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```									An Extended ME Methodology
for General QNMs and its
Application to ATM Switch
Architectures
Demetres Kouvatsos
Presented by : Ravindra Vaishampayan
QNM
• Queuing Network Model. A complex
network of Queues and Servers
• Useful for analysis of computer,
communication and manufacturing systems
• We are interested in the QNM which
models an ATM switch
QNM modelling ATM Switch
•   Finite Capacity Queues
•   Multiple classes
•   Time and Space priority
•   Non-Exponential interarrival and service
time distributions.
Time and Space Priority
• Time priority refers to the fact that some
services can tolerate lower delay that others
e.g. voice Vs data
• Space priority controls allocation of buffer
space to an arriving cell
• A sequence of buffer class thresholds (N1,
N2 … NR) defines the buffer class
thresholds of priority classes 1-R
Time and Space Priority
• Ni < N where i = 1 .. R and N is the total
buffer capacity of the Queue
• Packets for a class i are dropped if the
number of packets of class i exceeds Ni.
This scheme is also known as PBS i.e.
Partial Buffer Sharing.
Contribution of the Paper
• The problem is that an exact closed form
solution for such a QNM (which models an
ATM switch) is not known except for
special cases.
• Paper provides a numerically cost-effective
approximation for the solution of such a
QNM.
Approach of the solution
• sGGeo (shifted Generalised Geometric)
• GGeo ( Generalised Geometric)
• The author first provides a solution for a single
sGGeo/GGeo/1/N1,N2….NR queue.
• He then describes how such a solution can be
used as a building block for an open QNM with an
arbitrary configuration i.e. any number of
independent queues with any transition probability
between different queues.
Background
• Batch Renewal Process : Defined by two
distributions : E(s) and K(s) where s is the
batch number. Both E(s) and K(s) are
independent and identically distributed. E(s)
gives the time between sth and (s-1)th
batch, and K(s) gives the count of the sth
batch.
• P[E(s)=t] = a(t) and P[K(s) = n] = b(n)
Background
• Given only correlation of counts and
correlation of intervals the least biased
choice of process is a batch renewal
process.
• sGGeo Batch renewal process :
Background
• Given first two moments of message size and first
two moments of interarrival time between
messages and that the measured covariances are
geometric, sGGeo batch renewal process is the
least biased choice of the traffic model
• However an sGGeo process may be modelled as a
GGeo process so that both processes satisfy the
same first two moments of counts distribution.
ME Analysis of a censored
sGGeo/Ggeo/1/N Queue
ME Analysis of a censored
sGGeo/Ggeo/1/N Queue
ME Analysis of arbitrary queuing
networks
• 1. Initialize blocking probabilities per class
• 2. Solve P(n) separately for all queues
• 3. For each queue, calculate the flow
transition probabilities
• 4. Calculate flow balance eqns per class
• 5. Calculate first two moments of service
time, and first two moments of interarrival
time per class
ME Analysis of arbitrary queuing
networks
• 6. Obtain new blocking probabilities by applying
Newton-Raphson method
• 7. Calculate the first two moments of the
interdeparture times per class.
• 8. Calculate new value for interarrival time SCV