A bit old this question, but let's answer. I split it in three different cases:
1. You want to say that the simulation can run in a reasonable time
In this case, I usually write "The simulation run for X hours on a standard workstation.". No details needed, you just want to show that it is feasible to run the simulation and give a very approximate idea, no one cares how much RAM/which CPU you have. The goal is only to show that it is feasible on a normal computer and if it takes 2 hours or 5 hours, it is not very important.
2. You want to provide the exact time
First of all, please don't run it on your laptop. Use a dedicated machine, with the minimal amount of software running to minimize the interference. Depending on the specific domain "minimize the interference" may require simple or very complex strategies. For instance, if you need to obtain the performance of your MATLAB code, you can just close all the other applications and it will be ok. But if you need the performance of a hard real-time program, probably you need to remove the operating system and write bare metal code.
In any case, it is essential to get many samples of the execution time and provide in the article average, variance/standard deviation and number of samples.
Regarding the specification itself, write the most important information: CPU, RAM, Operating System, Compiler/Interpreter version, any other information you think is essential to replicate the experiment.
3. You want to compare your algorithm with another one
This is the most complex case. All the consideration of point 2 applies. However, it is very unlikely that the specification provided by the other article are sufficient for you to correctly replicate the experimental setup, especially in General Purpose computers (for instance, how can you get the same exact software installed? How can you run the CPU at the same exact temperature that may impact performance?).
So, usually, what you should do, it is to replicate the original article experiment in your machine (by impementing their algorithm), where you will run then your algorithm. This is the only way to get a fair comparison.
Direct answers to your questions
does Bigger RAM necessarily means shorter simulation time?
No. Not even increasing the CPU frequency necessarily means reducing the simulation time.
Does quadcore laptop necessary implies that the algorithm performs better compared to dual core laptops?
No, it depends if the algorithm (effectively) exploits parallelism.