Is the function of my system a Partial Differential Equation (PDE)?

Question

I have a system that aggregates items based on its key (an item is a key-value) that is flowing in it. It aggregates regarding some parameter $L$. For instance, it sums up all items with the same key and emit one item which has a key-value and its value is the sum of all items aggregated.

I have a function that balances the workload of outgoing items based on the key of each item. This function balances using the aggregate parameter $L$. I calculate the balance using the function $L = λ/min(λ)$ ($λ$ is the throughput or number of item per second) which I can also express as $f = x/y$. As you can see I have two variables $λ$ and $min(λ)$ ($x$ and $y$).

The design of my system is expressed in the figure below. $F1$ aggregates the items and emit them to $F2$. The system is constantly monitoring $F2$ to set how many items $F1$ has to aggregate. The function that governs this behavior is defined as $L = λ/min(λ)$.

The table below exemplifies how I am using the function $L = λ/min(λ)$ to get the value of $L$.

+----+---+---------+-------------+
|key | λ  | min(λ) | L           |
+----+---+---------+-------------+
|k1  | 80 |   20   | 80/20 = 4   |
|k2  | 20 |   20   | 20/20 = 1   |
+----+----+--------+-------------+
|k1  | 80 |   20   | 80/20 = 4   |
|k2  | 20 |   20   | 20/20 = 1   |
|k3  | 50 |   20   | 50/20 = 2.5 |
+----+----+--------+-------------+
|k1  | 80 |   20   | 80/20 = 4   |
|k2  | 20 |   20   | 20/20 = 1   |
|k3  | 50 |   20   | 50/20 = 2.5 |
|k4  |200 |   20   |200/20 = 10  |
+----+----+--------+-------------+
|k1  |500 |   20   |500/20 = 25  |
|k2  | 20 |   20   | 20/20 = 1   |
|k3  |700 |   20   |700/20 = 35  |
|k4  |200 |   20   |200/20 = 10  |
+----+----+--------+-------------+

I have to derivate my function to use it in the control system. To derivate it I need to know if my function is an Ordinary Differential Equation (ODE) or a Partial Differential Equation (PDE). I believe that it is a PDE because there is more than one variable $f(λ) = λ/min(λ)$ or $f(x,y) = x/y$. Is it correct?

After this, I used the partial derivative technic to derivate it.

$∂f/∂x = x^1/y = 1x^0/y = 1/y$

$∂f/∂y = x * 1/y = x * y^{-1} = x * y^{-1-1} = x * y^{-2} = -x/y^2$

Are my assumptions correct? if so, how do I transform the PDE to an ODE in order to apply Laplace transform on it?

Thanks!