There's a large set of objects. Set is dynamic: objects can be added or deleted any time. Let's call the total number of objects N.
Each object has two properties: mass (M) and time (T) of last update.
Every X minutes a small batch of those should be selected for processing, which updates their T to current time. Total M of all objects in a batch is limited: not more than L.
I am looking to solve three tasks here:
find a next batch object picking algorithm;
introduce object classes: simple, priority (granted fit into at least each n-th batch) and frequent (fit into each batch);
forecast system capacity exhaust (time to add next server = increase L).
What kind of model best describes such a system?
The whole thing is about a service that processes the "objects" in time intervals. Each object should be "measured" each N hours. N can vary in a range. X is fixed.
Objects are added/deleted by humans. N grows exponentially, rather slow, with some spikes caused by publications. Of course forecast can't be precise, just some estimate. M varies from 0 to 1E7 with exponential distribution, most are closer to 0.
I see there can be several strategies here:
A. full throttle - pack each batch as much as close to 100%. As N grows, average interval a particular object gets a hit will grow.
B. equal temperament :) - try to keep an average interval around some value. A batch fill level will be growing from some low level. When it reaches closer to 100% – time to get more servers.
C. - ?
Here is a pretty complete design for your problem.
Your question does not optimally match your description of the system this is for. So I'll assume that the description is accurate.
When you schedule a measurement you should pass an object, a first time it can be measured, and when you want the measurement to happen by. The object should have a weight attribute and a measured method. When the measurement happens, the measured method will be called, and the difference between your classes is whether, and with what parameters, they will reschedule themselves.
Internally you will need a couple of priority queues. See http://en.wikipedia.org/wiki/Heap_(data_structure) for details on how to implement one.
The first queue is by time the measurement can happen, all of the objects that can't be measured yet. Every time you schedule a batch you will use that to find all of the new measurements that can happen.
The second queue is of measurements that are ready to go now, and is organized by which scheduling period they should happen by, and then weight. I would make them both ascending. You can schedule a batch by pulling items off of that queue until you've got enough to send off.
Now you need to know how much to put in each batch. Given the system that you have described, a spike of events can be put in manually, but over time you'd like those spikes to smooth out. Therefore I would recommend option B, equal temperament. So to do this, as you put each object into the "ready now" queue, you can calculate its "average work weight" as its weight divided by the number of periods until it is supposed to happen. Store that with the object, and keep a running total of what run rate you should be at. Every period I would suggest that you keep adding to the batch until one of three conditions has been met:
You run out of objects.
You hit your maximum batch capacity.
You exceed 1.1 times your running total of your average work weight. The extra 10% is because it is better to use a bit more capacity now than to run out of capacity later.
And finally, capacity planning.
For this you need to use some heuristic. Here is a reasonable one which may need some tweaking for your system. Maintain an array of your past 10 measurements of running total of average work weight. Maintain an "exponentially damped average of your high water mark." Do that by updating each time according to the formula:
average_high_water_mark
= 0.95 * average_high_water_mark
+ 0.5 * max(last 10 running work weight)
If average_high_water_mark ever gets within, say, 2 servers of your maximum capacity, then add more servers. (The idea is that a server should be able to die without leaving you hosed.)
I think answer A is good. Bin packing is to maximize or minimize and you have only one batch. Sort the objects by m and n.
Related
Certain sensors are to trigger a signal based on the rate of change of the value rather than a threshold.
For instance, heat detectors in fire alarms are supposed to trigger an alarm quicker if the rate of temperature rise is higher: A temperature rise of 1K/min should trigger an alarm after 30 minutes, a rise of 5K/min after 5 minutes and a rise of 30K/min after 30 seconds.
I am wondering how this is implemented in embedded systems, where resources are scares. Is there a clever data structure to minimize the data stored?
The naive approach would be to measure the temperature every 5 seconds or so and keep the data for 30 minutes. On these data one can calculate change rates over arbitrary time windows. But this requires a lot of memory.
I thought about small windows (e.g. 10 seconds) for which min and max are stored, but this would not save much memory.
From a mathematical point of view, the examples you have described can be greatly simplified:
1K/min for 30 mins equals a total change of 30K
5K/min for 5 mins equals a total change of 25K
Obviously there is some adjustment to be made because you have picked round numbers for the example, but it sounds like what you care about is having a single threshold for the total change. This makes sense because taking the integral of a differential results in just a delta.
However, if we disregard the numeric example and just focus on your original question then here are some answers:
First, it has already been mentioned in the comments that one byte every five seconds for half an hour is really not very much memory at all for almost any modern microcontroller, as long as you are able to keep your main RAM turned on between samples, which you usually can.
If however you need to discard the contents of RAM between samples to preserve battery life, then a simpler method is just to calculate one differential at a time.
In your example you want to have a much higher sample rate (every 5 seconds) than the time you wish to calculate the delta over (eg: 30 mins). You can reduce your storage needs to a single data point if you make your sample rate equal to your delta period. The single previous value could be stored in a small battery retained memory (eg: backup registers on STM32).
Obviously if you choose this approach you will have to compromise between accuracy and latency, but maybe 30 seconds would be a suitable timebase for your temperature alarm example.
You can also set several thresholds of K/sec, and then allocate counters to count how many consecutive times the each threshold has been exceeded. This requires only one extra integer per threshold.
In signal processing terms, the procedure you want to perform is:
Apply a low-pass filter to smooth quick variations in the temperature
Take the derivative of its output
The cut-off frequency of the filter would be set according to the time frame. There are 2 ways to do this.
You could apply a FIR (finite impulse response) filter, which is a weighted moving average over the time frame of interest. Naively, this requires a lot of memory, but it's not bad if you do a multi-stage decimation first to reduce your sample rate. It ends up being a little complicated, but you have fine control over the response.
You could apply in IIR (Infinite impulse response) filter, which utilizes feedback of the output. The exponential moving average is the simplest example of this. These filters require far less memory -- only a few samples' worth, but your control over the precise shape of the response is limited. A classic example like the Butterworth filter would probably be great for your application, though.
I'm looking for best algorithm for message schedule. What I mean with message schedule is a way to send a messages on the bus when we have many consumers at different rate.
Example :
Suppose that we have data D1 to Dn
. D1 to send to many consumer C1 every 5ms, C2 every 19ms, C3 every 30ms, Cn every Rn ms
. Dn to send to C1 every 10ms, C2 every 31ms , Cn every 50ms
What is best algorithm which schedule this actions with the best performance (CPU, Memory, IO)?
Regards
I can think of quite a few options, each with their own costs and benefits. It really comes down to exactly what your needs are -- what really defines "best" for you. I've pseudocoded a couple possibilities below to hopefully help you get started.
Option 1: Execute the following every time unit (in your example, millisecond)
func callEachMs
time = getCurrentTime()
for each datum
for each customer
if time % datum.customer.rate == 0
sendMsg()
This has the advantage of requiring no consistently stored memory -- you just check at each time unit whether your should be sending a message. This can also deal with messages that weren't sent at time == 0 -- just store the time the message was initially sent modulo the rate, and replace the conditional with if time % datum.customer.rate == data.customer.firstMsgTimeMod.
A downside to this method is it is completely reliant on always being called at a rate of 1 ms. If there's lag caused by another process on a CPU and it misses a cycle, you may miss sending a message altogether (as opposed to sending it a little late).
Option 2: Maintain a list of lists of tuples, where each entry represents the tasks that need to be done at that millisecond. Make your list at least as long as the longest rate divided by the time unit (if your longest rate is 50 ms and you're going by ms, your list must be at least 50 long). When you start your program, place the first time a message will be sent into the queue. And then each time you send a message, update the next time you'll send it in that list.
func buildList(&list)
for each datum
for each customer
if list.size < datum.customer.rate
list.resize(datum.customer.rate+1)
list[customer.rate].push_back(tuple(datum.name, customer.name))
func callEachMs(&list)
for each (datum.name, customer.name) in list[0]
sendMsg()
list[customer.rate].push_back((datum.name, customer.name))
list.pop_front()
list.push_back(empty list)
This has the advantage of avoiding the many unnecessary modulus calculations option 1 required. However, that comes with the cost of increased memory usage. This implementation would also not be efficient if there's a large disparity in the rate of your various messages (although you could modify this to deal with algorithms with longer rates more efficiently). And it still has to be called every millisecond.
Finally, you'll have to think very carefully about what data structure you use, as this will make a huge difference in its efficiency. Because you pop from the front and push from the back at every iteration, and the list is a fixed size, you may want to implement a circular buffer to avoid unneeded moving of values. For the lists of tuples, since they're only ever iterated over (random access isn't needed), and there are frequent additions, a singly-linked list may be your best solution.
.
Obviously, there are many more ways that you could do this, but hopefully, these ideas can get you started. Also, keep in mind that the nature of the system you're running this on could have a strong effect on which method works better, or whether you want to do something else entirely. For example, both methods require that they can be reliably called at a certain rate. I also haven't described parallellized implementations, which may be the best option if your application supports them.
Like Helium_1s2 described, there is a second way which based on what I called a schedule table and this is what I used now but this solution has its limits.
Suppose that we have one data to send and two consumer C1 and C2 :
Like you can see we must extract our schedule table and we must identify the repeating transmission cycle and the value of IDLE MINIMUM PERIOD. In fact, it is useless to loop on the smallest peace of time ex 1ms or 1ns or 1mn or 1h (depending on the case) BUT it is not always the best period and we can optimize this loop as follows.
for example one (C1 at 6 and C2 at 9), we remark that there is cycle which repeats from 0 to 18. with a minimal difference of two consecutive send event equal to 3.
so :
HCF(6,9) = 3 = IDLE MINIMUM PERIOD
LCM(6,9) = 18 = transmission cycle length
LCM/HCF = 6 = size of our schedule table
And the schedule table is :
and the sending loop looks like :
while(1) {
sleep(IDLE_MINIMUM_PERIOD); // free CPU for idle min period
i++; // initialized at 0
send(ScheduleTable[i]);
if (i == sizeof(ScheduleTable)) i=0;
}
The problem with this method is that this array will grows if LCM grows which is the case if we have bad combination like with rate = prime number, etc.
I am building an agent-based model for product usage. I am trying to develop a function to decide whether the user is using the product at a given time, while incorporating randomness.
So, say we know the user spends a total of 1 hour per day using the product, and we know the average distribution of this time (e.g., most used at 6-8pm).
How can I generate a set of usage/non-usage times (i.e., during each 10 minute block is the user active or not) while ensuring that at the end of the day the total active time sums to one hour.
In most cases I would just run the distributor without concern for the total, and then at the end normalize by making it proportional to the total target time so the total was 1 hour. However, I can't do that because time blocks must be 10 minutes. I think this is a different question because I'm really not computing time ranges, I'm computing booleans to associate with different 10 minute time blocks (e.g., the user was/was not active during a given block).
Is there a standard way to do this?
I did some more thinking and figured it out, if anyone else is looking at this.
The approach to take is this: You know the allowed number n of 10-minute time blocks for a given agent.
Iterate n times, and on each iteration select a time block out of the day subject to your activity distribution function.
Main point is to iterate over the number of time blocks you want to place, not over the entire day.
I am trying to implement something along the lines of a Moving Average.
In this system, there are no guarantees of a quantity of Integers per time period. I do need to calculate the Average for each period. Therefore, I cannot simply slide over the list of integers by quantity as this would not be relative to time.
I can keep a record of each value with its associated time. We will have a ton of data running through the system so it is important to 'garbage collect' the old data.
It may also be important to note that I need to save the average to disk after the end of each period. However, they may be some overlap between saving the data to disk and having data from a new period being introduced.
What are some efficient data structures I can use to store, slide, and garbage collect this type of data?
The description of the problem and the question conflict: what is described is not a moving average, since the average for each time period is distinct. ("I need to compute the average for each period.") So that admits a truly trivial solution:
For each period, maintain a count and a sum of observations.
At the end of the period, compute the average
I suspect that what is actually wanted is something like: Every second (computation period), I want to know the average observation over the past minute (aggregation period).
This can be solved simply with a circular buffer of buckets, each of which represents the value for one computation period. There will be aggregation period / computation period such buckets. Again, each bucket contains a count and a sum. Also, a current total/sum and a cumulative total sum/count are maintained. Each observation is added to the current total/sum.
At the end of a each computation period:
subtract the sum/count for the (circularly) first period from the cumulative sum/count
add the current sum/count to the cumulative sum/count
report the average based on the cumulative sum/count
replace the values of the first period with the current sum/count
clear the current sum/count
advance the origin of the circular buffer.
If you really need to be able to compute at any time at all the average of the previous observations over some given period, you'd need a more complicated data structure, basically an expandable circular buffer. However, such precise computations are rarely actually necessary, and a bucketed approximation, as per the above algorithm, is usually adequate for data purposes, and is much more sustainable over the long term for memory management, since its memory requirements are fixed from the start.
I would like to ask if someone would have an idea on the best(fastest) algorithm for the following scenario:
X processes generate a list of very large files. Each process generates one file at a time
Y processes are being notified that a file is ready. Each Y process has its own queue to collect the notifications
At a given time 1 X process will notify 1 Y process through a Load Balancer that has the Round Rubin algorithm
Each file has a size and naturally, bigger files will keep both X and Y more busy
Limitations
Once a file gets on a Y process it would be impractical to remove it and move it to another Y process.
I can't think of other limitations at the moment.
Disadvantages to this approach
sometimes X falls behind(files are no longer pushed). It's not really impacted by the queueing system and no matter if I change it it will still have slow/good times.
sometimes Y falls behind(a lot of files gather in the queues). Again, the same thing like before.
1 Y process is busy with a very large file. It also has several small files in its queue that could be taken on by other Y processes.
The notification itself is through HTTP and seems somehow unreliable sometimes. Notifications fail and debugging has not revealed anything.
There are some more details that would help to see the picture more clearly.
Y processes are DB threads/jobs
X processes are web apps
Once files reach the X processes, these would also burn resources from the DB side by querying it. It has an impact on the producing part
Now I considered the following approach:
X will produce files like it has before but will not notify Y. It will hold a buffer (table) to populate the file list
Y will constantly search for files in the buffer and retrieve them itself and store them in its own queue.
Now would this change be practical? Like I said, each Y process has its own queue, it doesn't seem to be efficient to keep it anymore. If so, then I'm still undecided on the next bit:
How to decide which files to fetch
I've read through the knapsack problem and I think that has application if I would have the entire list of files from the beginning which I don't. Actually, I do have the list and the size of each file but I wouldn't know when each file would be ready to be taken.
I've gone through the producer-consumer problem but that centers around a fixed buffer and optimising that but in this scenario the buffer is unlimited and I don't really care if it is large or small.
The next best option would be a greedy approach where each Y process locks on the smallest file and takes it. At first it does appear to be the fastest approach and I'm currently building a simulation to verify that but a second opinion would be fantastic.
Update
Just to be sure that everyone gets the big picture, I'm linking here a fast-done diagram.
Jobs are independent from Processes. They will run at a speed and process how many files are possible.
When a Job finishes with a file it will send a HTTP request to the LB
Each process queues requests (files) coming from the LB
The LB works on a round robin rule
Diagram
The current LB idea is not good
The load balancer as you've described it is a bad idea because it's needlessly required to predict the future, which you are saying is impossible. Moreover, round-robin is a terrible scheduling strategy when jobs have varying lengths.
Just have consumers notify the LB when they're idle. When a new job arrives from a producer, it selects the first idle consumer and sends the job there. When there are no idle consumers, the producer's job is queued in the LB waiting for a free consumer to appear.
This way consumers will always be optimally busy.
You say "Having one queue to serve 100 apps (for example) would be inefficient." This is a huge leap of intuition that's probably wrong. A work queue that's only handling file names can be fast. You need it only to be 100 times faster (because you infer there are 100 consumers) than the average "very large file" handling operation. File handling is normally 10th of seconds or seconds. A queue handler based, say, on an Apache mod or Redis for two random choices, could pretty easily serve 10,000 requests per second. This is a factor of 10 away from being a bottleneck.
If you select from idle consumers on a FIFO basis, the behavior will be round-robin when all jobs are equal length.
If the LB absolutelly cannot queue work
Then let Ty(t) be the total future time needed to complete the work in the queue of consumer y at the current epoch t. The LB's goal is to make Ty(t) values equal for all y and t. This is the ideal.
To get as close as possible to the ideal, it needs an internal model to compute these Ty(t) values. When a new job arrives from a producer at epoch t, it finds consumer y with the the minimum Ty(t) value, assigns the job to this y, and adjusts the model accordingly. This is a variation of the "least time remaining" scheduling strategy, which is optimal for this situation.
The model must inevitably be an approximation. The quality of the approximation will determine its usefulness.
A standard approach (e.g. from OS scheduling), will be to maintain a pair [t, T]_y for each consumer y. T is the estimate of Ty(t) that was computed at the past epoch t. Thus at a later epoch t+d, we can estimate Ty(t+d) as max(T-t,0). The max is because for d>t, the estimated job time has expired, so the consumer should be complete.
The LB uses whatever information it can get to update the model. Examples are estimates of time a job will require (from your description probably based on file size and other characteristics), notification that the consumer has actually finished a job (LB decreases T by the esimated duration of the completed job and updates t), assignment of a new job (LB increases T by the estimated duration of the new job and updates t), and intermediate progress updates of estimated time remaining from consumers during long jobs.
If the information available to the LB is detailed, you will want to replace the total time T in the [t, T]_y pair with a more complete model of the work queued at y: for example a list of estimated job durations, where the head of the list is the one currently being executed.
The more accurate the LB model, the less likely a consumer will starve when work is available, which is what you are trying to avoid.