A Queueing Analysis of Multi-type Servers and Multi-type Customers System based on Gas Stations

Nowadays, cars are essential to life, and most cars used in society need refueling. In gas stations, an odd phenomenon often occurs where the server (refueling lane) is available, but the service is not available, and this is due to the mismatch between the type of the customer (car) and the type of the server. In this paper, we model some types of the system of gas stations as queueing models and analyze them. In addition, we derive performance measures and compare these types of systems. Some counter-intuitive results emerge in this study.