This paper discusses two M/G/1 queueing models with server’s vacation and exhaustive service discipline where customers arrive in batches of variable size, service is one at a time and vacation times are independently and identically distributed. In the first model, the server on its return from a vacation will wait in the system for an arrival if the system is found empty while in the second the server will immediately leave the system for another vacation in such a situation. For both the models, distributions of occupation period and cycle time as well as the conditional distributions of delay to a customer given that the latter arrives during a busy period or during a vacation (of the server) have been obtained in terms of their Laplace Stieltjes Transforms, assuming vacation times to follow a general distribution.
