Service Reliability Modeling for a Population of Service Systems with Random Demand Switches under a Two-dimensional Maintenance Policy

Abstract

The service systems such as charging piles and gas stations have been substantially deployed worldwide. These systems are typically installed in batches and provide service to meet the randomly arrived demands. Throughout their designed life, these systems transit among “idle and functional”, “in operational use” and “failed” states and are subjected to state-dependent failure modes. To meet a demand, an idle and functional system needs to be picked and function normally (i.e., stay in the “in operational use” state) for a random duration. If the system fails during the operating duration, the ongoing service would randomly switch to another idle and functional system and transit it from “idle and functional” state to “in operational use” state, until the demand is met. Measured as the proportion of completed demands, the service reliability of such a service population is a crucial factor of service quality. To maintain the service reliability of the population, the operator of the service population monitors (which however, is imperfect) and meanwhile, solicitate from the customers about the status of the systems. Maintenance actions are accordingly taken on the service population. Herein, we consider the imperfectness of both monitoring and customer reporting, and implement a two-dimensional maintenance policy that incorporates both number of failed system and operation hours. The population state transition model is developed by analyzing the dynamic and random transitions of all systems, based on which the long-term service reliability is obtained. We also optimize the two-dimensional maintenance policy to guarantee the desired operation of the entire population.