UvA

We consider a finite capacity Erlang loss system that alternates between active and inactive states according to a two state modulating Markov process. Work arrives to the system as a Poisson process but is blocked from entry when the system is at capacity or inactive. Blocked jobs cost the owner a fixed amount that depends on whether blockage was due to the system being at capacity or due to the system being inactive. Jobs which are present in the system when it becomes inactive pause processing until the system becomes active again.

A Laplace transform expression for the expected undiscounted revenue lost in [0, t] due to blocking is found. Further, an expression for the total time discounted expected lost revenue in [0,?) is provided. We also derive a second order approximation to the former that can be used when the computing power to invert the Laplace transform is not available. These expressions can be used to ascribe a value to four alternatives for improving system performance: (i) increasing capacity, (ii) increasing the service rate, (iii) increasing the repair rate, or (iv) decreasing the failure rate.