9 research outputs found
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)
Stability of Service under Time-of-Use Pricing
We consider "time-of-use" pricing as a technique for matching supply and
demand of temporal resources with the goal of maximizing social welfare.
Relevant examples include energy, computing resources on a cloud computing
platform, and charging stations for electric vehicles, among many others. A
client/job in this setting has a window of time during which he needs service,
and a particular value for obtaining it. We assume a stochastic model for
demand, where each job materializes with some probability via an independent
Bernoulli trial. Given a per-time-unit pricing of resources, any realized job
will first try to get served by the cheapest available resource in its window
and, failing that, will try to find service at the next cheapest available
resource, and so on. Thus, the natural stochastic fluctuations in demand have
the potential to lead to cascading overload events. Our main result shows that
setting prices so as to optimally handle the {\em expected} demand works well:
with high probability, when the actual demand is instantiated, the system is
stable and the expected value of the jobs served is very close to that of the
optimal offline algorithm.Comment: To appear in STOC'1
Pricing for Online Resource Allocation: Intervals and Paths
We present pricing mechanisms for several online resource allocation problems
which obtain tight or nearly tight approximations to social welfare. In our
settings, buyers arrive online and purchase bundles of items; buyers' values
for the bundles are drawn from known distributions. This problem is closely
related to the so-called prophet-inequality of Krengel and Sucheston and its
extensions in recent literature. Motivated by applications to cloud economics,
we consider two kinds of buyer preferences. In the first, items correspond to
different units of time at which a resource is available; the items are
arranged in a total order and buyers desire intervals of items. The second
corresponds to bandwidth allocation over a tree network; the items are edges in
the network and buyers desire paths.
Because buyers' preferences have complementarities in the settings we
consider, recent constant-factor approximations via item prices do not apply,
and indeed strong negative results are known. We develop static, anonymous
bundle pricing mechanisms.
For the interval preferences setting, we show that static, anonymous bundle
pricings achieve a sublogarithmic competitive ratio, which is optimal (within
constant factors) over the class of all online allocation algorithms, truthful
or not. For the path preferences setting, we obtain a nearly-tight logarithmic
competitive ratio. Both of these results exhibit an exponential improvement
over item pricings for these settings. Our results extend to settings where the
seller has multiple copies of each item, with the competitive ratio decreasing
linearly with supply. Such a gradual tradeoff between supply and the
competitive ratio for welfare was previously known only for the single item
prophet inequality
Prompt mechanisms for online auctions
We study the following online problem: at each time unit, one of m identical items is offered for sale. Bidders arrive and depart dynamically, and each bidder is interested in winning one item between his arrival and departure. Our goal is to design truthful mechanisms that maximize the welfare, the sum of the utilities of winning bidders. We first consider this problem under the assumption that the private information for each bidder is his value for getting an item. In this model constant-competitive mechanisms are known, but we observe that these mechanisms suffer from the following disadvantage: a bidder might learn his payment only when he departs. We argue that these mechanism are essentially unusable, because they impose several seemingly undesirable requirements on any implementation of the mechanisms. To crystalize these issues, we define the notions of prompt and tardy mechanisms. We present two prompt truthful mechanisms – one deterministic and the other randomized, that guarantee a constant competitive ratio. We also prove that our deterministic mechanism is optimal for this setting. We then study a model in which both the value and the departure time are private information. While in the deterministic setting only a trivial competitive ratio can be guaranteed, we use ran-1 domization to obtain a prompt truthful Θ( log m)-competitive mechanism. Finally, we show that no in this model. truthful randomized mechanism can achieve a ratio better than 1