Time-Of-Flight (TOF) positron emission tomography (PET) was studied and preliminarily developed in the 80s, but the lack of a scintillator able to deliver proper time resolution and stopping power at the same time had prevented it becoming viable technique. Today newly discovered scintillators with greater light yield and/or stopping power, along with advances in photomultiplier tubes and electronics, are rekindling interest in TOF. In this study we performed Monte Carlo simulation using GATE to explore what gains in PET performance could be achieved if the timing resolution in the LYSO-based PET component of Discovery RX PET/CT scanner were improved. For this investigation, count rate performance in different activity concentrations was simulated for different coincidence timing windows and temporal resolutions. Strong evidence of the simulation accuracy was found in the good agreement between measured and simulated data. The results show that the random event rate can be reduced by using a narrower coincidence timing window with increasing the peak NECR by 50%. However, utilization of TOF information improves NECR proportionally with the dramatical reduction of random coincidences as a function of timing resolution. As the TOF performance potential improvements are substantial and the fast electronics and newly scintillators gives us the means to obtain them without other sacrifices, efforts to improve PET timing should resume after their long dormancy.