Relationship between Delay and System Contents in Multiserver Queues with Geometric Service Times

In this paper, we consider a discrete-time multiserver queueing system with infinite buffer size, geometric service times and a FCFS (first-come-first-served) queueing discipline. A relationship between the probability distributions of the system contents and the packet delay is established. The relationship is general in the sense that it doesn’t require knowledge of the exact nature of the arrival process. By means of the relationship, results for the characteristics of the system contents for various discrete-time queueing models can be transformed into corresponding results for the delay characteristics, thus making a separate delay analysis superfluous. Key-Words: Discrete-time queueing, multiserver system, geometric service times, analytical techniques, generating functions