Blocking Probability Approximations and Bounds for Best-Effort Calls in an Integrated Service System

In this paper, we consider an integrated service system, providing multirate guaranteed services and homogeneous best-effort services. The total system capacity is shared by both service types, while the guaranteed service customers are treated as high priority and are allocated fixed data rate bandwidth units. The best-effort service customers are supported by the remaining capacity leftover by the guaranteed services, in a processor-sharing manner. Admission control on the best-effort service customers is adopted to provide a certain level of quality of service (not guaranteed) to avoid the effect of repeated attempts. The best-effort customer blocking probability is an important metric for network dimensioning. In this integrated service system, we observe that the blocking probability of the best-effort customers is not insensitive to the shapes of their flow-size distributions and the guaranteed customers' holding-time distributions. We obtain here by light computation, for the best-effort customers, blocking probability bounds, and approximations, which possess the insensitivity property. Considering that the distributions for customers' holding times and flow sizes may be unknown, the proposed insensitive bounds and approximations will facilitate system design and network dimensioning with predictable and acceptable performance.