Renewal approximations for the departure processes of batch systems

In this paper we consider three standard batch arrival/service systems and develop renewal process approximations for the inter-departure time squared coefficient of variations. The systems considered are: (i) batch arrival with individual service; (ii) batching for setup reduction for a single server system; and (iii) batch processing. The random version of the batch arrival with individual service case naturally results from random branching of individuals following a batch service process. This case is also developed with the intent of improving the modeling results for downstream workstations following a batch service process.