Distribution-Free Analysis of M/G/1 and G/M/1 Queues

The substantial gap between the state of the art of queuing theory and its application to real-world problems has been commented on by several authors: existing queuing models are either too specialized to be applied to a general problem or too generalized (usually in terms of Laplace transforms and/or generating functions) to be applied to a specific problem. This paper bridges this gap by constructing queuing models without making assumptions about the interarrival or service-time distributions. It obtains results for the M/G/1 and G/M/1 queues, where the “G” distributions are constructed from the observations on the queue.