An approximation method for blocking probabilities in M/D/1/K₁→ •/D/1/K₂ queues

Obtaining exact blocking probabilities for tandem queues with finite capacities is not a trivial problem. In this paper, we propose a computational approximation method using max-plus algebra for computing blocking probability in a Poisson-driven 2-node tandem queue with finite capacities and constant service times. The blocking probability of a finite-capacity queueing system can be obtained from either the tail probability of stationary waiting time or the difference between two expected stationary waiting times at the first node of the corresponding extended 3-node tandem queue. The computational results in this study show that the proposed approach provides a good approximation of the blocking probability, and in particular, it works well under moderately to heavily loaded situations. The proposed approach is not limited to a particular blocking policy, system structure, or service time; hence, it is applicable to general queues with finite buffer capacities and various blocking policies.