Exponential Models: Approximations for Probabilities

Exponential Approximations for Tail Probabilities in Queues: Sojourn Time and Workload

In this paper, we focus on simple exponential approximations for steady-state tail probabilities in G/GI/1 queues based on large-time asymptotics. We relate the large-time asymptotics for the steady-state waiting time, sojourn time and workload. We evaluate the exponential approximations based on the exact asymptotic parameters and their approximations by making comparisons with exact numerical...

Exponential Approximations for Tail Probabilities in Queues II: Sojourn Time and Workload

We continue to focus on simple exponential approximations for steady-state tail probabilities in queues based on asymptotics. For the G/GI/1 model with i.i.d. service times that are independent of an arbitrary stationary arrival process, we relate the asymptotics for the steadystate waiting time, sojourn time and workload. We show that the three asymptotic decay rates coincide and that the thre...

On Matrix Exponential Approximations of Ruin Probabilities for the Classic and Brownian Perturbed Cramér-lundberg Processes

Padé rational approximations are a very convenient approximation tool, due to the easiness of obtaining them, as solutions of linear systems. Not surprisingly, many matrix exponential approximations used in applied probability are particular cases of first and second order ”admissible Padé approximations” of a Laplace transform, where admissible stands for nonnegative in the case of a density, ...

Simple approximations of ruin probabilities

A “simple approximation” of a ruin probability is an approximation using only some moments of the claim distribution and not the detailed tail behaviour of that distribution. Such approximations may be based on limit theorems or on more or less ad hoc arguments. The most successful simple approximation is certainly the De Vylder approximation, which is based on the idea to replace the risk proc...

Exponential Approximations of Geometri Sums for Reliability