Waiting-Time Distributions for Application to a Series of Service Centers

The method described in this paper is a result of analyzing job shop production processes as a network of waiting lines at machine (production) centers. The waiting time distribution for a series of N work centers, P[∑ j=1 j=N X j ≦ τ], is derived as a function of the waiting-time distributions at the individual work centers, P[X j ≦ τ], j = 1, 2, …, N, where the cumulative waiting-time probability distribution at each work center is of the form P[X j ≦ τ] = l − K j exp(C j τ), with C j and K j constant. The resulting formula for total waiting time is amenable to desk computation and may be useful in estimating job flow time distributions in production control applications for which the first-come, first-served, steady-state model described below is applicable. Also, the method of proof may suggest an approach for convolution in other waiting-line models.