In this note, we consider the steady-state probability of delay in the C2/G/1 queue and the steady-state probability of loss in the C2/G/1 loss system, in both of which the interarrival time has a two-phase Coxian distribution. We show that, for cx2<1, where cx is the coefficient of variation of the interarrival time, both probabilities are increasing in the Laplace–Stieltjes transform of the general service-time distribution. This generalises earlier results for the GE2/G/1 queue and the GE2/G/1 loss system. The practical significance of this is that, for cx2<1, the probabilities are both increasing in the variability of the service time.
