Calculation Methods of Maximum Waiting Space Required for a Process Involving Many Machine Groups

Abstract

A flow-shop has n machine groups in series, where the k-th machine group (machine group k) consists of m_k parallel servers, each having the same constant processing-time s_k. Jobs enter the first machine group and pass through the machine groups, in order, on a first-come-first-served queuing basis and on an unlimited queuing basis. Every job passes all machine groups. For arbitrary input of jobs, this paper shows that the maximum queue length and the maximum waiting time at the machine group k exist if s_k-1/m_k-1>__=s_k/m_k. The maximum queue length and waiting time are calculated and the waiting space required between machine groups is theoretically determined. The filter effect of the machine group is also explained.