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The workload loss ratio (WLR) is a key parameter from the point of quality of service (QoS) provisioning in packet switched networks and it's estimation is an important issue. The existing results in the area of WLR approximation usually interpret the workload loss as a product of some well assessable quantities. We call this approach as the indirect approximation of the WLR. The drawback of this approach is, that each estimation has an error and the product of these errors could result in highly inaccurate bound. This work deals with the upper approximation of the workload loss ratio based on it's original definition and proposes direct bounds on the WLR. Besides the presentation of the new bounds an extensive systematic performance analysis of the results is also given, in which we show that the direct approach gives closer bound in most cases.