A note on the C₂/G/1 queue and the C₂/G/1 loss system

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 (p_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 c²_x < 1, where c_X is the coefficient of variation of the interarrival time, both p_loss 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 c²_X < 1, p_loss 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.