From Field Data to Analytical Queueing Model A Two-Periode Assessment of M/M/2 Service Capacity at a Gas Station
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Abstract
Queueing systems at gas stations (SPBU) exhibit variable arrival and service characteristics; thus, selecting an appropriate queueing model requires aligning assumptions with empirical conditions. This study aims to identify the probability distribution characteristics of inter-arrival times and service times and to evaluate their fit with the assumptions of the M/M/2 queueing model at the Tugu 44.552.15 gas station. Data were collected through customer-level observations during two sessions—July 10, 2026, and August 12, 2026—between 12:00 and 15:00. Arrival and service time data were processed to derive inter-arrival and service times, which were then analyzed using distribution fitting in the Arena Input Analyzer. Several probability distributions were compared based on squared error and goodness-of-fit test results. The analysis revealed that the exponential distribution lacked statistical support to represent either inter-arrival times or service times. This pattern was consistently observed across both sessions. Thus, the system's empirical characteristics during the observation period do not support the Markovian assumptions underlying the M/M/2 model. These findings suggest that the M/M/2 model relies on relatively restrictive assumptions for representing the observed system, implying that empirical-based approaches—such as discrete-event simulation—may be suitable for further analysis.
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Accepted 2026-08-17
Published 2026-08-17
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References
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