Waiting time distribution in single-channel deterministic flow lines with discrete inter-arrival time distributions

Abstract

Although previous studies proved that deterministic flow lines can be analysed separately by an exact decomposition method called a channel method and that the delay an item experiences in each machine possesses a Markovian property, the exact performance measures for the system with general arrival process cannot be obtained due to the lack of the results on relevant GI/D/1 queue. The solution obtained only for the system with specific arrival patterns such as geometric distribution or JIT arrivals considering setups. In this paper, exact decomposition methods are investigated through the systems consisting of one channel. Assuming general and discrete inter-arrival times, we introduce a procedure to calculate the equilibrium probabilities for waiting time distributions. It is demonstrated that probabilities can be computed by a matrix analytic method and recursions based on the decomposition methods. Inspired by the steel product manufacturing process, two-stage conveyor belt systems are analysed as an application. [Received: 28 July 2020; Accepted: 1 March 2021]