5 ms·

From the article: > We assume customer arrivals and customer service times are random (details later). Where are those details? I expected some math about the

From the article: > We assume customer arrivals and customer service times are random (details later). Where are those details? I expected some math about the random distribution and how that adds up, but I can't even find the corresponding text passage to explain anything related to that.

moandcompany 7y ago
They probably intend to discuss the Poisson distribution which is commonly used to characterize random customer inter-arrival times, and similar or other distributions for how long it takes to process the customer's request. https://www.wikiwand.com/en/Poisson_distribution https://www.wikiwand.com/en/Poisson_distribution Queueing theory is a pretty common topic in Electrical Engineering and Computer Science curriculum related to scheduling or computer networks. Also part of Operations Research curriculum. Probably worth reading more about Leonard Kleinrock's work if you are interested in this topic and the context where it was applied: https://www.wikiwand.com/en/Leonard_Kleinrock https://www.wikiwand.com/en/Leonard_Kleinrock
- Animats 7y ago
  Reading that, years ago, was what led me to figure out how to approach congestion control. Everybody was reading Kleinrock and assuming random arrival rates. Klienrock had done a study of Western Union Plan 55-A, which was Sendmail for telegrams, built with paper tape for buffering and telephone switches for routing. That led to the original analyses of how the Arpanet should work. The trouble with that approach is that it assumes packets just arrive randomly no matter what the network is doing. That was true for Plan 55-A; delays in the network had little influence on the submission rate for new telegrams. But it's not true once you put a protocol with backpressure, like TCP, on top of the raw packets. Now congestion becomes a feedback control system. I figured that out in the early 1980s and wrote RFC 970.[1] The idea of having one big line was introduced by banks some time in the 1970s. It helped some. But the big breakthrough came from Walter Wriston [2], CEO of what is now Citibank, who pushed his people to develop in-bank terminals and then ATMs, to get rid of the lines entirely. A classic piece of advice from retail consultants is "never place an obstacle in front of a customer who is ready to buy". Amazon's "one-click ordering" is the classic on-line example. Gap stores used to be noted for getting this. They had big, empty counters and more than enough people ready to check customers out. All that crap retailers put at checkouts? Few customers buy it, and it limits how much merchandise the customer can put on the counter. The big queuing theory insight for line management is that if you don't have some idle time, in an open loop situation the line length will go to infinity. In the real world, you start to lose customers. That's how closed loop feedback reacts to retailer incompetence. [1] https://tools.ietf.org/html/rfc970 https://tools.ietf.org/html/rfc970 [2] https://en.wikipedia.org/wiki/Walter_Wriston https://en.wikipedia.org/wiki/Walter_Wriston
  - iamnotacrook 7y ago
    "All that crap retailers put at checkouts? Few customers buy it, and it limits how much merchandise the customer can put on the counter." People select less stuff when they're shopping because they're concerned it won't fit on the counter, or they take a bunch of stuff there but end up not paying for it because it won't fit, or what?
    - setr 7y ago
      I think the issue is that it slows down processing time, reducing overall throughput, for little to no gain And the bigger the line, the more likely customers drop out (at least, I do, especially if the purchase is small/insignificant)
    - Animats 7y ago
      People select less stuff when they're shopping because they're concerned it won't fit on the counter. Yes. This is an issue for stores that don't use shopping carts.
- soVeryTired 7y ago
  > They probably intend to discuss the Poisson distribution which is commonly used to characterize random customer inter-arrival times Wouldn't that be the exponential distribution? The poisson distribution would tell you how many customers would arrive in any given time interval.
  - moandcompany 7y ago
    Arrival processes are often characterized using Poisson distributions Service processes are often characterized using exponential distributions Some wikipedia rabbit holes to dive down: https://en.wikipedia.org/wiki/Queueing_theory https://en.wikipedia.org/wiki/Queueing_theory https://en.wikipedia.org/wiki/Kendall%27s_notation https://en.wikipedia.org/wiki/Kendall%27s_notation https://en.wikipedia.org/wiki/Jackson_network https://en.wikipedia.org/wiki/Jackson_network
Pazzaz 7y ago
That is actually a quote from the John Cook article[0] and so you can find the details of the random process there. [0]: https://www.johndcook.com/blog/2008/10/21/what-happens-when-you-add-a-new-teller/ https://www.johndcook.com/blog/2008/10/21/what-happens-when-...
lapinot 7y ago
Indeed some stuff is missing... Poisson distributions model independently random events that have a given average rate. Its variable counts the number of events occurring before t. Waiting time between events is an exponential distribution (derived by computing the probability that 0 event occur before t). Fun application: suppose you want to take a bus, on average they are independently 10mins apart (rate 1/10). On average when you arrive uniformly random, the next bus will arrive in 10mins (and likewise the last one was 10mins ago). This can be intuitively understood because you have more chances to arrive at a time when buses are further apart. The mean of the waiting time is 1/rate and not 1/(2*rate) like we could imagine.
buckminster 7y ago
Surprisingly, the distribution is not important. See Little's Law. https://en.m.wikipedia.org/wiki/Little%27s_law https://en.m.wikipedia.org/wiki/Little%27s_law
- plorkyeran 7y ago
  Little's Law is not directly applicable here. LL tells us the average wait time given the arrival rate and average size of the queue. Only one of those three things are known, and the distribution is relevant for calculating a second (letting us use LL to find the third). There's a really obvious counterexample to "the distribution doesn't matter": with a uniform distribution, the average wait time will be zero.

moandcompany 7y ago

They probably intend to discuss the Poisson distribution which is commonly used to characterize random customer inter-arrival times, and similar or other distributions for how long it takes to process the customer's request. https://www.wikiwand.com/en/Poisson_distribution https://www.wikiwand.com/en/Poisson_distribution Queueing theory is a pretty common topic in Electrical Engineering and Computer Science curriculum related to scheduling or computer networks. Also part of Operations Research curriculum. Probably worth reading more about Leonard Kleinrock's work if you are interested in this topic and the context where it was applied: https://www.wikiwand.com/en/Leonard_Kleinrock https://www.wikiwand.com/en/Leonard_Kleinrock

Animats 7y ago
Reading that, years ago, was what led me to figure out how to approach congestion control. Everybody was reading Kleinrock and assuming random arrival rates. Klienrock had done a study of Western Union Plan 55-A, which was Sendmail for telegrams, built with paper tape for buffering and telephone switches for routing. That led to the original analyses of how the Arpanet should work. The trouble with that approach is that it assumes packets just arrive randomly no matter what the network is doing. That was true for Plan 55-A; delays in the network had little influence on the submission rate for new telegrams. But it's not true once you put a protocol with backpressure, like TCP, on top of the raw packets. Now congestion becomes a feedback control system. I figured that out in the early 1980s and wrote RFC 970.[1] The idea of having one big line was introduced by banks some time in the 1970s. It helped some. But the big breakthrough came from Walter Wriston [2], CEO of what is now Citibank, who pushed his people to develop in-bank terminals and then ATMs, to get rid of the lines entirely. A classic piece of advice from retail consultants is "never place an obstacle in front of a customer who is ready to buy". Amazon's "one-click ordering" is the classic on-line example. Gap stores used to be noted for getting this. They had big, empty counters and more than enough people ready to check customers out. All that crap retailers put at checkouts? Few customers buy it, and it limits how much merchandise the customer can put on the counter. The big queuing theory insight for line management is that if you don't have some idle time, in an open loop situation the line length will go to infinity. In the real world, you start to lose customers. That's how closed loop feedback reacts to retailer incompetence. [1] https://tools.ietf.org/html/rfc970 https://tools.ietf.org/html/rfc970 [2] https://en.wikipedia.org/wiki/Walter_Wriston https://en.wikipedia.org/wiki/Walter_Wriston
- iamnotacrook 7y ago
  "All that crap retailers put at checkouts? Few customers buy it, and it limits how much merchandise the customer can put on the counter." People select less stuff when they're shopping because they're concerned it won't fit on the counter, or they take a bunch of stuff there but end up not paying for it because it won't fit, or what?
  - setr 7y ago
    I think the issue is that it slows down processing time, reducing overall throughput, for little to no gain And the bigger the line, the more likely customers drop out (at least, I do, especially if the purchase is small/insignificant)
  - Animats 7y ago
    People select less stuff when they're shopping because they're concerned it won't fit on the counter. Yes. This is an issue for stores that don't use shopping carts.
soVeryTired 7y ago
> They probably intend to discuss the Poisson distribution which is commonly used to characterize random customer inter-arrival times Wouldn't that be the exponential distribution? The poisson distribution would tell you how many customers would arrive in any given time interval.
- moandcompany 7y ago
  Arrival processes are often characterized using Poisson distributions Service processes are often characterized using exponential distributions Some wikipedia rabbit holes to dive down: https://en.wikipedia.org/wiki/Queueing_theory https://en.wikipedia.org/wiki/Queueing_theory https://en.wikipedia.org/wiki/Kendall%27s_notation https://en.wikipedia.org/wiki/Kendall%27s_notation https://en.wikipedia.org/wiki/Jackson_network https://en.wikipedia.org/wiki/Jackson_network

Pazzaz 7y ago

That is actually a quote from the John Cook article[0] and so you can find the details of the random process there. [0]: https://www.johndcook.com/blog/2008/10/21/what-happens-when-you-add-a-new-teller/ https://www.johndcook.com/blog/2008/10/21/what-happens-when-...

lapinot 7y ago

Indeed some stuff is missing... Poisson distributions model independently random events that have a given average rate. Its variable counts the number of events occurring before t. Waiting time between events is an exponential distribution (derived by computing the probability that 0 event occur before t). Fun application: suppose you want to take a bus, on average they are independently 10mins apart (rate 1/10). On average when you arrive uniformly random, the next bus will arrive in 10mins (and likewise the last one was 10mins ago). This can be intuitively understood because you have more chances to arrive at a time when buses are further apart. The mean of the waiting time is 1/rate and not 1/(2*rate) like we could imagine.

buckminster 7y ago

Surprisingly, the distribution is not important. See Little's Law. https://en.m.wikipedia.org/wiki/Little%27s_law https://en.m.wikipedia.org/wiki/Little%27s_law

plorkyeran 7y ago
Little's Law is not directly applicable here. LL tells us the average wait time given the arrival rate and average size of the queue. Only one of those three things are known, and the distribution is relevant for calculating a second (letting us use LL to find the third). There's a really obvious counterexample to "the distribution doesn't matter": with a uniform distribution, the average wait time will be zero.