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In this paper, a novel mathematical approach to evaluate the performance of adaptive or flexible resource allocation (FRA) strategies with uniform quality of service (QoS) provisioning in multiservices wireless cellular networks, in terms of the call blocking probabilities and transmission delay, is proposed. FRA strategies improve channel utilization by dynamically adjusting user transmission rates. Based on the available cell capacity, the bandwidth offered to users can be adjusted in accordance with the elasticities of their service types. When an FRA strategy provides similar QoS to all the calls of the same service type, it is known as an FRA with uniform QoS provisioning. In multiservices wireless cellular networks, calls can be identified as belonging to one of four service classes (i.e., conversational, streaming, interactive, and background). Transmission delay is one of the most important performance measurements of interactive and background service classes. Transmission delay, however, has not been addressed in previous studies on FRA with uniform QoS provisioning either in conjunction with interactive or background service classes. This is because such studies have been based on the Markov property of the negative exponential distribution of the service time which lacks time delay information. The analytical approach in this paper is based on the fact that in FRA strategies with uniform QoS provisioning, calls of all service types tend to use an average number of resources (i.e., the number of resources available for a service type divided by the number of active users of that service type). This feature facilitates the assessment of the mean service time and the number of resources allocated to a call during its lifetime and, consequently, a call's transmission delay. The study also considers the fact that the probability density function (pdf) of the normalized transmission delay is almost a symmetrical function and has low variance. The accuracy of the proposed mathematical analysis is then corroborated by means of semianalytical methods and by discrete event computer simulation.