1,117 research outputs found
Non-clairvoyant Scheduling Games
In a scheduling game, each player owns a job and chooses a machine to execute
it. While the social cost is the maximal load over all machines (makespan), the
cost (disutility) of each player is the completion time of its own job. In the
game, players may follow selfish strategies to optimize their cost and
therefore their behaviors do not necessarily lead the game to an equilibrium.
Even in the case there is an equilibrium, its makespan might be much larger
than the social optimum, and this inefficiency is measured by the price of
anarchy -- the worst ratio between the makespan of an equilibrium and the
optimum. Coordination mechanisms aim to reduce the price of anarchy by
designing scheduling policies that specify how jobs assigned to a same machine
are to be scheduled. Typically these policies define the schedule according to
the processing times as announced by the jobs. One could wonder if there are
policies that do not require this knowledge, and still provide a good price of
anarchy. This would make the processing times be private information and avoid
the problem of truthfulness. In this paper we study these so-called
non-clairvoyant policies. In particular, we study the RANDOM policy that
schedules the jobs in a random order without preemption, and the EQUI policy
that schedules the jobs in parallel using time-multiplexing, assigning each job
an equal fraction of CPU time
Energy-Efficient Multiprocessor Scheduling for Flow Time and Makespan
We consider energy-efficient scheduling on multiprocessors, where the speed
of each processor can be individually scaled, and a processor consumes power
when running at speed , for . A scheduling algorithm
needs to decide at any time both processor allocations and processor speeds for
a set of parallel jobs with time-varying parallelism. The objective is to
minimize the sum of the total energy consumption and certain performance
metric, which in this paper includes total flow time and makespan. For both
objectives, we present instantaneous parallelism clairvoyant (IP-clairvoyant)
algorithms that are aware of the instantaneous parallelism of the jobs at any
time but not their future characteristics, such as remaining parallelism and
work. For total flow time plus energy, we present an -competitive
algorithm, which significantly improves upon the best known non-clairvoyant
algorithm and is the first constant competitive result on multiprocessor speed
scaling for parallel jobs. In the case of makespan plus energy, which is
considered for the first time in the literature, we present an
-competitive algorithm, where is the total number of
processors. We show that this algorithm is asymptotically optimal by providing
a matching lower bound. In addition, we also study non-clairvoyant scheduling
for total flow time plus energy, and present an algorithm that achieves -competitive for jobs with arbitrary release time and
-competitive for jobs with identical release time. Finally,
we prove an lower bound on the competitive ratio of
any non-clairvoyant algorithm, matching the upper bound of our algorithm for
jobs with identical release time
Non-Clairvoyant Precedence Constrained Scheduling
We consider the online problem of scheduling jobs on identical machines, where jobs have precedence constraints. We are interested in the demanding setting where the jobs sizes are not known up-front, but are revealed only upon completion (the non-clairvoyant setting). Such precedence-constrained scheduling problems routinely arise in map-reduce and large-scale optimization. For minimizing the total weighted completion time, we give a constant-competitive algorithm. And for total weighted flow-time, we give an O(1/epsilon^2)-competitive algorithm under (1+epsilon)-speed augmentation and a natural "no-surprises" assumption on release dates of jobs (which we show is necessary in this context).
Our algorithm proceeds by assigning virtual rates to all waiting jobs, including the ones which are dependent on other uncompleted jobs. We then use these virtual rates to decide on the actual rates of minimal jobs (i.e., jobs which do not have dependencies and hence are eligible to run). Interestingly, the virtual rates are obtained by allocating time in a fair manner, using a Eisenberg-Gale-type convex program (which we can solve optimally using a primal-dual scheme). The optimality condition of this convex program allows us to show dual-fitting proofs more easily, without having to guess and hand-craft the duals. This idea of using fair virtual rates may have broader applicability in scheduling problems
Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games
We study coordination mechanisms for Scheduling Games (with unrelated
machines). In these games, each job represents a player, who needs to choose a
machine for its execution, and intends to complete earliest possible. Our goal
is to design scheduling policies that always admit a pure Nash equilibrium and
guarantee a small price of anarchy for the l_k-norm social cost --- the
objective balances overall quality of service and fairness. We consider
policies with different amount of knowledge about jobs: non-clairvoyant,
strongly-local and local. The analysis relies on the smooth argument together
with adequate inequalities, called smooth inequalities. With this unified
framework, we are able to prove the following results.
First, we study the inefficiency in l_k-norm social costs of a strongly-local
policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy
of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all
deterministic, non-preemptive, strongly-local and non-waiting policies
(non-waiting policies produce schedules without idle times). These results
ensure that SPT is close to optimal with respect to the class of l_k-norm
social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price
of anarchy O(2^k).
Second, we consider the makespan (l_infty-norm) social cost by making
connection within the l_k-norm functions. We revisit some local policies and
provide simpler, unified proofs from the framework's point of view. With the
highlight of the approach, we derive a local policy Balance. This policy
guarantees a price of anarchy of O(log m), which makes it the currently best
known policy among the anonymous local policies that always admit a pure Nash
equilibrium.Comment: 25 pages, 1 figur
Non-Clairvoyant Batch Sets Scheduling: Fairness is Fair enough
Scheduling questions arise naturally in many different areas among which
operating system design, compiling,... In real life systems, the
characteristics of the jobs (such as release time and processing time) are
usually unknown and unpredictable beforehand. The system is typically unaware
of the remaining work in each job or of the ability of the job to take
advantage of more resources. Following these observations, we adopt the job
model by Edmonds et al (2000, 2003) in which the jobs go through a sequence of
different phases. Each phase consists of a certain quantity of work and a
speed-up function that models how it takes advantage of the number of
processors it receives. We consider the non-clairvoyant online setting where a
collection of jobs arrives at time 0. We consider the metrics setflowtime
introduced by Robert et al (2007). The goal is to minimize the sum of the
completion time of the sets, where a set is completed when all of its jobs are
done. If the input consists of a single set of jobs, this is simply the
makespan of the jobs; and if the input consists of a collection of singleton
sets, it is simply the flowtime of the jobs. We show that the non-clairvoyant
strategy EQUIoEQUI that evenly splits the available processors among the still
unserved sets and then evenly splits these processors among the still
uncompleted jobs of each unserved set, achieves a competitive ratio
(2+\sqrt3+o(1))\frac{ln n}{lnln n} for the setflowtime minimization and that
this is asymptotically optimal (up to a constant factor), where n is the size
of the largest set. For makespan minimization, we show that the non-clairvoyant
strategy EQUI achieves a competitive ratio of (1+o(1))\frac{ln n}{lnln n},
which is again asymptotically optimal.Comment: 12 pages, 1 figur
Speed-Oblivious Online Scheduling: Knowing (Precise) Speeds is not Necessary
We consider online scheduling on unrelated (heterogeneous) machines in a
speed-oblivious setting, where an algorithm is unaware of the exact
job-dependent processing speeds. We show strong impossibility results for
clairvoyant and non-clairvoyant algorithms and overcome them in models inspired
by practical settings: (i) we provide competitive learning-augmented
algorithms, assuming that (possibly erroneous) predictions on the speeds are
given, and (ii) we provide competitive algorithms for the speed-ordered model,
where a single global order of machines according to their unknown
job-dependent speeds is known. We prove strong theoretical guarantees and
evaluate our findings on a representative heterogeneous multi-core processor.
These seem to be the first empirical results for scheduling algorithms with
predictions that are evaluated in a non-synthetic hardware environment.Comment: To appear at ICML 202
Schedulability Analysis for Adaptive Mixed Criticality Systems with Arbitrary Deadlines and Semi-Clairvoyance
This paper provides analysis of the Adaptive Mixed Criticality (AMC) scheduling scheme for mixed-criticality systems that include tasks with arbitrary deadlines and semi-clairvoyant behavior. An arbitrary deadline task is one that can have a deadline that may be greater than its period. A semi-clairvoyant task is one that upon arrival of each job, reveals which of its two WCET parameters will be respected. This enables an earlier switch to be made from the normal mode of operation to the abnormal mode. The previously published schedulability test AMC-max is modified to cater for both of these extensions. Evaluation shows that there is a significant improvement in schedulability for semi-clairvoyant tasks over non-clairvoyant, and for arbitrary-deadline tasks over considering those deadlines as being constrained by the task’s period
Truth and Regret in Online Scheduling
We consider a scheduling problem where a cloud service provider has multiple
units of a resource available over time. Selfish clients submit jobs, each with
an arrival time, deadline, length, and value. The service provider's goal is to
implement a truthful online mechanism for scheduling jobs so as to maximize the
social welfare of the schedule. Recent work shows that under a stochastic
assumption on job arrivals, there is a single-parameter family of mechanisms
that achieves near-optimal social welfare. We show that given any such family
of near-optimal online mechanisms, there exists an online mechanism that in the
worst case performs nearly as well as the best of the given mechanisms. Our
mechanism is truthful whenever the mechanisms in the given family are truthful
and prompt, and achieves optimal (within constant factors) regret.
We model the problem of competing against a family of online scheduling
mechanisms as one of learning from expert advice. A primary challenge is that
any scheduling decisions we make affect not only the payoff at the current
step, but also the resource availability and payoffs in future steps.
Furthermore, switching from one algorithm (a.k.a. expert) to another in an
online fashion is challenging both because it requires synchronization with the
state of the latter algorithm as well as because it affects the incentive
structure of the algorithms. We further show how to adapt our algorithm to a
non-clairvoyant setting where job lengths are unknown until jobs are run to
completion. Once again, in this setting, we obtain truthfulness along with
asymptotically optimal regret (within poly-logarithmic factors)
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