Beyond fifth-generation (B5G) or sixth-generation (6G) communication systems will feature a significant number of gadgets and a wide range of services, most of which will have steep processing needs and stringent latency constraints. To meet such expectations, multi-access edge computing (MEC) will play a crucial function in the evolution of cloud systems. Users may offload their tasks/programs to edge servers, which are capable of executing computational operations and reacting rapidly with an output. Intelligent reflecting surface (IRS) is already recognized as one of the major facilitating mechanisms for forthcoming wireless transmission networks because of its capability to dynamically adjust the phase shift of reflecting electromagnetic signals to establish a suitable propagation atmosphere. Since IRS can enhance the propagation environment both academia and industry are already engaged in research on the inclusion of IRS technology in MEC to improve the latency requirement. Therefore, the work aimed to enhance the uplink signal-to-interference ratio (SIR)-coverage probability-aware or SIR-threshold-based coverage probability-aware communication and computation capacity of a latency-aware MEC system attached to a micro base station of a two-tier network by optimal resource allocation, i.e., transmit power and bandwidth. The work deployed IRS in a micro cell operating under a macro cell base station, i.e., forming a two-tier network aiming to complete computation tasks within the required latency assuring energy and bandwidth efficiency. It compared the deployment of a MEC system considering both the conventional two-tier network and the IRS-assisted two-tier network in which the IRS is deployed between the micro base station and the user. The work adopting MATLAB software-based simulation approach derived that the deployment of an IRS can offer successful task completion within the required task completion time with significantly minimizing the energy and bandwidth consumption. © 2023, The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.