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An intelligent reflecting surface (IRS) is an emerging technology in the next-generation (B5G and 6G) wireless communications with the aim of improving the spectral/energy efficiency of the wireless networks. In this paper, we focus on multiple IRS-aided multiuser multiple-input single-output (MISO) downlink network, where each IRS is deployed near to the cell boundary of the cellular network in order to help the downlink transmission to the cell-edge users. To achieve the significant performance benefits provided by the rate-splitting (RS) transmission in multiuser scenario, two-layer hierarchical rate splitting (2L-HRS) technique is deployed at the base station (BS) to serve all the users. Furthermore, we propose an On-Off scheme for controlling the IRSs with practical phase shifts. In order to analyze the performance of the users, we derive the closed-form expressions of outage probability for both cell-edge users …