An organization may suffer large losses if its computer service is interrupted. For protection, it can purchase computer backup service from the outside market which temporarily provides service replacement from a central facility. A dynamic probabilistic model is developed which describes such a computer backup service system. The parties involved have conflicting motivations. The supplier is interested in optimizing his expected profits subject to a given set of parameters while the subscriber will evaluate the service contract to his own best interest. This paper analyzes how the economic interests of the supplier and subscribers interact based on a dynamic reliability analysis of their respective computer systems. Assuming all physical parameters fixed, the supplier's optimal value in terms of economic parameters is determined. An algorithmic procedure is developed for computing such values. Some numerical examples are presented in order to gain insights into the system.

Let TBP be the server busy period of an M/G/1 queueing system characterized by arrival intensity λ and service time c.d.f. A(τ). In this paper, we investigate the regularity structure of the Laplace transform σBP(s)=E[] on the complex s-plane. It is shown, under certain broad conditions, that finite singular points of σBP(s) are all branch points. Furthermore the branch point s0 having the greatest real part is always purely negative and is of multiplicity two. The basic branch point s0 and the associated complex structure provide a basis for an asymptotic representation of various descriptive distributions of interest. For a natural relaxation time |s0|-1 of the M/G/1 system, some useful bounds are obtained and the asymptotic behavior as traffic intensity approaches one is also discussed. Detailed results of engineering value are provided for two important classes of service time distributions, the completely monotone class and the Erlang class.