M/D/c queue

In queueing theory, a discipline within the mathematical theory of probability, an M/D/c queue represents the queue length in a system having c servers, where arrivals are determined by a Poisson process and job service times are fixed (deterministic). The model name is written in Kendall's notation. Agner Krarup Erlang first published on this model in 1909, starting the subject of queueing theory. The model is an extension of the M/D/1 queue which has only a single server.An M/D/c queue is a stochastic process whose state space is the set {0,1,2,3,...} where the value corresponds to the number of customers in the system, including any currently in service. Erlang showed that when ρ = (λ D)/c < 1, the waiting time distribution has distribution F(y) given by