When the random variable has a completely monotone density function, we call it bursty (BRST) random variable. At first, we prove that the entropy of inter-arrival time is smaller than or equal to the entropy of inter-departure time in an infinite-server system GI/GI/∞ having general renewal arrivals. On the basis of that result, we prove that a BRST/GI/∞ having bursty arrivals and the associated loss system BRST/GI/c/c have the following paradoxical behavior: In the BRST/GI/∞, the stationary number of customers as well as the inter-departure time become stochastically less variable, as the service time becomes stochastically more variable. Also for the loss system BRST/GI/c/c, the blocking probability decreases and the inter-departure time becomes stochastically less variable, as the service time becomes stochastically more variable.

We propose a finite-capacity single-vacation model, with close-down/setup times and a Markovian arrival process (MAP), for SVC-based IP-over-ATM networks. This model considers the SVC processing overhead and the bursty nature of IP packet arrivals. Specifically, the setup time corresponds to the SVC setup time and the vacation time corresponds to the SVC release time, while the close-down time corresponds to the SVC timeout. The MAP is a versatile point process by which typical bursty arrival processes like the IPP (interrupted Poisson process) or the MMPP (Markov modulated Poisson process) is treated as a special case. The approach we take here is the supplementary variable technique. Compared with the embedded Markov chain approach, it is more straightforward to obtain the steady-state probabilities at an arbitrary instant and the practical performance measures such as packet loss probability, packet delay time, and SVC setup rate. For the purpose of optimal design of the SVC-based IP-over-ATM networks, we also propose and derive a new performance measure called the SVC utilization ratio. Numerical results show the sensitivity of these performance measures to the SVC timeout period as well as to the burstiness of the input process.