This report is devoted to the optimal resource allocation problem where the goal is to achieve the best quality of service for the number of available customers. The service corresponds to the maintenance of printing machines on customer sites, the resources needed for this purpose are humans (engineers) or time resources, and the quality of service is speci¯ed by the Service Level Agreement (SLA). The violation of SLA conditions leads to penalties for the service provider. When more resources are assigned to the customer, the risk of missing SLA is reduced. The task is to allocate bounded available resources in order to minimize the aggregated risk of missing SLA among all customers.The motivation for this paper is the manuscript [2] where the author addressed this problem under two main assumptions: the independence and the gaussian distribution of the SLA quantity increment" values. We would like to go beyond these assumptions by constructing more general mathematical model of the problem, which takes into account the possible backlog issue in processing the demand, in order to get a better ¯t with practical situations. The optimization using this model is more involved. But it provides a more accurate time-varying resource allocation policy that may su±ciently reduce the risk of violating the SLA contracts at the end of the review period.As an optimization tool we used the stochastic gradient method, which shows a good convergence results in simulations. The dynamic programming technique can also be used for such purposes, which is worth to be applied in the future.