Efficiency Analysis of the  Analysis of Diesel Fuel Refilling Queue Efficiency Using Queueing Theory at the Hawai Sentani Gas Station, Jayapura Regency

Saul Weipsa; Yekson Soll

doi:10.59976/jurit.v4i2.391

Authors

Saul Weipsa Universitas Internasional Papua
Yekson Soll Universitas Internasional Papua

DOI:

https://doi.org/10.59976/jurit.v4i2.391

Abstract

The diesel-fuel line at SPBU Hawai Sentani, Jayapura Regency, reportedly experiences heavy queuing, although its operating characteristics had not been quantitatively established. This study evaluates the existing single-server queue and an analytical two-server scenario. Vehicle arrivals were recorded on seven observation days—August 5–10 and 12, 2026—during the 07:00–17:00 WIT operating period. August 11 was not observed for an undocumented reason. A total of 2,680 arrivals produced an average arrival rate of 38.29 vehicles per hour. Based on 10 timed observations, mean service time was 1.35 minutes (SD = 0.158), corresponding to a service rate of 44.44 vehicles per hour. The existing system was modeled as M/M/1, while the two-server configuration was evaluated analytically as M/M/2. Because the observed service-time coefficient of variation was only 11.7%, substantially below the 100% implied by an exponential distribution, an M/G/1 Pollaczek–Khinchine calculation using empirical variance was included as a cross-check. Under M/M/1, utilization was 0.8616, average queue length was 5.36 vehicles, and average waiting time was 8.41 minutes. Under M/M/2, per-server utilization was 43.08%, P0 was 0.398, average queue length was 0.196 vehicles, waiting time was 0.31 minutes, and the Erlang-C probability of waiting was 0.259. The M/G/1 model predicted a 4.25-minute wait, approximately half the M/M/1 estimate. Sensitivity analysis showed waiting time increasing sharply as arrivals approached service capacity. Limitations include the small service-time sample, absence of hourly arrival data, untested distributional assumptions, and unresolved discrepancies between modeled averages and reported multi-hour waits. Thus, the two-server scenario conditionally predicts shorter waits but does not establish that adding a service line is the optimal investment. Decisions also require analysis of costs, available land, staffing, fuel supply, operational disruptions, and direct field validation.

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