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In this paper, we analyze the impact of end-to-end (E2E) delay variation on stripped sessions, whose packets are distributed over multiple links of multi-mode mobile terminal (MMT). The results of this analysis signify the importance of minimized out-of-sequence (OOS) arrival of packets belonging to a stream, while traversing through multiple radio networks to reach their destination. We, then propose a multi-server delay-budget ordered (MDO) scheduling scheme, that schedules back-logged packets on multiple interfaces of MMT according to their residual delay-budget metrics. In the proposed scheme, the impact of E2E delay variation on in-order packet arrival has been minimized through a link ranking function that reduces the impact of delay fluctuations. The simulation results show a consistently high performance metrics for the scheme with respect to end-to-end delay variations, packet drop rate, E2E throughput and in-order arrival which are highly desirable for interactive/ live, and buffered video streams running on MMT devices in uplink or/and downlink paths.