Cost-Effective Management of Bulk Arrival Queuing Systems with Vacation and Setup Periods: A Case Study on Engine Piston Production

Abstract

In this paper, we explore a single-server queuing system where arrivals follow a compound Poisson process, while service times have a general distribution. We introduce a concept of a threshold for idle times, assuming that when the server has been idle for a certain duration, it needs a random setup time before starting to serve again. We derive steady-state distributions for both system size and waiting time, and we also calculate the expected cycle time for each model. Additionally, we show that the system size and waiting time distributions can be broken down into three distinct, meaningful parts. For the threshold model, we present a method to determine the optimal threshold that minimizes the total expected operating cost. A numerical example, focusing on the cost model?s relevance to engine piston production, further demonstrates the models practical application