Queueing and Occupancy: The Linear Case

Imagine a parking lot, consisting of a long, linear strip of slots. Cars enter at one end and leave by the other. Let’s also stipulate that each arriving car takes the first available slot that it encounters, that is, it will park in the first empty slot that is nearest to the parking lot entrance. Cars arrive randomly, with a given, average interarrival time $\tau_A$. Furthermore, cars occupy each slot for a random amount of time, but all with a common average dwell time $\tau_D$.

If we number the slots, starting at the entrance, we may now ask the question: what is the probability that the slot with index $n$ is occupied?

Ants and Chips

Imagine a bunch of wood chips randomly distributed on a surface. Now add an ant, randomly walking around amongst the chips. Whenever it bumps into a chip, the ant picks up the chip; if it bumps into another chip, it drops the one it is carrying and keeps walking.

How will such a system evolve over time?

Go is Weird

Go is weird. For all its intended (and frequently achieved) simplicity and straightforwardness, I keep being surprised by its rough edges and seemingly arbitrary corner cases. Here is one.

Who is Responsible for Writing Go Interfaces, Anyway?

For every function, data type, or other such code artifact, there are two bits of code: the part that defines and implements it, and the one that uses it.

As I have been thinking (here and here) about the proper use and understanding of Go’s interface construct, the question came up, who is actually responsible for writing the interface: the person who defines the data type, or the person who uses it?

Go Interfaces and the Handle/Body Idiom

The interface construct in the Go language is one of its most immediately visible features. Interfaces in Go are ubiquitous, but I am afraid that the best way to use them has not yet fully been explored. Moreover, in practice, Go interfaces seem to be used in ways that were not intended, and are not necessarily entirely beneficial, such as an implementation shortcut to the classic Handle/Body idiom that hides interchangeable implementations behind a common, well, interface.

Nelder-Mead Simplex Optimization

The Nelder-Mead-Algorithm (also known as the “Simplex Algorithm” or even as the “Amoeba Algorithm”) is an algorithm for the minimization of non-linear functions in several variables. In contrast to other non-linear minimization methods, it does not require gradient information. This makes it less efficient, but also less prone to divergence problems. In contrast to other methods, it is not necessary for the minimum to be bracketed by the initial guess: the algorithm performs a limited “global” search. (It may still converge to a local, rather than the global extremum, of course.) Finally, the algorithm is fairly simple to implement as a stand-alone routine, which makes it a natural choice for multi-dimensional minimization if function evaluations are not prohibitively expensive.