models for quality of service (qos) routing and...
TRANSCRIPT
Venkatesh SaranganComputer Science Department
Oklahoma State [email protected]
Donna Ghosh, Raj AcharyaDept. of Comp. Sci. & Eng.
Pennsylvania State Universitydghosh,[email protected]
Models for Quality of Service (QoS) routing and Performance analysis in a multi-class
Internet
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Outline
n Introduction to QoS routingn Work done on inter-domain QoS routingn Work done on analyzing multi-class networksn Other on-going projects
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QoS Routing
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n Current IP routing follows the shortest path in terms of hops
Voice over IP from Source to Receiver
n 7 bw units required
n Current IP routing n Path: Src � C �Rcvn Poor quality !
n Better path exists: Src �A �B �Rcv
Voice over IP from Source to Receiver
n 7 bw units required
n Current IP routing n Path: Src � C �Rcvn Poor quality !
n Better path exists: Src �A �B �Rcv
n Need mechanisms that route a connection based on its resource requirements, rather than just the hop count
n Need QoS routing
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QoS Routing (contd.)
n Basic goal is to find a feasible path for a given connectionn Additionally, can optimize network resource utilization
n Routing involves two basic tasks:n Collecting network state information and keeping it up-to-
daten Using this information to compute a feasible path
n Route computation depends on how much state information is collected and where it is storedn QoS routing strategies - Source, Distributed, and
Hierarchical
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Hierarchical QoS Routing
n Source and distributed schemes can’t scale for large networks n Hence ‘hierarchical’ schemes
n Nodes are clustered into groups recursively creating a multi-level hierarchyn A node maintains an aggregated state information about
other groups and detailed information about its own group
n Advantages: n Can scale to large networks when compared with the
other two schemes
n Disadvantages:n How to aggregate resources concisely and accurately ?
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Aggregation for Hierarchical QoS routing
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n Aggregation involvesn Summarizing the domain connectivityn Summarizing the resource availability
A B
C
AB
C
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Resource (Bandwidth) Aggregation
n Resource aggregate is the bandwidth in the best path between a border router pair
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Existing aggregates �� ��
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More accurate aggregate
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n Does not consider a domain’s finite capacity to route traffic
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How to estimate the routing capacity?
n Maximum volume of traffic a domain can handle from a neighbor
n Possible estimate: the installed capacityn Indeed, the maximum that a domain can handlen May over-estimate bandwidth, if more than one neighbor
n Need a parameter thatn Does not over-estimate/under-estimate bandwidthn Varies with network traffic conditions
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An observation
n ISP 2’s routing capacity w. r. to ISP 1 is the sum of:n ISP 1’s traffic flowing thru 2n Additional traffic that ISP 1 can
send to 2n depends on free BW available in
ISP 2
ISP 1 ISP 2
ISP 3
ISP 4
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n C12 = T12 + �C12
n T12 is maintained by ISP 1’s router connecting to 2
n �C12 is advertised by ISP 2 to 1
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Estimating �C12
ISP 1 ISP 2
ISP 3
ISP 4
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ISP 2(flow graph)
C2i: capacity of ISP i w. r. to ISP 2
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How to use the capacity as an aggregate ?
n ISP 1 forwards a request to ISP 2, only ifn T12 + b <= C12
n b < widest path BW
n Routing capacity is not used alonen It is not clear if there is any single path in ISP 2 with a width of
at least b
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Routing capacity in a probabilistic setting
n Bandwidth available in a link varies with timen Can do better by modeling these fluctuations
n Model link bandwidths as random variablesn Ping the links periodically and use the time histories as the
pmfs, orn Construct the pmfs through some knowledge of the link state
updates
n Goal:n To estimate the distribution of a domain’s routing capacity
n Solve for max-flow in a deterministic graph with probabilistic edge weights
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Max-flow with probabilistic edge weights
We approximate the min of a joint distribution by t he random variable with the lowest mean .
n pmf of max-flow = pmf of min cut (Max-flow, Min-cut theorem)n Difficult problem, exponential time in # of edges in graph
n Existing approximation algorithms have restrictive assumptions n i.i.d. edge weights
n Proposed heuristic:n Create graph G’ with deterministic edge weights – replace the
random weights with their meann Find the min cut in G’ n Find the distribution of the above cut in Gn Distribution of max-flow in G � distribution of min cut in G’
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Goodness measures
n Bandwidth admission ratio (BAR)n Ratio of BW admitted to BW requested
n Bandwidth Over-estimation Ratio (BOR)n Ratio of BW dropped inside a domain to BW forwarded
n Bandwidth Under-estimation Ratio (BUR)n Ratio of non-forwarded BW that could have been successful to
BW forwarded
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Methods Compared
n Det-CAR (Capacity aware routing)n Routing capacity + widest path bandwidth in a deterministic setting
n Det-nCAR (Non capacity aware routing)n Widest path bandwidth alone in a deterministic setting
n Prob-CARn Routing capacity + widest path bandwidth in a probabilistic setting
n Prob-nCARn Widest path bandwidth alone in a probabilistic setting
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Sample results: w. r. to routing updates
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0 50 100 150 200 250 300 350 400 450 500 550
Ba
nd
wid
th O
ve
r-e
stim
atio
n R
atio
(in
%)
Inter-domain update interval (in sec)
Prob-CARProb-nCAR
Det-CARDet-nCAR
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0 50 100 150 200 250 300 350 400 450 500 550
Ba
nd
wid
th U
nd
er-
estim
atio
n R
atio
(in
%)
Inter-domain update interval (in sec)
Prob-CARProb-nCAR
Det-CARDet-nCAR
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Sample results: w. r. to routing updates
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0 50 100 150 200 250 300 350 400 450 500 550
Ba
nd
wid
th A
dm
issi
on
Ra
tio (
in %
)
Inter-domain update interval (in sec)
Prob-CARProb-nCAR
Det-CARDet-nCAR
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0 50 100 150 200 250 300 350 400 450 500 550P
erc
en
tag
e im
pro
vem
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t in
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Inter-domain update interval (in sec)
Prob-CAR over Prob-nCARDet-CAR over Det-nCAR
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Summary
n Using routing capacity as an aggregate can lead to improved routing performancen Reduces over-estimation & increases under-estimation
n Current workn Developing schemes for estimating routing capacity when
cross-traffic pattern is known
n Aggregation schemes for multicast requests
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Models for Performance analysis
n Connection oriented scenario such as multi-class MPLS networks
n To answer questions such as “How many LSPs can be supported in a network with capacity ‘C’ BW units ?”
n Obtain parameters that describe the network’s steady state behavior
n Utilization, LSP blocking probability, Occupancy distribution…
n Useful in design/planning, network optimization etc.
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Multi-class MPLS Networks
n “call”: request for a bandwidth guaranteed LSPn C ≡ Network capacity assigned for calls between I and II
n Calls of various classes share this Cn Chosen model –
n Stochastic Knapsack
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Stochastic Knapsack
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n Class i arrivals are independent of other classes
n Class i parameters –n λi : arrival raten 1/µi : mean residence timen bi : resource requirement
of class i arrivals
n Admission Policy – Complete Sharing (FCFS)
n Multi-class loss system –blocked arrivals do not wait
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Stochastic Knapsack with non-Poisson arrivals
n Internet trace studies show bursty (LRD) call arrivalsn Hence, the need to solve a stochastic knapsack with bursty
arrivalsn As the first step, we obtain an heuristic approximation for
a knapsack with non-Poisson arrivals
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Our Approach
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Our Approach
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Concepts
n Reversible Processn Reverse time � Statistical properties remain SAME
n Joint process of independent reversible processes is also reversible
Y(t): Reversible Markov process, state space S, equilibrium distribution ππππ(j), j∈∈∈∈S
X(t): Truncated Y(t), state space A ⊂⊂⊂⊂ S
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Proposed solution
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Schemes compared
n Actual system behaviorn Studied through simulations
n Poisson modeln Assume bursty arrival process ∼ Poisson with same mean
n Heuristic approachn Find the solution assuming that the per class queuing
processes with bursty arrivals are reversible
n Proposed modeln Approach discussed so far
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Performance measures
n L1 Norm
n Average number of calls
n Average utilization
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Performance under high burstiness
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Class-3 Slope parameter
PoissonHeuristic
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Performance under high burstiness
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Class-3 Slope parameter
PoissonHeuristic
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Summary
n A step towards solving for stochastic knapsack with bursty call arrivalsn Better than the naïve Poisson approximation
n Need to in-corporate characteristics specific for bursty arrivals
n Need to generalize for non-exponential call holding timesn Need to obtain call blocking probabilities
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Other on-going projects…
n Ad-hoc networksn Exploring hierarchical QoS routing for MANETs
n Sensor networksn Energy conserving MAC protocols that co-ordinate their on-
off schedules depending on their neighbor’s schedulesn Topology control for energy-efficient, delay-constrained data
transfer
n IP packet trace-backn Solutions for tracing back packets over long paths
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Thank You!
Questions…?