In this note, we consider the steady-state probability of delay (PW) in the C2/G/1 queue and the steady-state probability of loss (ploss) 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 (ploss) and PW are increasing in β(s), 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, (ploss) in the C2/G/1 loss system and PW in the C2/G/1 queue are both increasing in the variability of the service time.
