If you are thinking Adobe’s “Portable Document Format,” you are understandably astray – acronyms leave so much to be desired. I actually hate them, and my medical newsletters are packed with them. Does OA mean Osteo-arthritis, or does it mean Older Adults? Does PD mean Parkinson’s Disease or does it refer to Paroxysmal Dyspnea. I don’t know why the medical newsletters have become so filled with acronyms, but I don’t think that “digital ink” is so expensive that it warrants this bullshit.
In this case, PDF means Probability Distribution Function, and Erlang is the name of a mathematician researcher whose work delved into AT&T’s question of how many telephone switchboard operators it would take to answer incoming calls within a given waiting period. Without getting needlessly nerdy, let me say that this question touches on many issues regarding queues – not just telephone switchboard matters. Questions like, “How many cashiers do we need to keep customers moving through a cafeteria such that wait times are less than x-minutes?” The same principles apply to how we organize data on a hard drive in order to minimize file read/write transfer times. There are many other examples, of course.
What the Erlang function addresses is the inter-arrival times of events – things like phone calls, or cars moving down a street or highway past an intersection or exit. These kinds of problems involve unpredictable events that occur according to a particular probability distribution function. Some inter-arrival intervals are common, and others are rare. For instance, not getting a single phone call in 30-minutes may be rare for a call center. Getting 60 calls in one minute in the same call center might be equally rare. On average, perhaps there is one call every minute or two. So, how many “Jakes” at State Farm do you need so that no caller is ever left on hold for longer than x-minutes? Erlang to the rescue.
I’m obsessing about the Erlang tonight not only because I studied it in a course in Operations Research in graduate school, but because I occasionally reflect on the common wisdom that “misfortunes occur in threes.” I’ve touched on this matter in another essay a year or more ago, but today it seems especially germane.
Misfortune 1: A couple of weeks ago, I lost my college graduation ring. My stroke late last year left me with impaired sensation on the right-side face and limbs. The net effect is that I have “pin and needle” sensations on that side 24/7. The practical manifestation of this sensory misinformation is a certain degree of clumsiness. Sometimes I drop things like my keys or a cup because I am not aware that I am holding them too lightly. I am not as aware of jewelry on my right hand as I am of similar items on my left hand.
This wasn’t a big deal until I noticed a couple of weeks ago that I was no longer wearing my graduation ring and could not find it. Over the next two weeks, I looked high and low for it. I ultimately became resigned to having lost it forever; it probably fell off while I was outside in the back yard or perhaps as I walked around in the grocery store. Alas, it had deep sentimental value for me since I had bought it in 1967, at the age of 18, with my own hard-earned dollars.
Misfortune 2: Our 55″ Samsung TV gave up its last gasp (HDMI input port) a couple of weeks ago. It was an old model with less than a GED to show for its age – not a “smart TV” by today’s TV standards. We put it out on the curb for bulky trash collection, and I ordered a new 65″ OLED unit. So, the bedroom TV went to the curb; the living room 65″ OLED went to the bedroom, and the new 65″ OLED went to the living room. Musical TVs or a right shift of TVs, if you prefer.
Misfortune 3: Last night, as I sat watching a program in the bedroom, the TV went blank. After some rudimentary systems analysis, I determined that the problem was an electronics failure in the TV itself. Bummer: the unit is only 24-36 months old, and the warranty was only for 12 months. I’ll try to have it repaired if the cost is less than the expense of a replacement.
So, here we have a text-book case of the triad of misfortunes. It seems like a triad simply because longer runs of misfortune are quite uncommon, and the Erlang function says that there is likely a reprieve from misfortune to follow. Why do I have such faith in mathematical principles? Is it because I studied the Erlang in graduate school? Is it because I trust in science, and because mathematics is the language of science? No.
It is because as Susan was rearranging boxes in my study so that Kedi could move around more easily, Kedi reached up on a shelf and brought something down with a CLINK! What was it? My college graduation ring, of course.
Good Kedi; good girl. 🙂