oranının %10’dan %100’e kadar artırılması durumunda, her iki model de artan yoğunluğu karşılamış, ancak M/M/c modeli stabil performans sergilerken, M/G/c modeli daha hassas ama gerçekçi sonuçlar sunmuştur. %70-80 yoğunluk oranı hedeflenerek mevcut doktor sayısının genellikle yeterli olduğu belirlenmiştir. Ancak aşırı talep durumunda ek kaynak planlaması gerekebileceği vurgulanmıştır. Sonuç olarak, kuyruk teorisi modelleri, bekleme sürelerini optimize etme, hasta memnuniyetini artırma ve kaynakları etkin kullanma açısından stratejik bir araçtır. Özellikle değişken talep koşullarında M/G/c modeli daha uygun bir çözüm sunmaktadır.

Keywords

Kuyruk Teorisi , M/M/c Modeli , M/G/c Modeli , Hasta Bekleme Süreleri , Ortopedi Polikliniği , Sağlık Hizmeti Verimliliği

Queuing Theory Analysis of Patient Waiting Times in University Hospitals: M/M/c and M/G/c Models

Abstract

This study was conducted to improve service processes and optimize resource utilization by analyzing patient waiting times in the orthopedics outpatient clinic of a university hospital. Using the queuing theory models M/M/c and M/G/c, the system’s current performance was assessed, and scenarios simulating increased service demand were examined. The M/M/c model showed that the system operates efficiently under low-density conditions. Assuming exponential distribution of service times. The queue waiting time was calculated as 17.85 minutes, and total system waiting time as 34.02 minutes. The model revealed that patient demands were met with the number of doctors available. The M/G/c model provided more realistic results by taking into account variations in service times. Queue waiting time was calculated as 9.06 minutes and total waiting time as 25.22 minutes. However, service time variability during peak hours caused an increase in waiting times. In the scenario analyses, when the patient arrival rate was increased from 10% to 100%, both models handled the increased load. However, while the M/M/c model maintained stable performance, the M/G/c model yielded more accurate and realistic results. Targeting a 70-80% density rate, it was determined that the number of available doctors was generally sufficient. However, it was emphasized that additional resource planning may be required in case of excessive demand. In conclusion, queuing theory models are a strategic tool for optimizing waiting times, increasing patient satisfaction and using resources efficiently. Especially under variable demand conditions, the M/G/c model offers a more appropriate solution.

Keywords

Queuing Theory , M/M/c Model , M/G/c Model , Patient Waiting Times , Orthopedics Outpatient Clinic , Health Service Efficiency

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