1. List of formulae and physical constants:
2. Speed of light in optical fiber: c ? 2 ? 108 m?s?1
3. Permeability of vacuum or air: ?0 = 4 ?? ?× 10?7 H?m?1
4. Capacitance of wire per unit length, cl ? 2 x 10-10 F?m?1
5. Conductor resistivity: ? = 1.68 x 10-8 ?m
6. A Data Centre cluster is formed of 4 racks each hosting 16 servers connected by a spine-leaf circuit switched network.
(a) Having a subscription ratio of 16 downlinks to 10 uplinks, each link connecting a different spine switch,
(i) draw the topology and calculate the blocking probability under 50% load.
(ii) Measure the total number of crosspoints required for the whole network.
(b) Form a strictly non-blocking network and re-calculate the number of crosspoints, the subscription ratio and blocking probability under 80% load.
(c) Assume a time-division multiplexed circuit switched network with 100 timeslots per link and a maximum of 4 slots given to any connection. Calculate the number of leaf switches needed to design a strictly non-blocking network?
(d) InfiniBand is the communication protocol of choice for this data centre. The Infiniband network is formed of two sub-nets each supporting 2 Racks and make use optical fibres for links.
(i) Draw and explain the revised network topology that is needed to support two sub-nets and explain the method used to detect an erroneous bit introduced within a switch?
(ii) With the aid of a diagram describe and calculate the minimum and maximum delay required to send 20KB of data between two servers.
Assumptions:
? The optical link length between server and leaf switch is 3 meters and the optical link between leaf and spine switches is 100m length.
? There is no contention.
? The host channel adapter supports 2 network ports (one for data and one for control), operates at 64-bit and the de/serialiser at 156.25 MHz.
? The port to port delay is 20 Clock Cycles for an Infiniband switch (or a server to port task) and 50 CCs for an Infiniband router while both operate at 500 MHz.
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