On the Steady-State Solution of the M/C₂(a, b)/s Queueing System

This study solves the bulk queueing system M/C₂ (a, b)/s with Poisson arrivals and service time pdf of Coxian-2 type. When a server becomes free a group of customers of size at most b can be served. The server is not allowed to process a group of size less than a, 1 ≤ a ≤ b. Using the generalized method of stages, an explicit form is found for the probabilities of states with all servers busy and then through a recursive structure the problem is reduced to a linear system of s + 1 equations with s + 1 unknowns. An O(as³) algorithm is proposed. Closed form expressions for the waiting-time, idle-servers and service-batch distributions are derived.