A note on the C-2/G/1 queue and the C-2/G/1 loss system

In this note, we consider the steady-state probability of delay (PW) in the C-2/G/1 queue and the steady-state probability of loss (p(loss)) in the C- 2/G/1 loss system, in both of which the interarrival time has a two-phase C oxian distribution. We show that, for c(X)(2)<1, where c(X) is the coeffici ent of variation of the interarrival time, both p(loss) and PW are increasi ng in beta>(*) over bar * (s), the Laplace-Stieltjes transform of the gener al service-time distribution. This generalises earlier results for the GE(2 )/G/1 queue and the GE(2)/G/1 loss system. The practical significance of th is is that, for c(X)(2)<1, p(loss) in the C-2/G/1 loss system and PW in the C-2/G/1 queue are both increasing in the variability of the service time.