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All Journal Jejak digital: Jurnal Ilmiah Multidisiplin
Sabrina Aisha Putri Lubis
Universitas Islam Negeri Sumatera Utara
Economics, Econometrics & Finance Education Languange, Linguistic, Communication & Media Social Sciences Other

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Kajian Teori Antrian Model M/M/1 dan Implementasinya pada Berbagai Sistem Pelayanan Maulana Hasan; Sabrina Aisha Putri Lubis; Siti Izzati Sarah; Halimatussya’diyah Purba; Siti Salamah Br. Ginting
Jejak digital: Jurnal Ilmiah Multidisiplin Vol. 2 No. 1 (2026): JANUARI
Publisher : INDO PUBLISHING

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.63822/31ahp913

Abstract

The M/M/1 queuing model is one of the most fundamental mathematical approaches in queuing theory for analyzing single-server service systems. This article aims to examine the basic concepts of the M/M/1 model, its performance measures, and its implementation in various service systems through a Systematic Literature Review (SLR) approach to Indonesian-language publications. The results show that the M/M/1 model is widely applied in the banking, health, transportation, energy, and public service sectors. This model effectively predicts utilization rates (ρ), queue lengths (Lq), and waiting times (Wq). Limitations arise in systems with utilization >0.85, which cause instability. Increasing efficiency does not always require additional servers, but can be done through innovations such as digital queuing systems. The M/M/1 model serves as an analysis and strategic planning tool to maximize operational efficiency. Future research is recommended to explore complex models such as M/M/c or M/G/1 and integrate simulation methods.  
Co-Authors Halimatussya’diyah Purba Maulana Hasan Siti izzati Sarah Siti Salamah Br. Ginting