Abstract
In this paper, a versatile Markovian queueing system is considered. Given a fixed threshold levelc, the server serves customers one a time when the queue length is less thanc, and in batches of fixed sizecwhen the queue length is greater than or equal toc. The server is subject to failure when serving either a single or a batch of customers. Service rates, failure rates, and repair rates, depend on whether the server is serving a single customer or a batch of customers. While the analytical method provides the initial probability vector, we use the entropy principle to obtain both the initial probability vector (for comparison) and the tail probability vector. The comparison shows the results obtained analytically and approximately are in good agreement, especially when the first two moments are used in the entropy approach.