A deterministic change to a time-varying queueing model is described as either changing the number of entities, the queue capacity, or the number of servers in the system at selected times. We use a surrogate distribution for N(t), the number of entities in the system at time t, to approximate deterministic changes to the Ph(t)/Ph(t)/1/c and the Ph(t)/M(t)/s/c queueing models. We develop a solution technique to minimize the number of state probabilities to be approximated. / Master of Science