Lecture 4
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
Time interval is divided into slots, 0,1,2,…..
Every link l has a vector of bandwidth availabilities: [bl[0],
bl[1], bl[2],……]
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,
t+1,…t+u, 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.
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, t+u]
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)
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)
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, t+u].
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,
w+u].
3)Stop if there exists one such path
4)If not, ww + 1
5)Go to (2) if wT-u
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))
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
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
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
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
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)