Refined Asymptotic Solution to an Inverse Problem for a Shared Unbuffered Resource

We consider an unbuffered resource having capacity C, which is shared by several different services. Calls of each service arrive in a Poisson stream and request a fixed, integral amount of capacity, which depends on the service. An arriving call is blocked and lost if there is not enough free capacity. Otherwise, the capacity of the call is held for the duration of the call, and the holding period is generally distributed. The inverse problem of determining the traffic intensities in terms of the measured values of the carried loads for each service is investigated. It is assumed that C and the traffic intensities are commensurately large. The inverse problem is solved asymptotically in the critically loaded regime, and a refinement of an earlier approximation is derived. Numerical results for two examples illustrate that the refined approximation provides a significant improvement, with only minimal additional numerical computations.