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Performance enhancements of cellular networks for passengers in high speed railway systems are investigated. Relays placed on top of each train car are proposed. These relays communicate with the cellular base station (BS) over Long Term Evolution (LTE) long range links and with the mobile terminals (MTs) inside the train cars using IEEE 802.11a short range links. Scenarios with unicasting and multicasting from the BS are studied, both in the presence and absence of the relays. In addition, LTE resource allocation is taken into account. The presence of the relays is shown to lead to significant enhancements in the effective data rates of the MTs, in addition to leading to huge savings in the energy consumption from the batteries of the MTs.