Hello,
In the simulation (5G in-house simulator), while evaluating the system-level performance, I observed that along with the arithmetic mean throughput it also considers the geometric mean throughput of the users in a cell. My question is what is the utility of geometric mean throughput when we are already considering arithmetic mean throughput?
Thanks
The geometric mean gives a higher fairness between the users, because every user must get a non-zero throughput. This is not the case for the geometric mean.
The theoretical rationale could be based on/ justified by the following two facts:
1st, in a queueing system (i.e., in general in queueing theory) an appealing assumption is saying that the arrivals* are coming from a Poisson arrival process with interarrival times following exponential distribution. (arrivals* of customers/ clients in a queueing system, or data packets in wireless network)
https://www.google.com/searchq=interarrival+times+following+exponential+distribution
2nd,
https://www.google.com/search?q=geometric+mean+usage
The geometric mean is often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature ...
The geometric mean throughput has several advantages over the arithmetic mean in assessing system-level performance of wireless networks:
Fairness:
- The geometric mean is more sensitive to low throughput values compared to the arithmetic mean. This means it is less affected by outliers and provides a better measure of how well the system performs for all users, not just those with the highest throughput.
- By focusing on fairness, the geometric mean encourages resource allocation strategies that ensure all users receive a minimum level of service, which is crucial for applications like voice and video calls where even short periods of low throughput can significantly impact user experience.
Robustness:
- The geometric mean is less sensitive to outliers like extreme fluctuations in individual user throughput caused by channel fading, interference, or other factors. This makes it a more reliable measure of overall system performance, especially in dynamic environments.
- Because it doesn't magnify the impact of outliers, the geometric mean provides a clearer picture of the system's true capacity and can be used to more accurately predict future performance under varying conditions.
Congestion control:
- In situations with limited resources, the geometric mean can be used to implement effective congestion control mechanisms. By prioritizing resource allocation to users with the lowest throughput, the system can prevent any single user from consuming an excessive amount of resources and ensure fair access for all.
- This is particularly relevant in scenarios like cellular networks where many users share a limited amount of bandwidth. By optimizing for geometric mean throughput, network operators can achieve a more balanced distribution of resources and improve overall network performance.
Additionally, here are some specific situations where the geometric mean throughput is particularly useful:
- Comparing different resource allocation schemes: When evaluating different resource allocation algorithms, the geometric mean provides a better indication of how well each scheme balances fairness and overall system performance.
- Characterizing the performance of heterogeneous networks: In networks with different types of users and devices, the geometric mean helps to ensure that all users experience a fair level of service, regardless of their specific capabilities or location.
- Analyzing the impact of interference: When considering scenarios with high levels of interference, the geometric mean can be used to assess how well the system performs for users at the cell edge who are most affected by interference.
Overall, the geometric mean throughput provides a more comprehensive and nuanced understanding of system-level performance in wireless networks compared to the arithmetic mean. By considering fairness, robustness, and specific application needs, the geometric mean serves as a valuable tool for evaluating and optimizing network performance for all users.
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