Network with Reservations

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Lecture 4
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Network with Reservations
Connections can also make reservations apriori
for its duration
Certain bandwidths will be available in certain
time ranges
Time is a dimension
Networks with Advanced Reservations The Routing
Perspective R. Guerin and A. Orda
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Time interval is divided into slots, 0,1,2,..
Every link l has a vector of bandwidth
availabilities bl0, bl1, bl2,
Given a source node s, destination node v,
bandwidth requirement B, starting time t,
duration u, find a path which supports this
connection
If a link does not have bandwidth B in any slot
in t, t1,tu, remove the link Find a path
between the source and the destination in the
remaining network
Complexity O(V E Eu) or O(Eu) if the graph
is fully connected.
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Given a source node s, destination node v,
bandwidth requirement B, starting time t, find a
path which supports this connection for the
maximum duration in the interval t, tu
For every link l in the network, find the maximum
value vl such that the link has B bandwidth
available in every slot in t, t vl and
vl?u Duration of a path is the minimum value of
vl in the links in the path Find a path between
the source and the destination of maximum
duration.
First see whether there is a path of duration
u (Depth first Search/Breadth first search)
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If there is, stop Else, try with u/2. If there is
such a path, try with 3u/2 If not, try with u/4 ,
.. Every time narrow the interval
Binary search
O(Eu Elog u) or O(Eu)
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Given a source node s, destination node v,
bandwidth requirement B, duration u, find a path
which finishes the connection the fastest in
interval 0, T.
For every path, there is an earliest time t in
interval 0, T, s.t. the path has B bandwidth in
all slots in t, tu.
Find the path with the earliest value of this
start time.
1)Start with w 0 2)Find if there exists a path
which supports the connection in w, wu. 3)Stop
if there exists one such path 4)If not, w?w
1 5)Go to (2) if w?T-u
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Complexity O(Eu(T-u))
A faster algorithm of complexity O(E(T u)) is
in the paper. The idea is to scan every slot in
every link a constant number of times. So the
overall complexity is O(E(T u))
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A connection may need to transmit a fixed amount
of data, but it can use different bandwidths in
different slots. Find the path which completes
the task in the minimum duration in interval 0,
T.
A connection needs to transmit B amount of data.
Say it is routed along path p. Let this path
provide bi bandwidth in slot i . The task
completes itself in p slots if b0 .. bp ? B
Computing the minimum duration is an NP-hard
problem. Heuristics
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Overall Delay constraints
Propagation delay (?l in link l) Queueing delay
(k/r in any link of bandwidth r)
A connection has a duration, a starting time, a
minimum bandwidth requirement in all links in the
connection, and
An additional requirement that the overall delay
be less than a constant D
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If every link of a path guarantees a bandwidth of
r and there are n(p) links in the path, then
depending on the traffic characteristics, the
total delay in the path is at most ??l
(?n(p)?)/r
The problem is to find a path which guarantees
the minimum bandwidth in every slot of the
duration, in every link, and has propagation
delays and bandwidth r in every link in the path
s.t. ??l (?n(p)?)/r
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Uncertainty in Information
R. Guerin and A. Orda. QoS-based Routing in
Networks with Inaccurate Information Theory and
Algorithms.'' IEEE/ACM Transaction on
Networking, Vol. 7, No. 3, June 1999, pp.
350-364.
Propagation delay information may not be
precisely known.
Available bandwidth information may not be known
correctly
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A probability distribution may be known With
certain probability, propagation delay is
this With certain probability, available
bandwidth is this.
Find a path which assures delay less than D with
certain probability
Most of these problems are intractable (NP-hard)