Explicit formulae for characteristics of finite-Capacity M/D/1 queues

Abstract

Even though many computational methods (recursive formulae) for blocking probabilities in finite-capacity M/D/1 queues have already been produced, these are forms of transforms or are limited to single-node queues. Using a distinctly different approach from the usual queueing theory, this study introduces explicit (transformfree) formulae for a blocking probability, a stationary probability, and mean sojourn time under either production or communication blocking policy. Additionally, the smallest buffer capacity subject to a given blocking probability can be determined numerically from these formulae. With proper selection of the overall offered load ρ, the approach described herein can be applicable to more general queues from a computational point of view if the explicit expressions of random vector Dn are available. © 2014 ETRI.