Explicit Formulae for Characteristics of Finite-Capacity M/D/1 Queues

Even though many computational methods (recursiveformulae) for blocking probabilities in finite-capacityM/D/1 queues have already been produced, these areforms of transforms or are limited to single-node queues. Using a distinctly different approach from the usualqueueing theory, this study introduces explicit (transformfree)formulae for a blocking probability, a stationaryprobability, and mean sojourn time under eitherproduction or communication blocking policy. Additionally, the smallest buffer capacity subject to agiven blocking probability can be determined numericallyfrom these formulae. With proper selection of the overalloffered load ρ, the approach described herein can beapplicable to more general queues from a computationalpoint of view if the explicit expressions of random vectorDn are available.