1. 2014 session 1 TELE4642: Network Performance Week 12 Review

2. Course Summary Performance aspects of data networks
Quantitative theory:
Stochastic processes: arrival and service
Continuous-Time Markov chains
M/M/1 systems and variants
Networks of queues
Discrete-time Markov chains
Page Rank, Slotted Aloha, Randomized Routing
Qualitative frameworks:
Traffic models, QoS: IntServ and DiffServ frameworks
SDN: disruptive technology with long-term impact
Further courses:
Tele3119: trusted networks
Tele9751: switching systems design
Tele9752: network operations and control
Tele9756: advanced networking
Gsoe9758: Network systems architecture
TELE4642: Network Performance

3. Final Exam Thursday 19 Jun 9am-12pm Problem-based:
Continuous-time Markov chains
Discrete-time Markov chains
SDN design/programming
Please complete teaching/course evaluation survey
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TELE4642: Network Performance

4. Exercise: continuous-time Markov Chain
Consider a network switch that has three output links: two of capacity 20 Mbps each and the third of capacity 10 Mbps. Packets arrive as a Poisson process to the switch, at rate 3 packets per millisecond, and the packet lengths are exponentially distributed with mean 10,000 bits. The switch operates in cut-through manner, i.e. bits of an incoming packet are sent on an outgoing link as they arrive, without any buffering. An arriving packet that finds all three output links busy is dropped. Otherwise, the arriving packet is transmitted on the available output link of highest capacity (if both 20Mbps links are available, either can be used).
Draw the Markov chain showing the states, transitions, and transition rates [Hint: first compute the service rate in packets/millisecond for each link.]
What fraction of arriving packets is lost at the switch? [Hint: You may find it easier if you express all state probabilities in terms of the probability of being in the state at which packets are lost.]
TELE4642: Network Performance

5. Exercise (contd.)
In order to perform maintenance on the switch, we now stop any new packets from entering the switch (the packets currently in service are allowed to complete). Suppose all three links are found to be busy at the time when we stop new packets from entering the switch.
What is the probability that the 10Mbps link will become idle before either of the other two links?
On average, how long would you have to wait before all three links of the switch become idle? [Hint: what is the relation between rate out of a state and the average time spent in that state?]
TELE4642: Network Performance