Dense random access channel (RACH) attempts by Internet of Things (IoT) devices result in radio access network (RAN) overload in a Long-Term Evolution-Advanced (LTE-A) cell. Currently, the Third-Generation Partnership Project (3GPP) proposes the macro eNodeB operate extended access barring (EAB) that employs time-randomization (T-R): a technique that randomizes RACH attempts in time to mitigate the RAN overload. However, another solution that 3GPP considers for the overload problem is a spatial-randomization technique that randomizes RACH attempts with space as a degree of freedom (along with which T-R can also be employed). This technique decentralizes RACH attempts to a set of spatially distributed aggregators (micro eNodeBs), deployed to exclusively serve the IoT devices in a LTE-A macrocell. However, there has been no work that analyzes only spatial-randomization (S-R) or S-R with aggregator-employed T-R (called as time-spatial randomization and denoted by TS-R) and compares their performances with macro eNodeB-employed T-R (T-R-M). In this regard, we develop analytical models for T-R-M, S-R, and TS-R techniques to estimate their performances. Simulation results show that our analytical models accurately estimate the performance of each technique. Using our analysis, we then show that the mean access delay for S-R and TS-R is extremely less compared to T-R-M for a fixed success probability. Next, we build an analytical model to compare the effect of all these techniques on eNodeB energy consumption, which is a key performance parameter. Our investigations reveal that factors like quality of service (QoS) and periodicity of IoT access cycles decide the least energy consuming technique. We use these observations to propose a self-organizing network architecture based time-spatial randomization (SONATS-R): a scheme that dynamically allocates the randomization technique, aiming to minimize energy consumption for the desired QoS.