We consider an M/M/1 queue with a time dependent arrival rate λ(t) and service rate μ(t). For a special form of the traffic intensity, we obtain an exact, explicit expression for the probability pn(t) that there are n customers at time t. If the service rate is constant (=μ), this corresponds to ρ(t)=λ(t)/μ=(b – aμt)–2. We also discuss the heavy traffic diffusion approximation to this model. We evaluate our results numerically.
