Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pathwise Performance of Debt Based Policies for Wireless Networks with
  Hard Delay Constraints   Hou et al have introduced a framework to serve clients over wireless channels
when there are hard deadline constraints along with a minimum delivery ratio
for each client's flow. Policies based on "debt," called maximum debt first
policies (MDF) were introduced, and shown to be throughput optimal. By
"throughput optimality" it is meant that if there exists a policy that fulfils
a set of clients with a given vector of delivery ratios and a vector of channel
reliabilities, then the MDF policy will also fulfill them. The debt of a user
is the difference between the number of packets that should have been delivered
so as to meet the delivery ratio and the number of packets that have been
delivered for that client. The maximum debt first (MDF) prioritizes the clients
in decreasing order of debts at the beginning of every period. Note that a
throughput optimal policy only guarantees that \begin{small} $\liminf_{T \to
\infty} \frac{1}{T}\sum_{t=1}^{T} \mathbbm{1}\{\{client $n$'s packet is
delivered in frame $t$} \} \geq q_{i}$ \end{small}, where the right hand side
is the required delivery ratio for client $i$. Thus, it only guarantees that
the debts of each user are $o(T)$, and can be otherwise arbitrarily large. This
raises the interesting question about what is the growth rate of the debts
under the MDF policy. We show the optimality of MDF policy in the case when the
channel reliabilities of all users are same, and obtain performance bounds for
the general case. For the performance bound we obtain the almost sure bounds on
$\limsup_{t\to\infty}\frac{d_{i}(t)}{\phi(t)}$ for all $i$, where $\phi(t) =
\sqrt{2t\log\log t}$.

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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph