Modeling the Health Service Queuing System Using Petri Net and Max-Plus Algebra at Integrated Health Service Post (Posyandu)

Syarif Abdullah; Himmatul Mursyidah; Ferdian Bangkit Wijaya; Miftahul Huda; Sri Istiyarti Uswatun Chasanah; Nadia Eka Nursafitri; Dinda Dwi Anugrah Pertiwi

doi:10.37905/euler.v14i1.35889

Modeling the Health Service Queuing System Using Petri Net and Max-Plus Algebra at Integrated Health Service Post (Posyandu)

Syarif Abdullah, Himmatul Mursyidah, Ferdian Bangkit Wijaya, Miftahul Huda, Sri Istiyarti Uswatun Chasanah, Nadia Eka Nursafitri, Dinda Dwi Anugrah Pertiwi

Abstract

This study models the health service queue system at the Integrated Health Service Post (Posyandu) in Cilegon City, Banten, using the Petri Net and Max-Plus Algebra approaches to analyze the flow of participant arrivals and completion times. The data used are observational data from Posyandu activities simulated through a discrete event model, which includes several types of participants, namely: babies not standing yet, babies standing, pregnant mothers, and family planning programs. Petri Net modeling is used to represent the relationship between service transitions, while Max-Plus Algebra is used to calculate the process cycle time based on the critical path. The results of the study showed that the categories of non-standing babies, standing babies, and pregnant women/participants in the family planning program had identical service time patterns, namely a total duration of 17 minutes 19 seconds, with the main stages including measurement, midwife intervention, and provision of additional food. Max-Plus analysis confirms that the measurement and midwife intervention stages are the critical path that determines the length of service time. This study concludes that the combination of Petri Net and Max-Plus Algebra is effective in describing the dynamics of Posyandu queues and is able to provide quantitative information needed to identify bottleneck points and the basis for improving the service flow.

Keywords

Health Services; Max-Plus Algebra; Petri Net; Posyandu; Queuing System

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DOI: https://doi.org/10.37905/euler.v14i1.35889