Scheduling Architecture

As I am working my way thru the Alea framework to continue my research.  I realized the Alea does not actually implement a scheduling algo, at least not a fairshare one.

Schedulers are difficult to write, but I have had the fortune to develop a few over the years.  Wanted to document the internal architecture of a “good” scheduler.  Frankly, it does not matter what type of scheduling algorithm you implement.  As long at you follow the following approach, you will be ok.

Schedulers need to have 3 distinct stages:
– Pre-processing of tasks

– Scheduling of tasks

– Dispatching of tasks

most people lump the first two together.  That’s a mistake!

– Step 1: preprocessing:

This is where you apply the desired policy to the incoming tasks.  If you are interested in a FCFS policy, well, then you make sure that you queue up your tasks in a FCFS manner, but putting all the tasks in the order of arrival in a queue.  If you are interested in SJF (shortest job first), well, then you sort the incoming tasks in a manner that the shortest jobs are first in the queue.  Maybe you have more than one queue; it does not matter.  The point here is that in the preprocessing, you are not actually scheduling anything, but rather enforcing a policy or set of desired policies to the incoming tasks.

– Step 2: scheduling:

After your tasks are sorted based on some policy, you are ready to schedule these tasks.  Scheduling is supply vs. demand.
The most common scheduling policy is fairshare.  I have many posts about fairshare, but the gist of it is that you are given a set of resources based on your “fair share”, which is determined by “you deserve more because you need more” mentality.  If A has 10x as many tasks as B, it will get 10x more resources.
There are other policies, like highest priority first, etc.

– Step 3: dispatching:

After you have decided which tasks should get executed first, you now need to dispatch the tasks.  Most scheduling systems use gang-bang scheduling in that a number of tasks are scheduled.  The reason here is efficiency and practicality.  You dont make a scheduling decision on one task, but rather a set of tasks.  I am classifying gang-bang in the dispatching of the tasks, as it does not make a scheduling decision.  Many papers (ref needed) simply claim that gang-bang is a scheduling policy of its own.  The dispatcher essentially goes thru the set of tasks assigned to be executed, and sends those tasks to the nodes.  Once the set is dispatched, it goes to the next set.

There are optimization that can be done at every step, but that’s where the innovation comes in.  Also, the steps are not discrete as they depend on each other.  You *can* and should make them as decoupled as possible, but that’s just a general software development rule of thumb!

Art Sedighi

Next steps

For my first laper, I showed that fairshare algorithm is actually not fair in a number of instances.  Furthermore,  I showed that in the most common case of resource sharing where two users have complementary workloads,  fairshare fails to fairly distribute the resources.
My first paper was a paper exercise (actually a very complex excel exercise).  For my second paper I intend to use the GridSim and the Alea software packages to simulate my hypothesis more concretely. 
I have look at the latest version of Alea and it is very buggy!  Not how software solid be written. Lots of hard-coded values, and inherently not adaptable to a new workload without manual changes to the environment and source code. I have been making source code modifications and I guess I should start a repo that will hold my updates.  
GridSim is more stable,  but it has been around for longer. I will need to make changes to that package as well.
Ad soon as my first paper is accepted,  I will post it here for reference,  and most of this will make more sense.  
Art Sedighi. 

Update on my progress

Hi everyone…

It has been a while since I posted on this site.  I wanted to post an update, and hopefully a more regular checking in will follow.

I have recently been accepted to the TTU (http://www.ttu.edu)  PhD program in the Industrial Engineering department.  I am very excited about the opportunity, and looking forward to continuing my education at TTU IE department.

To that effect, I am taking two classes at TTU towards my PhD:

IE-5311-Principles-Optimization:Instructor:Ismael De Farias;
IE-5345-Reliability Theory. Instructor: Timothy Matis;

I have also been working on  my paper, and I am happy to say that it is finished and has been submitted for publication.  I will be posting the PDF and the full version of the paper once it has been officially accepted for publication.

I am working on my second paper.  And you will see posting in regards to that in the coming weeks/months.

 

Great to be back!

Art Sedighi

Policy as it pertains to high-performance systems

I was recently asked to think about how high performance systems deal with policies?

Two clarifications are required here:

  1. What are high-performance systems in the context of Grid, HPC and scheduling?
  2. What are the policies that a typical high-performance system deals with or in other words, sets?

In the context of high-performance schedulers, a high-performance system is the scenario where we are dealing with a large number of tasks (potentially millions of tasks) that are fairy short in duration, and the total job is only complete once all the tasks have been completed.

What is “short” in our context?  I can easily say that short is in the order of milliseconds or even seconds, but more quantitatively, I will assume that a task is short in duration iff:

  1. Scheduling overhead directly impacts the speedup factor (i.e. the time that it takes to schedule that task cannot be neglected)
  2. The runtime of a give task is significantly shorter (two-orders of magnitude) than the overall runtime of given job.

The bigger question becomes what these policies actually are and why would they be of importance?

The following is a subset of policies that we could be referring to:

  1. Sharing policy
  2. Fair-share policy pertaining to scheduling
  3. (others – TBD)

In a sharing policy, a client can allow some or all if its resources to be shared (given out) to other client[s] that may need them.  This obviously has a risk that the resources are not immediately available when the original owner needs them back.  At the same time, if one waits before lending out resources, there could a high degree of unutilized resources.

 

The fair-share policy is scheduling is probably the most implicitly set policy in shared environments.  The users get their “fair-share” of the available resources based on some preset fair-share policy.  A user may assist or hint the policy with priorities, for example, but generally speaking, the policy is set and agreed to by all the users.

My research focuses on Fair-share policy and how it affects users – and to an extend resources.  Users agree to the fair-share policy with the assumption that what the scheduler does is “fair”.

Furthermore, users interact with the system unbeknownst to how the fair-share scheduling policy is affecting their runtime.  The side effect of a fair-share scheduler is that timing is severely affects the outcome.  Since there is no historical perspective kept to aid the scheduler to better aid the enforcement of such policy, and some users end up keep temporarily starved.

 

Art Sedighi

Hot-Potato pricing and utility algorithm

This is a place holder for my paper

Approach

Game theory can be used to explain behaviour in shared environments such as Grid or Cloud.

One could argue that a Cloud environment is much like non-cooperative game setting where one player is unaware of the other players.  An internal Grid, on the other hand, *may* still be non-cooperative but the other players are known.

Nash Equilibrium requires coordination between and amongst the parties in order to achieve an optimal solution.  The ratio of the solution achieved in NE vs. what really happens in the real-world is the Price of Anarchy.  The goal is reduce PoA for a shared environment.

 

Game Theory Building Blocks

Just a recap today…

A game is composed of players or the interacting parties, rules or “who can do what”, and results or outcomes.  Game theory is build atop of other theories, with each representing the three components of a game:

– decision theory

– representation theory

– solution theory

 

Decision Theory – is an extension of the von Neumann-Morgenstern decision theory that relate to making a decision under uncertainty.  Decision theory relates to game theory in that it provides a way to represent preferences.  Games are all about preferences and as such utility of the chosen preference.

Representation Theory – allows a formal way of representing rules of a give game.  Two representation theories pertain to our discussion: normal form and extensive form.

Normal form: complete plan that considers all contingencies are presented at the start of the game.  It has a static view of the game in how it is played.

Extensive form: it is like a decision tree or a flow chart in that each level of the tree is build only when the node has been reached.  Players have choices and those choices are made in real-time

Solution Theory – it deals with how to assign solutions to games.  It works based on the premise that each player is looking out for itself.  One of the main solution concepts that we will talk about is Nash’s Equilibrium which basically states that no one player can change its strategy and improve its utility.

Game theory puts these three theories together to try and explain a social interaction.  A solution prescribes how rational players should behave and not how they would actually behave in the real-world. 

 

Congestion Games

The concept of Congestion Games is a very interesting one as it pertains to Scheduling.  Rosenthal (1973) coined the term and defined a congestion game to be a scenario where the payoff of a given player depends on the resource it ends up on, and the how busy that resource may be based on how many other players are also on that resource.  Rosenthal, however, focused on having identical machines, and same-size jobs.

A scheduler may schedule a number of tasks on a given machine, if the number of pending tasks is greater than the total number of resources.  As the number of tasks scheduled on a given machine increases – they are all competing for the same resource (CPU, memory, etc) and therefore the utility perceived by a given client could change based on how “congested” a node gets.

The fact of the matter is that most schedulers schedule one task per CPU, so avoid congestion.  I do agree that there could be other processes running on that machine as part of the Operating System (for example, time sync daemon runs on a box every few minutes), but these processes in a dedicated node scenario consume very minimal resources and can be ignored.

In unrelated machines where the infrastructure is heterogeneous, Nir Andelman argues in Strong Price of Anarchy (2006),  that congestion does not take place since the load of a given task is different on different machines.  I strongly disagree with this sentiment.  Based on one of my previous postings called Utility of Master-worker Systems, we must start thinking about the utility of the node itself.  A node (CPU) desires a high utility as well, and that utility is to be idle.  Based on this, unrelated machines cannot be treated any different than related machines.   A system of nodes breaks down to its components of individual nodes with each node desiring a level of utility that matches the utility of all the other nodes.

In short, there is an intrinsic commonality between related and unrelated machines.  This commonaility is the fact that each CPU can achieve the same level of utility by doing the same thing (taking on the same strategy in GT lingo), and that is to finish the task that it was given as soon as possible.

Furthermore, we need to look at scheduling a job on a CPU as being two seperate and sometimes conflciting games:

– Macro-level: a game played by the job submitters trying to minimize their runtime (makespan)

-Micro-level: a game played by the job and the CPU where the CPU wishes to be idle and the job wishes to be compeleted.

 

Reference:

Strong Price of Anarchy N. Andelman, M. Feldman, Y. Mansour, 2006

 

The Matching Pennies Problem

So what is the Matching Pennies Problem anyway (MPP)?

Matching Pennies is a simple game but has very interesting properties that can be applied to many other types of complex games.

There are two players, and each select either Head or Tail.  Here are the rules of the game:

– if the choices differ (one player chooses Head while the other Tail), Player 1 pays Player 2 $1

– if the choices are the same (both players select Head or both select Tail), Player 2 pays Player 1 $1

 

Head Tail
Head 1,-1 -1,1
Tail -1,1 1,-1

This is a Zero-sum game in that one player’s win would mean a loss for the second player.  In another words, the choices are diametrically opposed to one another.  This game is a strictly competitive game and no amount of collaboration will help the situation.

Recap: To be in Nash’s Equilibrium, no player has an action yielding an outcome that he prefers to that of the current action, given that every other player chooses his equilibrium action.  In other words, no player can profitably deviate, given the actions of the other players.  In the MPP, if Player 2 and Player 1 have chosen Head, Player 2 end up paying Player 1.  If now Player 2 chooses to change his choice to Tail, so can Player 1 and the results are the still the same.  You can see what happens from Player 1’s perspective if the users’ selections were not the same to start.

But there is not a single solution that “stands” out in that there is no solution (or strategy) that has a better outcome for one player over the current action.

 

Art Sedighi

 

The Grid Problem

Determining if a problem/game has a Nash Equilibrium is not an easy problem.  In fact, it is harder than the classical NP problems and it is considered to be PPAD.  In this posting, I will look and classify the Grid Problem to be the following:

Grid is a shared infrastructure with a limited number of resources.  The limit could be high, but it must be less than what two players (users of the Grid) are able to consume.  We want to look at the Grid Problem and see if there exists a configuration where all the users/players are satisfied.  In short, we want to see if there exists a Nash’s Equilibrium point for the Grid Problem. 

Lets take a step back, and look at the classes of games that exist.  I want to do this to level-set and clarify my position about where various infrastructure types will fit into the different classes of games.

We have the following:

  1. Strategic Games (a.k.a Games in Normal Form)
  2. Extensive Games with perfect information
  3. Extensive Games without perfect information
  4. Coalitional Games

Strategic games are rather interesting in that both players (or N-players) make the decision in advance, and stick to that decision for the duration of the games.  Extensive games, however, players can modify their strategy between moves.

Lets look at a Grid infrastructure:

A. Resource are limited
B. Jobs are submitted to the Queue to be processed
C. Queues are most likely FIFO
D. A Player wants to get results asap without regards to the other players

Based on the above properties, we can deduce the following:

  • Property A makes this game a Zero-sum game.
  • Property B makes this game an imperfect information game
  • Properties C + D makes this game a non cooperative strictly competitive game

In a Strategic game, the player chooses his plan of action once and for all and independently of the other players.  Each plan is made based on a set of preferences, but those preferences *must* be selfish as we are dealing with a Zero-sum game.

If this problem can be reduced to the Matching Pennies problem, we can deduce that the Grid Problem does not have a Nash Equilibrium.

 

Art Sedighi

 

Protected: Draft – Paper

This content is password protected. To view it please enter your password below:

Not Fair

We can assume, as mentioned before, that the users of a Grid are playing a zero-sum game against each other.  In that one’s gain is another one’s loss.  Or more explicitly, if one user gets more CPU’s, the other[s] get less as a result.

This is fairly easy to prove as we have a set of CPU’s that does not change.  In a zero-sum game, there always exists a Nash’s Equilibrium.  Finding Nash’s Equilibrium is not easy; in-fact it falls under a calls of problems call PPAD, but we know that one does exist.

Two comments can therefore be made:

1. If we assume that Nash’s Equilibrium is in-fact the standard fairness point, then if the scheduler deviates from NE, it is not a fairshare scheduler.  Proving that fairshare is in-fact, not fair.

2. If a user by changing its strategy is able to increase its utility (i.e. get a higher portion of the available resources), then the system is not in Nash’s Equilibrium and the scheduler is not dividing up resources in a fair manner.

and 2.1. The user is inclined to change its strategy so it can get a larger portion of the system.  This is where we see “Price of Anarchy” developing.

Assumption:

One assumption we have made throughout is that Nash’s Equilibrium point presents the only fair point at which point all participants are treated fairly.

 

Art Sedighi

 

 

Zero-sum game

It is conceivable to think of a Grid Scheduler as the mediator to a zero-sum game.  The number of resources do not change — not taking into account the hype that is cloud these days with elastic computing.  If the number of resources available to a scheduler and in turn the clients/players of the system is constant, the number of CPU’s that one client gets assigned directly affects the number of CPU’s that has been “taken” away from the pool of resources available to the second client.

As the total number of resources does not change, and one players action based on fairshare scheduling affects the number of resources that it gets assigned, one can conclude:

Based on client’s task submission strategy, a client realizes a utility that is directly a result of the number of resources it received – or got assigned to by the scheduler.   

Fairness in scheduling

What does it mean to be fair when scheduling tasks across a Grid?

Depending on the perspective of the affected entity, fairness could mean different things.  For  a heavy user of the system, “fair” could mean:

“I need (should read “neeeed”) more, so it is fair for me to get more”

From a casual user’s perspective:

“As long as I get to do my work, it is fair”

From a light-user:

“I don’t use the system that often, so when I do, I should have higher priority”

There can be cases made for each of these scenarios.  The first scenario, the heavy user, is the one which more schedulers tend to please.  It is an implied favouritism in that in order to drain the pending queues the fastest, the scheduler schedules more tasks from the heavy user as it had a higher percentage of pending tasks.

What is fairshare?  how can schedulers pony up resources in a shared manner?

 

Art Sedighi

 

 

Games we play

In the previous post, we wrote about the utility of a Client vs. the Worker (CPU).  Let us now take that one more step and see what the utility of these two participants be throughout the course of a given job. 

Simple tertiary (-1,0,1) can be used to depict all the possibilities – a truth-table, but with three states. 

Client CPU Comment
0 0  This state is a very special state — which we will get to later
0 1  This is a state we want to stay away from. What it says is that the work is submitted, but it has not been “delivered” to the CPU yet for processing.  This state is caused by delay, and we will assume that we do not want it to exist.
0 -1  This state is valid and one of our primary states.  Client has submitted a job, and the CPU is working on it.
1 0  Not a valid state
1 1  The final and most desired state – the finish line.
1 -1  Not a valid state
-1 0  Not a valid state
-1 1  This state basically starts the process.  It says that the client has some work to be completed, and the CPU is idle.
-1 -1  Not a valid state

What we need to do at this point to draw these states on a two-dimensional plane, depicting various states of the system. 

 

 

We will cover the dash-line in a later posting, but what I wanted to focus on here is the area between the two solid-lines.  The “perfect” scenario is when we move from (-1,1) –> (0,0) –> (1,1).  This line represents the maximum utility that these two players can achieve during the game.  The goal is to minimize the area between the two lines – this will move this system to an equilibrium point, better known as Nash’s Equilibrium.

 

Art Sedighi

Utility of master-worker systems

For a small — very small — master-worker system, there are two players: one master and one worker.  The master is the user or the client that requires the worker to get something done, and the worker is the actual processor that does the work.

Let’s break each of these into their various state:

Mater:

1. Work pending

2. Work submitted for completion

3. Work completed and results returned

Worker:

1. Working

2. Work completed

3. Idle and results returned

Based on our earlier discussion around utility, we can further assign an arbitrary utility to each of these states.  We can then model the utility as a function of workload for the two participants.

 you can see that each of the states have been assigned a utility.  When the processor is working, it has the lowest utility of -1, and when it is idle, it has a highest utility of +1.  For a client, when there is work pending, the client is at its lowest utility, and when all the work has been completed, it has the highest utility.

There is an intrinsic time built into this model.  Imagine, if you will, that a given client goes from its lowest utility to its highest utility as more work is submitted and they completed.  This obviously is time dependant.

The same is true for the worker; a given CPU is at its lowest when it is working but as it completes the work given to it, it will move towards a higher utility.

 

Art Sedighi

From the worker (CPU) perspective

In a distributed/Grid system, the worker is the “end” processor that  does the actual work.  it is the CPU that calculates the average of two numbers; it is the CPU that executes the business logic, etc…

I call this processor the “end” processor, because there could be many intermediate nodes/processors that route the work to the end node. In a graph-based architecture, the leaf node is the node that does the actual work.  All the other nodes route the work to where it belongs.  In a Grid/HPC environment, the scheduler sits in the middle and routes the jobs to the appropriate end node.  We will ignore this middle portion for the time being and focus on the end nodes.

Anyhow, this end-node is the node that does the work. Its tendency, however, is to sit idle and not do anything.  in other words, a processor wants to be idle.  From an entropy perspective, “order” is when a processor is executing proper code, and “disorder” is when the processor is idle.

Do not focus on the fact that “we” as users want the processor to be busy all the time. The tendency of the processor is to sit idle.  The processor aims to finish the work as fast as possible and sit idle.  Another way of looking at this is that a processor upon receiving a jobs is in an ordered-place, and its tendency is towards disorder.  When a processor is idle, it is that state.

We as users, however, want the processor to be utilized 100% of the time.  That’s what we want.  We will get to this conflict of interest in later postings.

From a macro-level, it all makes perfect sense now…  Faster clock speeds, newer technology, etc, allow the processor to reach its preferred state faster:

Crossing the finish line is the only goal that both the master and the worker have in common

Art Sedighi

Perfect Information

In a “perfect game”, there is perfect information.  What this means is that all the players are aware of the current state of the game and are fully aware of their options.  Chess is an example of such game.

There are very few real-life scenarios that follow this pattern.  More commonly, not all the information nor the state of the system is available to all the players/users.

Under the most basic scenario – known as the Normal Game – there are ‘n’ players, each of which have perfect information and each player is aware of the pay-off  function and striving to win.  The pay-off function, however, depends on how the other participants play the game and their strategies.

 

Back to utility

Wikipedia defines utility as:

utility is a measure of satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service” (REF: http://en.wikipedia.org/wiki/Utility)

(Kuhn 1953) further explains that for each player, there is a linear utility function over all the possible outcomes of a given game.  So if a game is depicted using a tree, and the end leaf node is one of the possible outcomes of that game, there exists a utility function that defines these outcomes. It is important to metion here that the utility function defines and explains all the possible outcomes not just one.

This will be very useful to our research as we aim to maximize a utility function – which itself is a function of currnet state of the system (functional analysis).

 

game theory vs. graph theory in scheduling

Most scheduling systems, resource managers, HPC schedulers, etc, use some sort of fair share algorithm where the portion of share resource being scheduled (divided up) depends on a very simple ratio analysis of “the person who ‘deserves’ more, gets more”.  The amount that one deserves usually depends on the number of tasks pending to be completed.  Essentially, the scheduler takes a snapshot of the queue sizes, and makes a determination that in order to drain the queues faster, the large queue must get a larger portion of the available resources.

Without the loss of generality, assume that we have two users (A and B).  ‘A’ has a queue size of 10 and ‘B’ has a Queue size of 90.  ‘A’ ends up with 10% of the resources and ‘B’ ends up with 90% of the resources.  If you have only 8 machines available at a time, there is a good chance that ‘A’ is starved.

Scheduling systems follow ‘a’ graph algorithm to make a determination.  Whether that’s implicit or explicit, a graph algorithm is somehow used.  Graphs are essentially decision trees, and based on the number of levels and/or the fan-out, they could be either complicated or a simple binary decision tree of “if not this way, then it must be the other way”.  That is why a two-node system scheduling system is deterministic, and anything above a two-node system falls under the nondeterministic realm (exception is a 3-node system).

Graph algorithms do not consider history — how did i get here?  That is the main reason why most fair-share algorithms are not fair.

Games depend solely on the history of events or strategies.  There is an implicit history that is built in to each strategy that allows one to determine all the previous steps.  As such, one’s current state is not the only state required to make a decision about the next state.

As opposed to using a fair-share algorithm, if schedulers treated each transaction as a game, and each event a strategy of that game, schedulers would actually be fair. 

Art Sedighi